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Chapter 2
Resource Masters
Consumable Workbooks Many of the worksheets contained in the Chapter
Resource Masters are available as consumable workbooks in both English and
Spanish.
Study Guide and Intervention Workbook
Skills Practice Workbook
Practice Workbook
Word Problem Practice Workbook
MHID
0-07-878882-X
0-07-878884-6
0-07-878886-2
0-07-878888-9
ISBN
978-0-07-878882-6
978-0-07-878884-0
978-0-07-878886-4
978-0-07-878888-8
0-07-878883-8
0-07-878885-4
0-07-878887-0
0-07-878889-7
978-0-07-878883-3
978-0-07-878885-7
978-0-07-878887-1
978-0-07-878889-7
Spanish Versions
Study Guide and Intervention Workbook
Skills Practice Workbook
Practice Workbook
Word Problem Practice Workbook
Answers for Workbooks The answers for Chapter 2 of these workbooks can be
found in the back of this Chapter Resource Masters booklet.
StudentWorks PlusTM This CD-ROM includes the entire Student Edition test along
with the English workbooks listed above.
TeacherWorks PlusTM All of the materials found in this booklet are included for
viewing, printing, and editing in this CD-ROM.
Spanish Assessment Masters MHID: 0-07-878890-0 ISBN: 978-0-07-878890-1
These masters contain a Spanish version of Chapter 2 Test Form 2A and Form 2C.
Copyright © by the McGraw-Hill Companies, Inc. All rights reserved. Permission is
granted to reproduce the material contained herein on the condition that such
material be reproduced only for classroom use; be provided to students, teachers,
and families without charge; and be used solely in conjunction with Glencoe
California Mathematics, Grade 7. Any other reproduction, for use or sale, is
prohibited without prior written permission of the publisher.
Send all inquiries to:
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, OH 43240
ISBN: 978-0-07-878309-8
MHID: 0-07-878309-7
Printed in the United States of America
1 2 3 4 5 6 7 8 9 10 079 14 13 12 11 10 09 08 07
CAGR7 CRM2
CONTENTS
Teacher’s Guide to Using the Chapter 2
Resource Masters .........................................iv
Chapter Resources
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
2
2
2
2
2
2
2
Student-Made Glossary ....................1
Family Letter (English) ......................3
Family Activity (English) ....................4
Family Letter (Spanish) .....................5
Family Activity (Spanish)...................6
Anticipation Guide (English)..............7
Anticipation Guide (Spanish) ............8
Lesson 2-1 Rational Numbers
Lesson Reading Guide ......................................9
Study Guide and Intervention ..........................10
Skills Practice...................................................11
Practice ............................................................12
Word Problem Practice ....................................13
Enrichment .......................................................14
Lesson 2-2 Comparing and
Ordering Rational Numbers
Lesson Reading Guide ....................................15
Study Guide and Intervention ..........................16
Skills Practice...................................................17
Practice ............................................................18
Word Problem Practice ....................................19
Enrichment .......................................................20
Lesson 2-3 Multiplying Positive
and Negative Fractions
Lesson Reading Guide ....................................21
Study Guide and Intervention ..........................22
Skills Practice...................................................23
Practice ............................................................24
Word Problem Practice ....................................25
Enrichment .......................................................26
Lesson 2-4 Dividing Positive and
Negative Fractions
Lesson Reading Guide ....................................27
Study Guide and Intervention ..........................28
Skills Practice...................................................29
Practice ............................................................30
Word Problem Practice ....................................31
Enrichment .......................................................32
Lesson 2-5 Adding and
Subtracting Like Fractions
Lesson Reading Guide ....................................33
Study Guide and Intervention ..........................34
Skills Practice...................................................35
Practice ............................................................36
Word Problem Practice ....................................37
Enrichment .......................................................38
Lesson 2-6 Adding and
Subtracting Unlike Fractions
Skills Practice...................................................41
Practice ............................................................42
Word Problem Practice ....................................43
Enrichment .......................................................44
Lesson 2-7 Solving Equations with
Rational Numbers
Lesson Reading Guide ....................................45
Study Guide and Intervention ..........................46
Skills Practice...................................................47
Practice ............................................................48
Word Problem Practice ....................................49
Enrichment .......................................................50
TI-73 Activity ....................................................51
Lesson 2-8 Problem-Solving
Investigation: Look for a Pattern
Study Guide and Intervention ..........................52
Skills Practice...................................................53
Practice ............................................................54
Word Problem Practice ....................................55
Lesson 2-9 Powers and Exponents
Lesson Reading Guide ....................................56
Study Guide and Intervention ..........................57
Skills Practice...................................................58
Practice ............................................................59
Word Problem Practice ....................................60
Enrichment .......................................................61
Scientific Calculator Activity .............................62
Lesson 2-10 Scientific Notation
Lesson Reading Guide ....................................63
Study Guide and Intervention ..........................64
Skills Practice...................................................65
Practice ............................................................66
Word Problem Practice ....................................67
Enrichment .......................................................68
Assessment
Student Recording Sheet ................................69
Rubric for Scoring Pre-AP................................70
Chapter 2 Quizzes 1 and 2 ..............................71
Chapter 2 Quizzes 3 and 4 ..............................72
Chapter 2 Mid-Chapter Test .............................73
Chapter 2 Vocabulary Test ...............................74
Chapter 2 Test, Form 1 ....................................75
Chapter 2 Test, Form 2A ..................................77
Chapter 2 Test, Form 2B ..................................79
Chapter 2 Test, Form 2C..................................81
Chapter 2 Test, Form 2D..................................83
Chapter 2 Test, Form 3 ....................................85
Chapter 2 Extended-Response Test ................87
Chapter 2 Standardized Test Practice..............88
ANSWERS ...............................................A1-A41
Lesson Reading Guide ....................................39
Study Guide and Intervention ..........................40
iii
Teacher’s Guide to Using the
Chapter 2 Resource Masters
The Chapter 2 Resource Masters includes the core materials needed for Chapter 2. These
materials include worksheets, extensions, and assessment options. The answers for these
pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing on the
TeacherWorks PlusTM CD-ROM.
Chapter Resources
Lesson Resources
Student-Built Glossary (pages 1-2) These
masters are a student study tool that
presents up to twenty of the key vocabulary
terms from the chapter. Students are to
record definitions and/or examples for each
term. You may suggest that students
highlight or star the terms with which they
are not familiar. Give this to students before
beginning Lesson 2-1. Encourage them to
add these pages to their mathematics study
notebooks. Remind them to complete the
appropriate words as they study each lesson.
Lesson Reading Guide Get Ready for the
Lesson reiterates the questions from the
beginning of the Student Edition lesson.
Read the Lesson asks students to interpret
the context of and relationships among
terms in the lesson. Finally, Remember
What You Learned asks students to
summarize what they have learned using
various representation techniques. Use as a
study tool for note taking or as an informal
reading assignment. It is also a helpful tool
for ELL (English Language Learners).
Family Letter and Family Activity
(pages 3-6) The letter informs your students’
families of the mathematics they will be
learning in this chapter. The family activity
helps them to practice problems that are
similar to those on the state test. A full
solution for each problem is included.
Spanish versions of these pages are also
included. Give these to students to take
home before beginning the chapter.
Study Guide and Intervention This
master provides vocabulary, key concepts,
additional worked-out examples and Check
Your Progress exercises to use as a
reteaching activity. It can also be used in
conjunction with the Student Edition as an
instructional tool for students who have
been absent.
Skills Practice This master focuses more
on the computational nature of the lesson.
Use as an additional practice option or as
homework for second-day teaching of the
lesson.
Anticipation Guide (pages 7-8) This
master, presented in both English and
Spanish, is a survey used before beginning
the chapter to pinpoint what students may
or may not know about the concepts in the
chapter. Students will revisit this survey
after they complete the chapter to see if
their perceptions have changed.
Practice This master closely follows the
types of problems found in the Exercises
section of the Student Edition and includes
word problems. Use as an additional
practice option or as homework for secondday teaching of the lesson.
iv
Vocabulary Test This test is suitable for
all students. It includes a list of vocabulary
words and 10 questions to assess students’
knowledge of those words. This can also be
used in conjunction with one of the leveled
chapter tests.
Word Problem Practice This master
includes additional practice in solving word
problems that apply the concepts of the
lesson. Use as an additional practice or as
homework for second-day teaching of the
lesson.
Enrichment These activities may extend
the concepts of the lesson, offer an historical
or multicultural look at the concepts, or
widen students’ perspectives on the
mathematics they are learning. They are
written for use with all levels of students.
Leveled Chapter Tests
• Form 1 contains multiple-choice questions
and is intended for use with below grade
level students.
• Forms 2A and 2B contain multiple-choice
questions aimed at on grade level
students. These tests are similar in format
to offer comparable testing situations.
Graphing Calculator, Scientific
Calculator, or Spreadsheet Activities
These activities present ways in which
technology can be used with the concepts in
some lessons of this chapter. Use as an
alternative approach to some concepts or as
an integral part of your lesson presentation.
• Forms 2C and 2D contain free-response
questions aimed at on grade level
students. These tests are similar in format
to offer comparable testing situations.
• Form 3 is a free-response test for use with
above grade level students.
Assessment Options
All of the above mentioned tests include a
free-response Bonus question.
The assessment masters in the Chapter 2
Resources Masters offer a wide range of
assessment tools for formative (monitoring)
assessment and summative (final)
assessment.
Extended-Response Test Performance
assessment tasks are suitable for all
students. Sample answers and a scoring
rubric are included for evaluation.
Student Recording Sheet This master
corresponds with the standardized test
practice at the end of the chapter.
Standardized Test Practice These three
pages are cumulative in nature. It includes
three parts: multiple-choice questions with
bubble-in answer format, griddable
questions with answer grids, and shortanswer free-response questions.
Pre-AP Rubric This master provides
information for teachers and students on
how to assess performance on open-ended
questions.
Answers
• The answers for the Anticipation Guide
and Lesson Resources are provided as
reduced pages with answers appearing in
red.
Quizzes Four free-response quizzes offer
assessment at appropriate intervals in the
chapter.
• Full-size answer keys are provided for the
assessment masters.
Mid-Chapter Test This 1-page test
provides an option to assess the first half of
the chapter. It parallels the timing of the
Mid-Chapter Quiz in the Student Edition
and includes both multiple-choice and freeresponse questions.
v
NAME ________________________________________ DATE ______________ PERIOD _____
Student-Built Glossary
This is an alphabetical list of new vocabulary terms you will learn in
Chapter 2. As you study the chapter, complete each term’s definition
or description. Remember to add the page number where you found
the term. Add this page to your math study notebook to review
vocabulary at the end of the chapter.
Vocabulary Term
Found
on Page
Definition/Description/Example
bar notation
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
base
dimensional analysis
exponent
like fractions
multiplicative
inverses
Chapter 2
1
Glencoe California Mathematics, Grade 7
Chapter Resources
2
NAME ________________________________________ DATE ______________ PERIOD _____
2
Student-Built Glossary
Vocabulary Term
Found
on Page
(continued)
Definition/Description/Example
power
rational number
reciprocals
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
repeating decimal
scientific notation
terminating decimal
unlike fractions
Chapter 2
2
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
Family Letter
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Dear Parent or Guardian:
ntists use fractions and
Carpenters, architects, chefs, and scie
patterns to make decisions.
patterns. We also use fractions and
to multiply fractions if we
For example, we need to know how
gs when preparing a
want to change the number of servin
en facts learned in the
recipe. Making the connection betwe
helps students appreciate
classroom and real-world situations
in school.
the mathematical concepts they learn
mbers, your child will
In Chapter 2, Algebra: Rational Nu
to compare, order, and
learn about rational numbers and how
bers. Your child will also
compute with fractions and mixed num
numbers, and to solve
learn to solve equations with rational
ld will also learn how to
problems by using patterns. Your chi
and use scientific notation.
compute with powers and exponents
ld will complete a variety
In the study of this chapter, your chi
activities and possibly
of daily classroom assignments and
produce a chapter project .
it with your child, you
By signing this letter and returning
ting involved. Enclosed is
agree to encourage your child by get
ld that practices how the
an activity you can do with your chi
2 might be tested. You
math we will be learning in Chapter
th.com for self-check
may also wish to log on to ca.gr7ma
have any questions or
quizzes and other study help. If you
school.
comments, feel free to contact me at
Sincerely,
Signature of Parent or Guardian ______________________________________ Date ________
Chapter 2
3
Glencoe California Mathematics, Grade 7
Chapter Resources
2
NAME ________________________________________ DATE ______________ PERIOD _____
Family Activity
2
Standards Practice
Fold the page along the dashed line. Work each problem on another piece of
paper. Then unfold the page to check your work.
2. The sun is about 92,000,000 miles from
the Earth.
1. Use the model below to find the answer
to the following multiplication problem.
1
of 3
3
Mercury
Mars
Earth
Venus
Pluto
Jupiter
Saturn
Neptune
Uranus
1
What is the product for of 3?
3
A 1
How can this distance be expressed in
scientific notation?
A
B
C
D
B 1
C 1
D
3
2
3
9.2 106
9.2 107
9.2 108
9.2 109
Fold here
Solution
Solution
2. Hint: Scientific notation is used to
represent very large or very small
numbers and is written as the product of
a number and a factor of 10. The decimal
point is placed after the first non-zero digit
and the exponent is the number of spaces
that the decimal place is moved to the
right (for small numbers) or left (for large
numbers).
1.
1
3
1
3
1
3
1
1
1
3
or 1
3
3
3
3
In this case, the decimal is moved to the
left seven spaces, or
92000000
so the resulting scientific notation
is 9.2 107.
The answer is B.
The answer is B.
Chapter 2
4
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9
NOMBRE ______________________________________ FECHA ____________ PERÍODO
Carta a la familia
Chapter Resources
2
___
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Estimado padre o apoderado:
ineros y los científicos usan
Los carpinteros, los arquitectos, los coc
n fracciones y patrones para
fracciones y patrones. También se usa
os cambiar el número de
tomar decisiones. Por ejemplo, si querem
saber cómo multiplicar
porciones de una receta, necesitamos
los conocimientos adquiridos
fracciones. Establecer relaciones entre
a que los alumnos aprecien los
en clase y situaciones reales, ayudará
en la escuela.
conceptos matemáticos que aprenden
racionales, su hijo(a) aprenEn el Capítulo 2, Álgebra: Números
y a comparar, ordenar y hacer
derá acerca de los números racionales
. Su hijo(a) aprenderá tamcálculos con fracciones y número mixtos
s racionales y a resolver probién a resolver ecuaciones con número
ella aprenderá a hacer cálcublemas usando patrones. Además, él o
r la notación científica. En este
los con potencias y exponentes y a usa
iedad de tareas y actividades
capítulo, su hijo(a) completará una var
proyecto del capítulo.
diarias y es posible que trabaje en un
su hijo(a), usted se comproAl firmar esta carta y devolverla con
aprendizaje. Junto con esta
mete a ayudarlo(a) a participar en su
de realizar con él(ella) y la
carta, va incluida una actividad que pue
en las pruebas de los concepcual practica lo que podrían encontrar
Capítulo 2. Además, visiten
tos matemáticos que aprenderán en el
s y otras ayudas para el
ca.gr7math.com para ver autocontrole
comentario, por favor conestudio. Si tiene cualquier pregunta o
tácteme en la escuela.
Cordialmente,
Firma del padre o apoderado
Capítulo 2
________________________________________ Fecha
5
______
Glencoe California Mathematics, Grade 7
NOMBRE ______________________________________ FECHA ____________ PERÍODO
2
___
Actividad en familia
Práctica de estándares
Doblen la página a lo largo de las líneas punteadas. Resuelvan cada problema
en otra hoja de papel. Luego, desdoblen la página y revisen las respuestas.
1. Usen el siguiente modelo para calcular la
respuesta de la siguiente multiplicación.
2. La distancia entre el Sol y la Tierra es
cercana a 92,000,000 de millas.
1
de 3
3
Mercury
Mars
Earth
Venus
Jupiter
Pluto
Saturn
Neptune
Uranus
1
¿Cuál es el producto de por 3?
3
A 1
¿Cómo se expresa esta distancia en
notación científica?
A
B
C
D
B 1
C 1
D
3
2
3
9.2 106
9.2 107
9.2 108
9.2 109
Doblen aquí.
Solución
Solución
2. Ayuda: La notación científica sirve para
representar números muy grandes o muy
pequeños. Cuando se usa esta notación, el
número grande o pequeño se expresa
como el producto de un número por un
factor de 10. El punto decimal se coloca
luego del primero dígito distinto de cero y
el factor es el número de espacios que se
mueve el punto decimal hacia la derecha
(para números pequeños) o hacia la
izquierda (para números grandes).
En este caso, el decimal se debe mover
siete espacios hacia la izquierda, ó
1.
1
3
1
3
1
3
1
1
1
3
ó 1
3
3
3
3
92000000
por lo tanto, el número expresado en
notación científica es 9.2 107.
La respuesta es B.
Capítulo 2
La respuesta es B.
6
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9
NAME ________________________________________ DATE ______________ PERIOD _____
2
Anticipation Guide
Step 1
Before you begin Chapter 2
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree,
write NS (Not Sure).
STEP 1
A, D, or NS
STEP 2
A or D
Statement
1
2
3
5
1. 3, , 0.4, and 2 are all examples of rational numbers.
2. To write a fraction as a decimal, divide the numerator into the
denominator.
4
7
4
5
3. is greater than because 7 is greater than 5.
4. When multiplying two fractions, first find a common
denominator, and then multiply numerators and denominators.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Before multiplying two mixed numbers, rewrite both as
improper fractions.
1
2
6. 12 and are multiplicative inverses of each other.
7. To divide by a fraction, multiply by its opposite.
8. To subtract two fractions with a common denominator, subtract
the numerators and then the denominators.
9. A common denominator must be found before adding or
subtracting fractions with different denominators.
10. The equation 0.7 x 2.4 would be solved by addition.
11. Any number to the zero power equals 1.
12. Any number written as a product of a number and a power of
10 is written in scientific notation.
Step 2
After you complete Chapter 2
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an
example of why you disagree.
Chapter 2
7
Glencoe California Mathematics, Grade 7
Chapter Resources
Algebra: Rational Numbers
NOMBRE ______________________________________ FECHA ____________ PERÍODO
2
___
Ejercicios preparatorios
Álgebra: Números racionales
Paso 1
Antes de comenzar el Capítulo 2
• Lee cada enunciado.
• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.
• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,
escribe NS (No estoy seguro(a)).
PASO 1
A, D o NS
PASO 2
AoD
Enunciado
1
2
3
5
1. 3, , 0.4 y 2 son ejemplos de números racionales.
2. Para escribir una fracción como decimal, divide el numerador
entre el denominador.
4
7
4
5
3. es mayor que porque 7 es mayor que 5.
5. Antes de multiplicar dos números mixtos, convierte ambos
a fracciones impropias.
1
2
6. 12 y son inversos multiplicativos mutuos.
7. Para dividir por una fracción, multiplica por su opuesto.
8. Para sustraer dos fracciones con un común denominador,
sustrae los numeradores y luego los denominadores.
9. Un común denominador se debe hallar antes de añadir o
sustraer fracciones con distintos denominadores.
10. La ecuación 0.7 x 2.4 se resolvería mediante adición.
11. Cualquier número elevado a la potencia 0 da igual a 1.
12. Cualquier número escrito como un producto de un número y
una potencia de 10 se escribe en notación científica.
Paso 2
Después de completar el Capítulo 2
• Vuelve a leer cada enunciado y completa la última columna con una A o una D.
• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?
• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los
enunciados que marcaste con una D.
Capítulo 2
8
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Cuando se multiplican dos fracciones, primero encuentra un
común denominador y luego multiplica numeradores y
denominadores.
NAME ________________________________________ DATE ______________ PERIOD _____
3-1
2-1
2-1 Lesson Reading Guide
7NS1.3, 7NS1.5
Rational Numbers
Get Ready for the Lesson
Read the introduction at the top of page 84 in your textbook. Write
your answers below.
1. What fraction of the sites are in the United States?
2. What fraction of the sites are in Canada?
3. At what fraction of the sites might you see gray whales?
4. What fraction of the humpback viewing sites are in Mexico?
4
5. Explain the difference in meaning between the expressions 43 and 4 3 .
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
6. Explain the difference between the numbers 2.57
and 2.5
7
.
Remember What You Learned
7. Notice that the first five letters of the word rational is the word ratio.
Explain what a ratio is. If this term is not familiar to you, look it up in
the dictionary. Write a ratio and a rational number. Explain how they are
related.
Chapter 2
9
Glencoe California Mathematics, Grade 7
Lesson 2-1
Read the Lesson
NAME ________________________________________ DATE ______________ PERIOD _____
2-1
3-1
Study Guide and Intervention
7NS1.3, 7NS1.5
Rational Numbers
To express a fraction as a decimal, divide the numerator by the denominator.
Example 1
Write 3 as a decimal.
4
3
means 3 4.
4
The fraction 3 can be written as 0.75, since 3 4 0.75.
4
Example 2
Write 0.16 as a fraction.
16
0.16 100
4
25
0.16 is 16 hundredths.
Simplify.
The decimal 0.16 can be written as 4.
25
Example 3
Write 8.2
as a mixed number.
Let N 8.2
or 8.222… .
Then 10N 82.222… .
10N 82.222…
1N 8.222… N 1N
9N 74
10N 1N 9N
9N
74
9
9
N 82
9
Divide each side by 9.
Simplify.
The decimal 8.2
can be written as 82.
9
Exercises
Write each fraction or mixed number as a decimal.
2. 3
1. 2
10
5
5. 2
3
3. 7
16
4. 2
7. 62
8. 43
8
6. 12
9
3
25
11
Write each decimal as a fraction or mixed number in simplest form.
9. 0.8
Chapter 2
10. 0.15
11. 0.1
10
12. 1.7
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Subtract.
NAME ________________________________________ DATE ______________ PERIOD _____
3-1
2-1
Skills Practice
7NS1.3, 7NS1.5
Rational Numbers
Write each fraction or mixed number as a decimal.
1. 1
2. 1
3. 3
4. 4
21
5. 6. 39
7. 49
8. 7
4
50
25
9. 11
6
11. 5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
33
8
5
20
9
Lesson 2-1
10
10. 24
15
12. 73
11
Write each decimal as a fraction or mixed number in simplest form.
13. 0.9
14. 0.7
15. 0.84
16. 0.92
17. 1.12
18. 5.05
19. 2.35
20. 8.85
21. 0.1
22. 4.8
23. 6.7
24. 8.4
Chapter 2
11
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-1
Practice
7NS1.3, 7NS1.5
Rational Numbers
Write each fraction or mixed number as a decimal.
3
1. 5
5
2. 8
9
3. 20
37
4. 50
11
5. 16
9
6. 32
1
7. 3
5
3
8. 4
8
5
9. 33
7
10. 9
11
11. 8
18
11
12. 9
30
13. 0.8
14. 0.44
15. 1.35
16. 0.8
17. 1.5
18. 4.4
For Exercises 19–21, refer
to the table at the right.
POPULATION
Population of California by Race
19. Express the fraction for Asian as a
decimal.
20. Find the decimal equivalent for the
fraction of the population that
is African American.
21. Write the fraction for Hispanic as a
decimal. Round to the nearest
thousandth.
Race
Fraction of Total
Population
African American
1
10
1
16
1
3
Asian
Hispanic
Source: U.S. Census Bureau
MEASUREMENTS For Exercises 22 and 23,
use the figure at the right.
22. Write the width of the jellybean as a fraction.
in.
23. Write the width of the jellybean as a decimal.
Chapter 2
12
1
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write each decimal as a fraction or mixed number in simplest form.
NAME ________________________________________ DATE ______________ PERIOD _____
2-1
Word Problem Practice
7NS1.3, 7NS1.5
Rational Numbers
2. ENERGY Nuclear power provided 78% of
the energy used in France in 2005.
Write 0.78 as a fraction in simplest
form.
3. WEIGHTS AND MEASURES One pint is
about 0.55 liter. Write 0.55 liter as a
fraction in simplest form.
4. WEIGHTS AND MEASURES One inch is
25.4 millimeters. Write 25.4
millimeters as a mixed number in
simplest form.
5. EDUCATION A local middle school has
47 computers and 174 students. What
is the number of students per computer
at the school? Write your answer as
both a mixed number in simplest form
and a decimal rounded to the nearest
tenth.
6. BASEBALL In the 2005 season, the
Atlanta Braves won 90 out of 162
games. What was the ratio of wins to
total games? Write your answer as both
a fraction in simplest form and a
decimal rounded to the nearest
thousandth.
7. COLLEGES AND UNIVERSITIES Recently, a
small college had an enrollment of
1,342 students and a total of 215
faculty. What was the student-faculty
ratio for this college? Write your
answer as both a mixed number in
simplest form and a decimal rounded to
the nearest hundredth.
8. BASKETBALL In the 2004–2005 season,
Shaquille O’Neal made 658 field goals
out of 1,095 attempts. What was
Shaquille O’Neal’s ratio of successful
field goals to attempts? Write your
answer as both a fraction in simplest
form and a decimal rounded to the
nearest thousandth.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 2-1
1. ASTRONOMY The pull of gravity on the
surface of Mars is 0.38 that of Earth.
Write 0.38 as a fraction in simplest
form.
Chapter 2
13
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-1
Enrichment
7NS1.3
A Triangular Line Design
Connect each pair of equivalent rational numbers with a straight line
segment. Although you will draw only straight lines, the finished
design will appear curved!
1
2
0.875
1
5
0.083
2
3
0.166
1
18
0.05
1
6
0.666
1
12
0.2
7
8
0.5
1
16
3
4
0.333
1
4
0.142857
1
8
0.318
1
30
0.375
1
9
0.428571
5
9
0.384615
1
20
0.8125
0.0625 1
3
Chapter 2
0.25
7
22
0.03
3
7
0.5
13
16
0.05
14
5
13
0.11
3
8
0.125
1
7
0.75
7
11
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
0.6363
NAME ________________________________________ DATE ______________ PERIOD _____
3-1
2-2
Lesson Reading Guide
7NS1.1
Comparing and Ordering Rational Numbers
Get Ready for the Lesson
Read the introduction at the top of page 91 in your textbook. Write
your answers below.
1. Do we recycle more or less than half of the paper we produce? Explain.
2. Do we recycle more or less than half of the aluminum cans? Explain.
3. Which items have a recycle rate less than one half?
4. Which items have a recycle rate greater than one half?
Read the Lesson
6. Read Example 4 on page 93. Explain how to use a number line to
determine which of two rational numbers is the lesser number.
For Exercises 7 and 8, graph each pair of rational numbers on a
number line. Then identify the lesser number.
8. 4, 9
7. 1, 1
5 3
5
10
Remember What You Learned
9. Order the numbers 3, 3, 3, 3, and 3 from least to greatest. Then write
7 5 8 4
11
a rule that helps you compare two positive fractions with the same
numerator.
Chapter 2
15
Glencoe California Mathematics, Grade 7
Lesson 2-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Using this estimation method, can you order the rates from least to
greatest?
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention
2-2
7NS1.1
Comparing and Ordering Rational Numbers
When comparing two or more rational numbers, either write the numbers as fractions with the same
denominator or write the numbers as decimals.
Replace with , , or to make 4 7 a true sentence.
Example 1
5
10
Write as fractions with the same denominator. The least common denominator is 10.
42
8
4
or 52
10
5
7
71
7
or 10
10 1
10
Since 8 7, 4 7.
10
10 5
10
from
Order the set of rational numbers 3.25, 31, 32, and 3.25
3
5
least to greatest.
Example 2
Write 31 and 32 as decimals.
3.25
3.25, the numbers from least to greatest are
Since 3.4 3.3
32, 31, 3.25
, and 3.25.
5
3
Exercises
Replace each with , , or to make a true sentence.
1. 5 2
6
13
2. 4 3
5
3. 1 1
15
9
8
4. 2 7
5. 37 34
6. 23 24
7. 2.6 25
8. 41 4.16
9. 4.58
4.5
8
10
3
10
8
5
7
6
9
Order each set of rational numbers from least to greatest.
11. 2.4, 24, 2.13, 19
10. 0.5, 0.1, 1, 2
4 3
7
12. 1, 0.7, 0.25, 3
5
10
13. 12, 12, 1.45, 1.67
5
9
3
14. 21, 2.28, 2.7, 24
15. 42, 45, 4.6, 5.3
Chapter 2
16
4
5
3
6
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3
5
1
1
, so 3 3.3
.
0.3
3
3
2
2
0.4, so 3 3.4.
5
5
NAME ________________________________________ DATE ______________ PERIOD _____
2-2
Skills Practice
7NS1.1
Comparing and Ordering Rational Numbers
Replace each with , , or to make a true sentence.
1. 1 3
2. 1 1
3. 2 3
4. 2 1
5. 3 9
6. 3 2
2
4
9
3
3
4
7. 5 6
6
6
5
12
8
8. 4 5
7
9
10
10. 4.72 4
13
8
5
9. 5 0.55
11
9
11. 27 2.45
12. 5.25 5.2
5
14. 114 11.4
15. 1.2
7
1.27
15
13. 1.62 15
10
9
16. 0.3, 0.2, 1, 2
17. 12, 12, 1.55, 1.67
3 9
5
18. 2.7, 21, 3.13, 19
7
3
Lesson 2-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Order each set of rational numbers from least to greatest.
19. 1, 1.7, 0.2, 13
10
4
4
10
20. 2.21, 2.09, 21, 1
21. 3.1, 2.75, 17, 2
15
22. 67, 6
, 6.9, 5.3
23. 41, –4.19, –5.3, 51
24. 59, 5.93, 57, 5.81
25. 31, 41, 3.65, 34, 4.05
Chapter 2
17
9
8
11
16
20
11
8
6
4
3
3
8
11
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-2
Practice
7NS1.1
Comparing and Ordering Rational Numbers
Replace each with <, >, or = to make a true sentence.
3
5
5
7
4
9
1. 2
11
5. 0.2 8
13
5
11
2
11
2. 5
21
7. 8 8.3
3
8
7
15
7
8
2
5
8
17
4. 5 5
10
27
6. 0.25 5
13
1
9
3. 3 3
8
30
8. 4 4.3
6
7
2
9
9
11
9. 10. 11. 12. 13. 4.5 4.55
14. 6.14 6.15
15. 3.57 3.5
16. 1.9 1.99
3
8
4
11
5
13
17. Which is least: , 0.4, , 0.035
, or ?
7
9
11
13
Order each set of rational numbers from least to greatest.
3
4
3
5
19. 5.81, 5, 5, 5.69
1
9
1
11
20. 1.01, 1.1, 1, 1
21. Which point on the number line is
the graph of 0.875?
P
0
1
4
Q
1
2
SR
3
4
1
22. STATISTICS If you order a set of numbers from least to greatest, the
middle number is the median. Find the median of 43.7, 41.3, 44.5,
4
5
3
4
42, and 43.
Chapter 2
18
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
18. Which is greatest: , 0.778, 0.7
8
, , or 0.787?
NAME ________________________________________ DATE ______________ PERIOD _____
2-2
Word Problem Practice
7NS1.1
Comparing and Ordering Rational Numbers
2. SPORTS Central’s baseball team won
Percy made 7 of his free throws. For
12
the same period, Tariq made 4 of his
7
53
of its games last year, while
78
55
Southern’s team won of its games.
81
Which team had the better record?
free throws. Which player has the
better free throw record?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. MEASUREMENT Beaker A contains
4. NATURE The two trees in Opal’s back
41 fluid ounces of water, while beaker
3
B contains 43 fluid ounces of water.
10
yard have circumferences of 125 inches
Which beaker has the smaller amount
of water?
larger?
5. EXERCISE On Monday, Rob averaged
3.75 laps per minute. On Tuesday, he
8
and 123 inches. Which circumference is
5
6. FOOD Hector and Carla both gave
apples to their teacher. Hector’s apple
averaged 34 laps per minute. On which
weighed 67 ounces, while Carla’s
day did Rob run faster?
apple weighed 6.65 ounces. Which
apple weighed more?
5
7. SPORTS Christina ran one lap in 83.86
seconds, while Della’s time for one lap
was 837 seconds. Which runner had
8
the faster time?
12
8. STATISTICS The median of a set of
numbers can be found by first putting
the numbers in order from least to
greatest, then choosing the middle
number. Find the median of 5.79,
53, 57, 5.9, and 54.
4
Chapter 2
19
8
5
Glencoe California Mathematics, Grade 7
Lesson 2-2
1. BASKETBALL In the last ten games,
NAME ________________________________________ DATE ______________ PERIOD _____
2-2
Enrichment
7NS2.5
A Famous Line-Up
A number line can be used to graph a mixed number or an improper fraction.
G
H
0
1
2
The number line above shows the graph of two points. Point G is at 1 and
2
point H is at 3.
2
Graph each set of points on the number line. When you are finished,
the letters will spell the last names of some famous people.
10
1
2
6
1
1. point R at , point A at 1, point N at 4, point G at , point G at ,
0
1
3
3
2
3
3
4
5
2. point R at 1, point E at 3, point S at 2, point D at 3, point A at 1,
4
5
point H at , and point P at 1
4
4
2
2
1
2
0
1
2
3. point G at 21, point M at 1, point S at 5, point S at 11, point R at
6
6
11
1
, point O at , and point I at 5
6
3
3
6
3
1
2
0
4. Why are these three people famous?
Chapter 2
20
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3
3
13
point I at , and point A at 22
3
3
NAME ________________________________________ DATE ______________ PERIOD _____
2-3
Lesson Reading Guide
7NS1.2, 7MG1.3
Multiplying Positive and Negative Fractions
Get Ready for the Lesson
Complete the Mini Lab at the top of page 96 in your textbook.
Write your answers below.
1. What is the product of 1 and 2?
3
5
2. Use an area model to find each product.
a. 3 1
4
2
b. 2 2
5
3
c. 1 3
4
5
d. 2 4
3
5
3. What is the relationship between the numerators of the factors and the
numerator of the product?
4. What is the relationship between the denominators of the factors and the
denominator of the product?
Read the Lesson
6. How is the greatest common factor used when multiplying fractions?
7. How is dimensional analysis defined on page 98 in your textbook?
8. How is dimensional analysis used in Example 5 on page 98 in your
textbook?
Remember What You Learned
9. If you were to visit Europe, you may need to exchange some of your
money for Euros. The exchange rate tells you how many dollars equals
how many Euros. How would you use dimensional analysis to compute
the number of Euros you would get from $50?
Chapter 2
21
Glencoe California Mathematics, Grade 7
Lesson 2-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. What is the greatest common factor of two numbers?
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention
2-3
7NS1.2, 7MG1.3
Multiplying Positive and Negative Fractions
To multiply fractions, multiply the numerators and multiply the denominators.
Find 3 4. Write in simplest form.
Example 1
8
11
1
4
3 4
3
11
8 11
8
Divide 8 and 4 by their GCF, 4.
2
31
Multiply the numerators and denominators.
2 11
3
22
Simplify.
To multiply mixed numbers, first rewrite them as improper fractions.
Find 21 33. Write in simplest form.
Example 2
3
18
21 33 7 3
5
3
5
5
1
7 3
18
2 , 3 3
3 5
5
6
3
1
5
76
15
42
5
82
5
Divide 18 and 3 by their GCF, 3.
Multiply the numerators and denominators.
Simplify.
Write the result as a mixed number.
Exercises
Multiply. Write in simplest form.
1. 2 3
2. 4 3
4. 9 2
5. 5 4
7. 22 1
8. 31 11
2
9. 33 25
11. 13 21
12. 22 23
3
5
10
7
3
5
8
6
8
Chapter 2
5
2
9
3
10. 17 22
3. 1 7
4
4
9
3
6. 4 2
7
7
5
3
22
8
7
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
18
7 NAME ________________________________________ DATE ______________ PERIOD _____
2-3
Skills Practice
7NS1.2, 7MG1.3
Multiplying Positive and Negative Fractions
Multiply. Write in simplest form.
1. 1 2
8
2. 2 7
3
9
6
8
11
9
4. 4 3
5. 2 3
6. 3 5
7. 13 2
8. 4 43
9. 2 55
7
10
4
9
3
5
10. 13 11
7
7
5
8
15
11. 21 12
5
4
13. 31 12
11
12. 19 24
3
16
14. 22 21
3
4
6
5
5 5 15. 4 4
5
1
4
3
ALGEBRA Evaluate each expression if r , s , t , and v .
6
3
5
4
16. rv
17. st
18. rs
19. stv
20. rst
21. rtv
5
1
2
3
ALGEBRA Evaluate each expression if a , b , c , and d .
9
5
3
4
22. ad
Chapter 2
23. bc
24. abc
23
Glencoe California Mathematics, Grade 7
Lesson 2-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. 5 3
8
NAME ________________________________________ DATE ______________ PERIOD _____
2-3
Practice
7NS1.2, 7MG1.3
Multiplying Positive and Negative Fractions
Find each product. Write in simplest form.
1
4
4
5
6
7
1
2
3
10
2
3
1. 2. 15 4
4. 16 5
5. 6. 1
1
8. 1 1
4
5
9. 2 2
5
12. 10 8.56 1
4
3. 285 1156
1
5
7. 1 1
4
5
10. 15
7
4
78 17 2
3
1
3
14 1
2
11. 2 2 2
1
5,
2
3
7
8
3
4
ALGEBRA Evaluate each expression if a b , c , and d .
14. ab
15. abc
16. abd
1
4
17. COOKING A recipe calls for 2 cups of flour. How much flour would you
1
3
need to make of the recipe?
1
2
18. FARMING A farmer has 6 acres of land for growing crops. If she plants corn on
3
of the land, how many acres of corn will she have?
5
1
4
2
3
1
6
1
5
ALGEBRA Evaluate each expression if e 1, f 2, g 2, and h 1.
19. efh2
Chapter 2
20. e2h2
1
21. f 2g
8
24
22. 2ef(gh)
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. bc
NAME ________________________________________ DATE ______________ PERIOD _____
2-3
Word Problem Practice
7NS1.2, 7MG1.3
Multiplying Positive and Negative Fractions
2. ELECTIONS In the last election, 3 of the
1. NUTRITION Maria’s favorite granola bar
has 230 Calories. The nutrition label
8
voters in Afton voted for the incumbent
mayor. If 424 people voted in Afton in
the last election, how many voted for
the incumbent mayor?
states that 7 of the Calories come from
8
fat. How many Calories in the granola
bar come from fat?
3. HOBBIES Jerry is building a 1 scale
4. COOKING Enola’s recipe for cookies
9
calls for 21 cups of flour. If she wants
2
3
to make of a batch of cookies, how
4
much flour should she use?
5. TRANSPORTATION Hana’s car used 3 of
6. GEOMETRY The area of a rectangle is
found by multiplying its length times
its width. What is the area of a
4
a tank of gas to cross Arizona. The gas
tank on her car holds 151 gallons. How
rectangle with a length of 21 inches
2
4
many gallons of gas did it take to cross
Arizona?
and a width of 15 inches?
9
7. COOKING A recipe for ice cream calls
8. ADVERTISING A jewelry advertisement
shows a bracelet at 6 times its actual
size. If the actual length of the bracelet
for 31 cups of heavy cream. If Steve
3
wants to make 21 times the normal
2
is 53 inches, what is the length of the
10
amount, how much heavy cream should
he use?
Chapter 2
bracelet in the photograph?
25
Glencoe California Mathematics, Grade 7
Lesson 2-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
model of a race car. If the tires on the
actual car are 33 inches in diameter,
what is the diameter of the tires on the
model?
NAME ________________________________________ DATE ______________ PERIOD _____
2-3
2-1
Enrichment
7AF3.3
Rational Numbers as Ordered Pairs
If you think of a rational number as an ordered pair, it
can be located on a coordinate system. The example graph
d
shows the number 1. The horizontal axis is used for the
4
numerator and the vertical axis for the denominator.
2
3
0
1. 1 2 3 4
2
4
6
12
2. 4 8 8
3
6
d
8
d
16
6
12
4
8
2
4
0
3
3. 2
6
2
6
4
4
6
3
2
4 2
8
10
n
9
0
5
4. 6
4
2
4
10
4
2
16
12
8
20
15
12
5
2
d
8
2
4
2
4
12
6 n
8
4
16
10
4
d
4
O
n
4
O
2
4
4
8
20
n
15
6
4
8
12
16
n
5. Complete this generalization: A rational number a is shown on a
b
coordinate system using the ordered pair (a, b). Using this model,
equivalent rational numbers will
.
6. Show that this generalization is false: A rational number a is shown on a
b
coordinate system using the ordered pair (a, b). All ordered pairs on the
same line stand for equivalent rational numbers.
Chapter 2
26
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Graph the rational numbers as ordered pairs.
NAME ________________________________________ DATE ______________ PERIOD _____
2-4
Lesson Reading Guide
7NS1.2, 7MG1.3
Dividing Positive and Negative Fractions
Get Ready for the Lesson
Read the introduction at the top of page 102 in your textbook.
Write your answers below.
1. Find the value of 110 4.
2. Find the value of 110 1.
4
3. Compare the values of 110 4 and 110 1.
4
4. What can you conclude about the relationship between dividing by 4 and
multiplying by 1?
4
Read the Lesson
For Exercises 6–9, write the multiplicative inverse of each mixed
number.
6. 21
7. 13
5
8
8. 34
7
9. 55
9
10. Explain how to divide by a fraction.
11. Look at your answers for Exercises 6 and 10 above. How do you divide a
number by 21?
5
Remember What You Learned
12. Look up the word invert in the dictionary. Draw a simple picture and then
invert it. Explain how this helps you remember how to divide fractions.
Lesson 2-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Describe the process for finding the multiplicative inverse of a mixed
number.
Chapter 2
27
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-4
Study Guide and Intervention
7NS1.2, 7MG1.3
Dividing Positive and Negative Fractions
Two numbers whose product is 1 are multiplicative inverses, or reciprocals, of each other.
Write the multiplicative inverse of 23.
Example 1
4
11
23 Write 23 as an improper fraction.
4
4
11
4
Since 1, the multiplicative inverse of 23 is 4.
4
11
4
11
4
To divide by a fraction or mixed number, multiply by its multiplicative inverse.
Find 3 6. Write in simplest form.
Example 2
3
6
8
7
8
3 7
8 6
7
Multiply by the multiplicative inverse of 6, which is 7.
7
6
1
7
3
6
8
Divide 6 and 3 by their GCF, 3.
2
7
16
Simplify.
Write the multiplicative inverse of each number.
1. 3
2. 8
3. 1
5. 23
6. 12
7. 52
5
9
5
3
4. 1
10
6
8. 71
5
4
Divide. Write in simplest form.
9. 1 1
3
10. 2 4
6
5
11. 5 3
6
12. 11 21
4
7
5
4
13. 31 32
14. 4 2
15. 6 (4)
16. 5 21
Chapter 2
28
7
11
3
9
3
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
2-4
Skills Practice
7NS1.2, 7MG1.3
Dividing Positive and Negative Fractions
Write the multiplicative inverse of each number.
1. 2
2. 4
7
3. 1
4. 22
5. 9
14
6. 7. 15
8. 13
3
12
35
17
9. 23
13
7
10. 36
7
11. 48
11
12. 53
15
5
Divide. Write in simplest form.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7
14. 2 6
5
7
7
15. 5 3
14
16. 7 17. 4 8
18. 2 4
19. 13 21
20. 23 13
8
4
5
9
11
9
4
2
9
10
5
21. 34 11
7
15
14
10
22. 5
11
23. 4 3
24. 34 42
25. 91 53
26. 123 25
5
3
15
5
3
4
6
27. 24 62
28. 111 31
Chapter 2
29
9
7
5
9
Glencoe California Mathematics, Grade 7
Lesson 2-4
13. 3 3
NAME ________________________________________ DATE ______________ PERIOD _____
2-4
Practice
7NS1.2, 7MG1.3
Dividing Positive and Negative Fractions
Write the multiplicative inverse of each number.
4
5
7
12
1. 3
8
3. 20
2. 4. 5
Find each quotient. Write in simplest form.
1
4
2
5
5
6
6. 3
10
9. 6
4
5
8. 4
5
3
7
3
8
10. 3
6
7
6
11
13. 4
5
11. 10
12. 8
3
5
14. 12
5
2
3
15. 10
5
1
5
3
4
1
3
17. 4 1
6
11
7. 3
4
5
6
89 13
18
16. 1
2
18. 8 3
1
3
19. 10 2
1
4
7
8
20. OFFICE SUPPLIES A regular paper clip is 1 inches long, and a jumbo paper clip is 1
inches long. How many times longer is the jumbo paper clip than the regular paper
clip?
2
3
21. STORAGE The ceiling in a storage unit is 7 feet high. How many boxes may be stacked
3
4
in a single stack if each box is foot tall?
ALGEBRA Evaluate each expression for the given values.
7
20
7
15
4
9
11
12
22. r s if r and s 23. m n if m and n Chapter 2
30
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1
5
5. NAME ________________________________________ DATE ______________ PERIOD _____
2-4
Word Problem Practice
7NS1.2, 7MG1.3
Dividing Positive and Negative Fractions
2. MUSIC Doug has a shelf 93 inches long
1. CONTAINER GARDENING One bag of
4
potting soil contains 81 quarts of soil.
for storing CDs. Each CD is 3 inch
How many clay pots can be filled from
one bag of potting soil if each pot holds
wide. How many CDs will fit on one
shelf?
4
8
3
quart?
4
3. SERVING SIZE A box of cereal contains
4. HOME IMPROVEMENT Lori is building a
path in her backyard using square
153 ounces of cereal. If a bowl holds
5
2
2 ounces of cereal, how many bowls of
5
paving stones that are 13 feet on each
4
side. How many paving stones placed
end-to-end are needed to make a path
that is 21 feet long?
5. GEOMETRY Given the length of a
rectangle and its area, you can find the
width by dividing the area by the
6. GEOMETRY Given the length of a
rectangle and its area, you can find the
width by dividing the area by the
length. A rectangle has an area of 62
length. A rectangle has an area of 45
square inches and a length of 21
2
square feet and a length of 32 feet.
3
inches. What is the width of the
rectangle?
What is the width of the rectangle?
3
7
7. HOBBIES Dena has a picture frame that
8. YARD WORK Leon is mowing his yard,
is 131 inches wide. How many pictures
which is 212 feet wide. His lawn
that are 33 inches wide can be placed
8
mower makes a cut that is 12 feet wide
beside each other within the frame?
on each pass. How many passes will
Leon need to finish the lawn?
2
Chapter 2
3
3
31
Glencoe California Mathematics, Grade 7
Lesson 2–4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
cereal are in one box?
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
2-4
7NS2.2
Continued Fractions
The expression at the right is an example of a
continued fraction. The example shows how to
change an improper fraction into a continued
fraction.
72
Example
Write as a continued fraction.
Example
17
1
1
1
1
1 1
9
4
72
4 17
17
1
4 17
4
1
Notice that each fraction must
have a numerator of 1 before the
process is complete.
4 1
4 4
Exercises
13
1. 10
17
2. 25
3. 17
4. 11
13
6
Write each continued fraction as an improper fraction.
5. 1 Chapter 2
1
1
1
1 1
2
6. 1 1
1
1
1 1
3
32
7. 1 1
1
1
1 1
5
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Change each improper fraction to a continued fraction.
NAME ________________________________________ DATE ______________ PERIOD _____
2-5
Lesson Reading Guide
7NS1.2
Adding and Subtracting Like Fractions
Lesson 2-5
Get Ready for the Lesson
Read the introduction at the top of page 108 in your textbook.
Write your answers below.
1. What is the sum of the whole-number parts of the amounts?
2. How many 1 cups are there?
3
3. Can you combine these ingredients in a 4-cup mixing bowl? Explain.
Read the Lesson
4. Define like fractions.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
For Exercises 5–8, determine whether each pair of fractions are like
fractions.
5. 3, 3
6. 5, 7
5 7
7. 4, 5
8 8
7
8. 5, 2
7
9
3
9. Explain how to add like fractions.
10. Explain how to subtract like fractions.
Add or subtract. Write in simplest form.
11. 3 1
5
5
12. 5 7
8
8
13. 5 2
9
9
14. 4 5
7
7
Remember What You Learned
15. Talk with a partner about the word like. What does it usually mean? How
is this different from the way it is used in the lesson?
Chapter 2
33
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention
2-5
7NS1.2
Adding and Subtracting Like Fractions
Fractions that have the same denominator are called like fractions. To add like fractions, add the
numerators of the fractions and write the sum over the denominator.
5
Find 1 4 . Write in simplest form.
Example 1
5
1
4
5
5
1 (4)
Add the numerators. The denominators are the same.
5
3
3
or 5
Simplify.
5
To subtract like fractions, subtract the numerators of the fractions and write the difference over the
denominator.
Example 2
Find 4 7. Write in simplest form.
9
9
4 7
4 7 9
9
Subtract the numerators. The denominators are the same.
9
11
or 12
9
9
11
2
Rename as 1.
9
9
Example 3
Find 23 65. Write in simplest form.
7
17
47
23 65 7
7
7
7
17 47
7
64
or 91
7
7
7
Write the mixed numbers as improper fractions.
Add the numerators. The denominators are the same.
64
1
Rewrite as 9.
7
7
Exercises
Add or subtract. Write in simplest form.
2. 1 5
3. 5 1
4. 1 5
5. 3 7
6. 5 4
7. 4 3
8. 9 6
1. 4 2
7
10
7
6
6
5
5
10. 35 23
7
Chapter 2
7
8
13
10
9
8
11
13
11. 35 13
8
9
11
9. 21 11
4
4
12. 43 24
8
5
34
5
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
To add or subtract mixed numbers, first write the mixed numbers as improper fractions. Then add or
subtract the improper fractions and simplify the result.
NAME ________________________________________ DATE ______________ PERIOD _____
2-5
Skills Practice
7NS1.2
Adding and Subtracting Like Fractions
1. 1 3
5
2. 2 5
5
9
11
5. 4 8
7. 7 5
8. 1 4
4
12
9
12
16
16
13. 2 6
7
7
13
19. 56 32
7
7
Chapter 2
8
7
7
9. 5 3
7
13
6
12. 14. 4 7
15. 1 4
17. 23 12
18. 14 48
20. 67 31
21. 25 71
23. 52 24
24. 81 42
8
8
7
12
22. 43 27
8
7
11. 5 3
15
11
16. 3 13
11
6. 5 2
9
9
9
10. 9 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. 7 3
9
4. 1 3
4
Lesson 2-5
Add or subtract. Write in simplest form.
9
19
15
19
9
9
7
15
12
9
11
5
35
15
11
5
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-1 2-5
Practice
7NS1.2
Adding and Subtracting Like Fractions
Add or subtract. Write in simplest form.
3
8
18 3. 7
12
6. 1
4
3
4
2. 5
7
4
7
5. 1. 11
12
4. 3
4
3
4
7
10
7. 4 6
8
9
8
11
2
15
9
10
4
9
8. 5 9
8
9
4
5
10. 1 4
10
11
7
15
5
9
9. 7 3
4
5
5
6
11. 4 5
5
6
12. 8 3
3
4
13. SEWING Naomi needs 2 yards of fabric to make a banner for a football
1
4
game. The fabric store has 6 yards of the fabric she wants. How much of
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
the fabric will remain at the store after Naomi buys her fabric?
14. GEOMETRY Find the perimeter of the
triangle.
4 3 in.
8
2 7 in.
8
5 1 in.
8
Simplify each expression.
4
7
1
7
57 1
12
15. 5 2 3
11
12
7
12
16. 7 4 9
ALGEBRA Evaluate each expressions for the given values.
4
5
2
5
7
9
5
9
17. r s if r 8 and s 3 18. b c if b 2 and c 9
Chapter 2
36
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-5
Word Problem Practice
7NS1.2
1. GEOMETRY Find the perimeter of a
2. PETS Pat wants to find out how much
her dog Hunter weighs. Pat steps on
rectangle with a length of 42 inches
3
1
and a width of 3 inches.
3
the scale and reads her weight as 1263
8
pounds. The combined weight of Pat
and Hunter is 1377 pounds. How much
8
does Hunter weigh?
3. MEASUREMENTS Tate fills a 131 ounce
4. DECORATING Jeri has two posters. One
3
glass from a 212 ounce bottle of juice.
is 47 feet wide and the other is 51
How much juice is left in the bottle?
feet wide. Will the two posters fit beside
each other on a wall that is 10 feet
wide? Explain.
10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3
5. AGE Nida is 111 years old, while her
6. GEOMETRY A triangle has sides of
12
5
sister Yoki is 8 years old. What is
12
11 inches, 13 inches, and 15 inches.
8
8
8
What is the perimeter of the triangle?
the sum of the ages of the sisters?
7. HUMAN BODY Tom’s right foot
8. COMPUTERS Trey has two data files on
his computer that he is going to
measures 102 inches, while Randy’s
5
right foot measures 94 inches. How
5
combine. One file is 14 megabytes,
9
while the other file is 38 megabytes.
much longer is Tom’s foot than
Randy’s?
Chapter 2
10
9
What will be the size of the resulting
file?
37
Glencoe California Mathematics, Grade 7
Lesson 2-5
Adding and Subtracting Like Fractions
NAME ________________________________________ DATE ______________ PERIOD _____
2-5
Enrichment
7MR1.1
Extending Problems
When examining the solution of a problem, good problem solvers look for ways
to extend the problem. The questions on this page show you a way to examine
and extend the following pattern.
Row 1:
1
2
1
2
1
2
Row 2:
1
1
2
4
2
1
4
4
3
4
Row 3:
1
1
1
2
4
8
4
2
1
8
8
8
7
8
Row 4:
1
1
1
1
16
2
4
8
8
4
2
1
16
16
16
16
15
16
1. What is the relationship between the denominators of the fractions in the
first column?
3. In the space below, write Row 5 of the pattern.
4. What would be the fraction at the end of Row 6? Row 9?
5. Now complete the following pattern.
Row 1:
1
3
1
3
1
3
Row 2:
1
1
3
9
3
1
9
9
Row 3:
1
1
1
27
3
9
Row 4:
Row 5:
6. CHALLENGE Find this sum: 1 1 1 1 1 1.
4
Chapter 2
16
64
256
38
1,024
4,096
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. What is the relationship between the numerators of the fractions in the
second column?
NAME ________________________________________ DATE ______________ PERIOD _____
2-6
Lesson Reading Guide
7NS1.2, 7NS2.2
Adding and Subtracting Unlike Fractions
Get Ready for the Lesson
Read the introduction at the top of page 114 in your textbook.
Write your answers below.
1. What are the denominators of the fractions?
2. What is the least common multiple of the denominators?
4
Lesson 2-6
3. Find the missing value in 1 ?.
8
Read the Lesson
4. What do LCM and LCD stand for? Give a definition for each.
Find the LCM of each pair of numbers.
6. 4, 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. 2, 3
7. 5, 10
8. 9, 12
Find the LCD of each pair of fractions.
9. 3, 3
10. 5, 7
5 7
11. 4, 5
8 12
7
12. 5, 2
7
9
3
13. Explain how to add or subtract unlike fractions.
Rewrite each sum or difference in terms of like fractions. Then add
or subtract. Write in simplest form.
14. 3 1
2
15. 3 7
16. 5 2
17. 4 1
18. 3 3
19. 5 7
5
7
2
4
5
8
9
7
8
3
12
Remember What You Learned
20. Describe what the prefix un- usually means when it appears in front of a
word. How does this meaning relate to unlike fractions?
Chapter 2
39
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-6
Study Guide and Intervention
7NS1.2, 7NS2.2
Adding and Subtracting Unlike Fractions
Fractions with unlike denominators are called unlike fractions. To add or subtract unlike fractions,
rename the fractions using the least common denominator. Then add or subtract as with like fractions.
Example 1
Find 3 2. Write in simplest form.
5
3
3
2
3 3
2 5
5
3
5 3
3 5
9
10
15
15
9 10
15
19
or 14
15
15
Example 2
The LCD is 5
Rename each fraction using the LCD.
Add the numerators. The denominators are the same.
Simplify.
Find 31 15. Write in simplest form.
6
11
31 15 7 6
Write the mixed numbers as improper fractions.
2
6
7 3
11
2 3
6
21
11
6
6
21 11
6
32
16
1
or or 5
6
3
3
The LCD is 2
3 or 6.
Rename 7 using the LCD.
2
Subtract the numerators.
Simplify.
Exxercises
Add or subtract. Write in simplest form.
6
1. 2 3
2. 1 2
4. 3 5
5. 4 1
6. 12 4
8. 21 13
9. 33 11
5
10
4
3
6
10
2
10. 11 21
5
Chapter 2
4
9
3
5
7. 7 1
3. 5 1
9
4
3
8
4
11. 24 11
9
3
40
9
3
12. 33 22
5
3
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2
2
3 or 15.
NAME ________________________________________ DATE ______________ PERIOD _____
2-6
Skills Practice
7NS1.2, 7NS2.2
Adding and Subtracting Unlike Fractions
Add or subtract. Write in simplest form.
1. 1 1
2
2. 4 1
3. 7 1
4. 3 2
5. 6 3
6. 4 1
7. 1 5
8. 3 1
8
4
4
3
4
14
7
3
5
6
3
5
4
2
9. 3 2
10. 4 1
11. 32 21
12. 55 31
13. 31 41
14. 11 11
7
3
5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9
Lesson 2-6
6
7
3
6
7
4
2
2
5
3
15. 23 63
16. 51 22
17. 51 32
18. 33 9
19. 21 33
20. 21 45
4
8
12
4
3
5
4
3
21. 32 42
7
3
10
5
6
3
22. 57 21
9
23. 102 31
24. 21 54
Chapter 2
41
9
3
3
5
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
Practice
2-6
7NS1.2, 7NS2.2
Adding and Subtracting Unlike Fractions
Add or subtract. Write in simplest form.
1
2
7
10
1. 7
9
2
5
4. 1
5
59 3
4
4
5
1
12
3
4
7
10
5
9
3
5
1
3
7
8
23 6. 3
5
3
5
8. 1 5
10. 3 4
3. 5. 7. 4 6
2
3
5
6
2. 1
3
9. 7 5
9
10
5
12
11. 4 5
3
4
12. 18 14
1
5
1
6
13. POPULATION About of the world’s population lives in China, and of the world’s
population lives in India. What fraction of the world’s population lives in other
ALGEBRA For Exercises 14 and 15, evaluate each expression using the given information.
3
5
7
10
14. m n if m and n 10
5
9
5
6
15. j k if j and k 4
GEOMETRY Find the missing measure for each figure.
16.
17.
3 1 in.
3
x in.
5 1 in.
4
14 5 in.
8
17 3 in.
4
23
24
1
4
perimeter 12 in.
Chapter 2
10 1 in.
2
x in.
perimeter 59 in.
42
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
countries?
NAME ________________________________________ DATE ______________ PERIOD _____
2-6
Word Problems Practice
7NS1.2, 7NS2.2
Adding and Subtracting Unlike Fractions
1. GEOMETRY Two line segments have
2. COMPUTERS The biology class has
created two data files on the computer.
lengths of 31 inches and 11 inches.
4
3
One file is 21 megabytes, while the
What is the sum of the lengths of the
two line segments?
9
other file is 41 megabytes. How much
3. HUMAN BODY The index finger on
4. DECORATING Sugi has two pictures that
she wants to put beside each other in a
Pablo’s right hand measures 33 inches,
8
frame. One is 31 inches wide and the
while the index finger on his left hand
2
1
other is 5 inches wide. How wide
8
measures 35 inches. Which hand has
16
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
the longer index finger? How much
longer is it?
must the frame be to fit both pictures?
6. AGE Alma is 63 years old, while her
5. PETS Laura purchased two puppies
from a litter. One of the puppies weighs
4
brother David is 35 years old. What is
45 pounds and the other puppy weighs
6
51 pounds. How much more does the
2
6
the sum of the ages of Alma and David?
second puppy weigh than the first?
7. MEASUREMENT Ned pours 72 ounces of
8. GEOMETRY A triangle has sides of
5
water from a beaker containing
11 inches, 11 inches, and 12 inches.
101 ounces. How much water is left in
What is the perimeter of the triangle?
6
4
3
3
the beaker?
Chapter 2
43
Glencoe California Mathematics, Grade 7
Lesson 2-6
2
larger is the second file than the first?
NAME ________________________________________ DATE ______________ PERIOD _____
2-6
Enrichment
7NS1.2
Magic Squares
A magic square is an arrangement of numbers
such that the rows, columns, and diagonals all
have the same sum. In this magic square, the
magic sum is 15.
8
3
Column
1
5
4
9
6
Row
7
2
Diagonal
Find the magic sum for each square in
Exercises 1–5. Then fill in the empty cells.
1.
2.
3.
9
8
2 23
1
12
1
4
1 23
2
3
4
2
1
2
5
4
2
4.
5.
1
1
16
13
1
4
1
3
7
12
1
4
1
9
16
1
2
1
1 12
2
3
16
1
3
4
3
8
1
8
1
1
12
13
16
6. Arrange these numbers to make
a magic square.
1
2
1
3
1
6
1
12
Chapter 2
2
3
1
4
5
12
3
4
7
12
44
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2
3
NAME ________________________________________ DATE ______________ PERIOD _____
2-7
Lesson Reading Guide
7AF1.1, 7NS1.2
Solving Equations with Rational Numbers
Get Ready for the Lesson
Read the introduction at the top of page 119 in your textbook.
Write your answers below.
1. Multiply each side of the equation by 6. Then divide each side by 5. Write
the result.
2. Multiply each side of the original equation by the multiplicative
inverse of 5. Write the result.
6
3. What is the speed of a grizzly bear?
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Match the method of solving with the appropriate equation.
1.25a 3.75
_____
a. Subtract 3 from each side.
x 1.25 5.25
_____
b. Multiply each by 5.
3
7
m 5
10
_____
c. Add 1.25 to each side.
r – 1.25 4.5
_____
d. Divide each side by 1.25.
3
1
f 5
2
_____
e. Subtract 1.25 from each side.
5
3
Explain in words how to solve each equation.
6. y 1.1
3.2
7. 3 v 7
8
12
Remember What You Learned
8. The description of a problem often has more information than you need to
design an equation and solve it. Describe the process of writing an
equation to solve a problem.
Chapter 2
45
Glencoe California Mathematics, Grade 7
Lesson 2-7
4. Which method of solving the equation seems most efficient?
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention
2-7
7AF1.1, 7NS1.2
Solving Equations with Rational Numbers
The Addition, Subtraction, Multiplication, and Division Properties of Equality can be used to solve
equations with rational numbers.
Solve x 2.73 1.31. Check your solution.
Example 1
x 2.73 1.31
Write the equation.
x 2.73 2.73 1.31 2.73
Add 2.73 to each side.
x 4.04
Simplify.
x 2.73 1.31
Check
Write the original equation.
4.04 2.73 1.31
Replace x with 4.04.
1.31 1.31 ✓
Solve 4y 2. Check your solution.
5
4
y 5
5 4
y 4 5
2
3
5 2
4 3
y 5
6
4
2
y 5
3
4 5
2
5 6
3
2
2
✓
3
3
3
Write the equation.
Multiply each side by 5.
4
Simplify.
Write the original equation.
Replace y with 5.
6
Simplify.
Exercises
Solve each equation. Check your solution.
1. t 1.32 3.48
2. b 4.22 7.08
3. 8.07 r 4.48
4. h 4 7
5. 5 x 1
6. 2 f 3
7. 3.2c 9.6
8. 5.04 1.26d
9. 3x 6
9
9
10. 2 3t
3
Chapter 2
4
8
4
11. w 4.2
3
5
5
12. 13r 35
2.5
4
46
8
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Example 2
Check
Simplify.
NAME ________________________________________ DATE ______________ PERIOD _____
2-7
Skills Practice
7AF1.1, 7NS1.2
Solving Equations with Rational Numbers
Solve each equation. Check your solution.
1. x 2.62 6.37
2. y 3.16 7.92
3. 3.38 r 9.76
4. s 5 7
5. 5 x 1
6. 4 z 1
7. 3.4c 6.8
8. 1.56 0.26w
3
5
10
10. 3x 9
9. 12.8y 6.4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8
Lesson 2-7
6
8
4
11. 4 8a
12. 2s 4
13. 2 3t
19
14. 4w 15. 5.1 1.7r
16. z (3.2) 3.69
17. 2.11 w (5.81)
18. w 3.5
19. x 7.2
20. 21y 33
9
11
3
5
10
15
11
1.8
22
2.6
4
8
21. 22f 31
22. 1.5d 3
23. 7.5g 62
24. 21 c 4
5
5
3
Chapter 2
8
5
47
5
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-7
Practice
7AF1.1, 7NS1.2
Solving Equations with Rational Numbers
Solve each equation. Check your solution.
1. m 0.88 1.64
2. t 2.89 9.15
7
1
4. b 4
16
5.
13
16
17. MONEY
p
6.25
11. 7.5
12. 3.6
1
3
13. 2.5x 6. 2.5 n (5.37)
9. 2.94 0.42a
f
2.4
8.4 1.4y
5
6
14. 4.5w 8
2
3
15. 8 1.3
g
The currency in Switzerland is called a franc. On a certain day,
1
4
one U.S. dollar equaled 1 Swiss francs. Write and solve a multiplication
equation to find the number of U.S. dollars that would equal 15 Swiss
francs.
FOOTBALL For Exercise 18, refer to the table.
18. Let s equal the number of additional seats
that the Pittsburgh Steelers’ stadium needs
to equal the number of seats in Kansas City
Chiefs’ stadium. Write and solve an addition
equation to determine the number of seats
that the Steelers’ stadium needs to equal
the number of seats in the Chiefs’ stadium.
NFL Stadiums
Seating Capacity
Stadium
Seats
(thousands)
Dallas Cowboys
Kansas City Chiefs
Pittsburgh Steelers
San Diego Chargers
65.7
79.4
64.5
71.3
Source: stadiumsofnfl.com
Chapter 2
48
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10.
h (6.3) 8.12
3
8. v 27
7
5
8
7. k 25
3
5
3. d NAME ________________________________________ DATE ______________ PERIOD _____
2-7
Word Problem Practice
7AF1.1, 7NS1.2
1. NATURE The height of a certain tree is
12.85 meters. The length of its longest
branch can be found using the equation
3.23 12.85. Solve the equation.
2. SHOPPING Kristen went shopping and
spent $84.63 on books and CDs. The
equation 84.63 b 43.22 can be used
to determine the amount b that she
spent on books. Solve the equation.
3. ENERGY PRICES Suppose regular
unleaded gasoline costs $2.40 per
gallon. The price p of premium gasoline
can be found using the equation
4. DRIVING TIME Sam went for a drive last
Sunday. His average speed was 46
miles per hour and he drove 115 miles.
The equation 115 46t can be used to
find the time t that he spent driving.
Solve the equation.
p
2.40. What is the price of the
1.2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
premium gasoline?
5. AUTOMOBILES The bed of Julian’s truck
6. SPORTS Leo and Ted both ran in a race.
is 21 yards long. The length of the
3
Leo’s time was 9 minutes, which was 3
truck can be found by solving the
of Ted’s time. Using t for Ted’s time,
write a multiplication equation to
represent the situation.
4
equation 24 21. What is the
9
3
length of the truck?
7. SPEED Ella rode the bus to work today.
8. GEOMETRY A rectangle has area
The distance she traveled was 41 miles
4
and the ride took 1 of an hour. The
3
1
1
equation s 4 can be used to find
3
4
62 square inches and length 21 inches.
3
2
2
1
The equation 6 2w can be used to
3
2
find the width w of the rectangle. Solve
the equation.
the average speed s of the bus. What
was the average speed of the bus?
Chapter 2
49
Glencoe California Mathematics, Grade 7
Lesson
Lesson X–1
2-7
Solving Equations with Rational Numbers
NAME ________________________________________ DATE ______________ PERIOD _____
2-7
Enrichment
7AF1.2
Equation Hexa-Maze
To solve the maze, start with the number in the center. This number
must be the solution of the equation in the next cell. The number in
the new cell will then be the solution to the equation in the next cell.
At each move, you may only move to an adjacent cell. Each cell is
used only once.
n 3.7 7
19 n 17.9
40 40 n
11
1.5
End
n
4
3.3n 36.3
n 11 16
4
1.5
21 12n 13
14 0.5n 6
40
5
0.7n 4 0.9
n
2
Start Here
5.2 n 3.7
40
7
2
3
0.1 0
6n
9
2
9n
n
12
14
0.4
7
5n 2
29.2 36.2 n
2
3
11
9
2
6n 5 1
0.2
100
n
0.3
3 4.5 n
3
2
Chapter 2
2
3
43 n 41.5
3.3
9
2
0
90 32 n 30
2
3
1
3
2
15 5 n5
66 3
5.5
n 4.5 10
75n 50
1.5
20
50
2
3
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.1
NAME ________________________________________ DATE ______________ PERIOD _____
TI-73 Activity
2-7
Solving and Checking Equations
Use the Equation Solver feature in the
check your solutions.
x (4)
7
Choose Equation Solver.
6
MATH
Step 2
Enter the equation. (If an equation is already there, press
2nd
4.9
7
Step 3
menu to solve equations quickly or to
Solve 4.9 . Check your solution.
Example
Step 1
MATH
[TEXT] Done
(
(
)
4
CLEAR
b
)
.)
c
ENTER
In the Solve row, choose x. (Ignore any current value shown for x.)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 2-7
ENTER
Step 4
Read the value of x in the second row.
x 38.3
Step 5
Check the result. Evaluate the right side of the equation with the value 38.3 x for x.
2nd
F
D
[QUIT]
(
38.3
(
)
4
)
b
c
7
ENTER
ENTER
The calculator displays 4.9, which matches the left side of the equation. So the
result is correct.
Exercises
Solve each equation. Check your solution.
3. 423 114k
1. 4x 24.9
2. 6.9 c 2.6
4. p (17.1) 28.3
5. 5 g 8
4
3
6. 9.1 1.4t 18.9
7. The volume of a cylinder is given by the formula V = r2h, where r
is the radius of the base and h is the height of the cylinder. The
volume of a cylinder is 21.21 cubic centimeters. If the cylinder
has a height of 27 centimeters, what is its radius? Round to the
nearest hundredth.
Chapter 2
51
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-8
Study Guide and Intervention
7MR2.4, 7NS1.2
Problem-Solving Investigation: Look for a Pattern
You may need to look for a pattern to solve a problem.
Explore
Determine what information is given in the problem and what you need to find.
Plan
Select a strategy including a possible estimate.
Solve
Solve the problem by carrying out your plan.
Check
Examine your answer to see if it seems reasonable.
Example
Explore
You know that 3 people boarded the subway train at the first stop. At each
subsequent stop, 2 more people board the train than at the previous stop.
Plan
Look for a pattern and use the pattern to find how many people boarded the
train in all.
Solve
Complete the information for the first, second, and third stops. Continue the
pattern to solve the problem.
First Stop
3
3 people on
the train
Second Stop
5
3+5=8
people on
the train
Third Stop
7
8 + 7 = 15
people on
the train
Fourth Stop
9
15 + 9 = 24
people on
the train
Fifth Stop
11
24 + 11 = 35
people on
the train
Sixth Stop
13
35 + 13 = 48
people on
the train
Seventh Stop
15
48 + 15 = 63
people on
the train
At the seventh and final stop there were 63 people on the subway train.
Check
Check your pattern to make sure the answer is correct.
Exercises
Look for a pattern. Then use the pattern to solve each problem.
1
2
2
3
1. COOKING A muffin recipe calls for 2 cups of flour for every cup of sugar. How many
cups of flour should be used when 4 cups of sugar are used?
2. FUNDRAISER There were 256 people at a fundraiser. When the event was over, half of the
people who remained left every 5 minutes. How long after the event ended did the last
person leave?
Chapter 2
52
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Three people board the subway train at the first stop. Five people board the train at the
second stop. Seven people board the train at the third stop. If this pattern continues and no
one gets off the train, how many people are on the subway train when it reaches the seventh
and final stop?
NAME ________________________________________ DATE ______________ PERIOD _____
2-8
Skills Practice
7MR2.4, 7NS1.2
Problem-Solving Investigation: Look for a Pattern
Look for a pattern. Then use the pattern to solve each problem.
1. YARN A knitting shop is having a huge yarn sale. One skein sells for $1.00, 2 skeins sell
for $1.50, and 3 skeins sell for $2.00. If this pattern continues, how many skeins of yarn
can you buy for $5.00?
2. BIOLOGY Biologists place sensors in 8 concentric circles to
track the movement of grizzly bears throughout Yellowstone
National Park. Four sensors are placed in the inner circle.
Eight sensors are placed in the next circle. Sixteen sensors
are placed in the third circle, and so on. If the pattern
continues, how many sensors are needed in all?
4. CHEERLEADING The football cheerleaders will arrange themselves in rows to form a
pattern on the football field at halftime. In the first five rows there are 12, 10, 11, 9,
and 10 girls in each row. They will form a total of twelve rows. If the pattern continues,
how many girls will be in the back row?
5. GEOMETRY Find the perimeters of the next two figures in the pattern. The length of
each side of each small square is 3 feet.
6. HOT TUBS A hot tub holds 630 gallons of water when it is full. A hose fills the tub at a
rate of 6 gallons every five minutes. How long will it take to fill the hot tub?
Chapter 2
53
Glencoe California Mathematics, Grade 7
Lesson 2-8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. HONOR STUDENTS A local high school displays pictures of the honor students from each
school year on the office wall. The top row has 9 pictures displayed. The next 3 rows
have 7, 10, and 8 pictures displayed. The pattern continues to the bottom row, which
has 14 pictures in it. How many rows of pictures are there on the office wall?
NAME ________________________________________ DATE ______________ PERIOD _____
2-8
Practice
7MR2.4, 7NS1.2
Problem-Solving Investigation: Look for a Pattern
4. READING Ling read 175 pages by 1:00
P.M., 210 pages by 2:00 P.M., and 245
pages by 3:00 P.M. If she continues
reading at this rate, how many pages
will Ling have read by 4:00 P.M.?
Mixed Problem Solving
For Exercises 1 and 2, look for a
pattern. Then use the pattern to solve
the problem.
1. GEOMETRY Draw the next two angles in
the pattern.
a.
b.
10
20
c.
d.
40
30
Select the Operation
2. ANALYZE TABLES A falling object
continues to fall faster until it hits the
ground. How far will an object fall
during the fifth second?
Time Period
1st second
2nd second
3rd second
4th second
5. MOVIES The land area of Alaska is
about 570 thousand square miles. The
land area of Washington, D.C., is about
0.06 thousand square miles. How many
times larger is Alaska than Washington,
D.C.?
Distance Fallen
16 feet
48 feet
80 feet
112 feet
Use any strategy to solve Exercises 3
and 4. Some strategies are shown
below.
6. U.S. PRESIDENTS President Clinton
served 5 two-year terms as governor of
Arkansas and 2 four-year terms as
President of the United States. How
many total years did he serve in these
two government offices?
PROBLEM-SOLVING STRATEGIES
• Use the four-step plan.
• Look for a pattern.
1
8
3. YARD WORK Denzel can mow of his
yard every 7 minutes. If he has 40
3
4
minutes to mow of the yard, will he
have enough time?
Chapter 2
54
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
For Exercises 5 and 6, select an
appropriate operation to solve the
problem. Justify your solution and
solve the problem.
NAME ________________________________________ DATE ______________ PERIOD _____
2-8
Word Problem Practice
7MR2.4, 7NS1.2
Problem-Solving Investigation: Look for a Pattern
Look for a pattern. Then use the pattern to solve each problem.
Number of Total Cost
People in
per Group
Group
1
$1.00
2
$2.00
3
$2.90
4
$3.70
5
$4.40
1. Describe the pattern used to calculate
the cost for a group.
2. If the pattern continues, what would
the cost be for a group of 8 skaters?
3. SAVINGS Jordan saved $1 the first
week, $2 the second week, $4 the third
week, and $8 the fourth week. If this
pattern continues, how much will she
save the eighth week?
4. AGRICULTURE In a vegetable garden,
the second row is 8 inches from the
first row, the third row is 10 inches
from the second row, the fourth row is
14 inches from the third row, and the
fifth row is 20 inches from the fourth
row. If the pattern continues, how
far will the eighth row be from the
seventh row?
5. GARDENING Marial was planting
daisies in her garden. She planted 2
white daisies and 5 yellow daisies in
the first row, 4 white daisies and 6
yellow daisies in the second row, and 6
white daisies and 7 yellow daisies in
the third row. If she continues the
pattern, how many white and yellow
daisies will she plant in the sixth row?
6. BIOLOGY A newborn seal pup gains 4
pounds the first week, 8 pounds the
second week, 16 pounds the third week,
and 32 pounds the fourth week. If this
growth pattern continues, how many
weeks old will the seal pup be before it
weighs over 100 pounds?
Chapter 2
55
Glencoe California Mathematics, Grade 7
Lesson 2-8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
ENTERTAINMENT For Exercises 1 and 2, use the information
at the right, which shows the ticket prices at a skating rink.
NAME ________________________________________ DATE ______________ PERIOD _____
2-9
Lesson Reading Guide
7NS1.2, 7NS2.1, 7AF2.1
Powers and Exponents
Get Ready for the Lesson
Read the introduction at the top of page 126 in your textbook.
Write your answers below.
1. How many 2s are multiplied to determine the number of great
grandparents? great-great grandparents?
Read the Lesson
2. Define the terms base, exponent, and power.
For Exercises 4–6, identify the base, exponent, and power in each
expression.
3. 54
5. x8
6. Explain in words what 54 means.
Rewrite each expression using multiplication instead of an exponent.
7. 54
8. 95
9. c8
Evaluate each expression.
10. 54
11. 95
12. 63
13. 28
Remember What You Learned
14. Notice that 43 13 . A power with a negative exponent is not negative.
4
Write a true sentence using the terms negative exponent, power, positive,
and rational.
Chapter 2
56
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. 72
NAME ________________________________________ DATE ______________ PERIOD _____
2-9
Study Guide and Intervention
7NS1.2, 7NS2.1, 7AF2.1
Powers and Exponents
Expressions containing repeated factors can be written using exponents.
Example 1
Write 7 7 7 7 7 using exponents.
Since 7 is used as a factor 5 times, 7 7 7 7 7 75.
Example 2
Write p p p q q using exponents.
Since p is used as a factor 3 times and q is used as a factor 2 times, p p p q q p3 q2.
Any nonzero number to the zero power is 1. Any nonzero number to the negative n power is the
multiplicative inverse of nth power.
Example 3
Example 4
Evaluate 62.
62 6 6
36
5–3 ¬
¬
Definition of exponents
Simplify.
Evaluate 5–3.
1
53
1
125
Definition of negative exponents
Simplify.
Exercises
1. 8 8 8 8 8
2. 4 4 4 4
3. a a a a a a
4. g g g g g g g
5. 5 5 9 9 5 9 5 5
6. s w w s s s
Evaluate each expression.
7. 42
Lesson 2-9
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write each expression using exponents.
8. 53
9. 132
10. 23 32
11. 8–2
12. 24 52
13. 3–4
14. 34 72
Chapter 2
57
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-9
Skills Practice
7NS1.2, 7NS2.1, 7AF2.1
Powers and Exponents
Write each expression using exponents.
1. 2 2 2 2
2. 9 9
3. 7 7 7 7 7 7
4. x x x
5. c c c c c
6. s s s s s s s
7. 5 5 5 3 3
8. 4 4 4 4 6 6 6
11. m n n n m n
10. a a b a b a a
12. y x x y x y y
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. 8 8 2 2 2 2 8
Evaluate each expression.
13. 43
14. 25
15. 83
16. 54
17. 28
18. 23 52
19. 42 34
20. 26 62
21. 33 73
22. 23
23. 82
24. 74
Chapter 2
58
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-9
Practice
7NS1.2, 7NS2.1, 7AF2.1
Powers and Exponents
Write each expression using exponents.
1. 3 3 m
2. 2 d 5 d d 5
3. p 9 3 q p 9
4. g 7 7 g h 7 h
5. 2 5 r 7 s r 5 r 7 r s
6. x 8 y x 5 x 5 y 8 y y 5
9. 22 62
10. 23 52
7. 24
8. 53
11. 34
12. 83
13. 92
14. 53
15. 7 22 52
16. 32 6 102
17. 32 23
18. 7 33 54
ALGEBRA Evaluate each expression.
19. r3 s, if r 5 and s 4
20. m2 n3, if m 6 and n 2
21. f 4 g5, if f 3 and g 1
22. x5 y, if x 2 and y 8
23. Complete the following pattern.
54 625, 53 125, 52 25, 51 5, 50 ? , 51 ? , 52 ? , 53 ?
24. MONEY Suppose $100 is deposited into an account and the amount doubles
every 8 years. How much will be in the account after 40 years?
25. EPIDEMICS At the beginning of an epidemic, 50 people are sick. If the
number of sick people triples every other day, how many people will be
sick at the end of 2 weeks?
Chapter 2
59
Glencoe California Mathematics, Grade 7
Lesson 2-9
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Evaluate each expression.
NAME ________________________________________ DATE ______________ PERIOD _____
2-9
Word Problem Practice
7NS1.2, 7NS2.1, 7AF2.1
1. SPORTS In the first round of a local
tennis tournament there are 25
matches. Find the number of matches.
2. GEOMETRY The volume of a box can be
found by multiplying the length, width,
and height of the box. If the length,
width, and height of the box are all 5
inches, write the volume of the box
using an exponent.
3. MONEY An apartment complex has 3
buildings. Each building has 3
apartments. There are 3 people living
in each apartment, and each person
pays 3 dollars per month for pool
maintenance. The expression 34
denotes the amount paid each month
for pool maintenance. Find this
amount.
4. ACTIVISM A petition drive is being held
in 10 cities. In each city, 10 people have
collected 10 signatures each. The
expression 103 denotes the number of
signatures that have been collected
altogether. Find this number.
5. MEASUREMENT There are 106
millimeters in a kilometer. Write the
number of millimeters in a kilometer.
6. NATURE Suppose a certain forest fire
doubles in size every 12 hours. If the
initial size of the fire was 1 acre, how
many acres will the fire cover in
2 days?
7. BANKING Suppose that a dollar placed
into an account triples every 12 years.
How much will be in the account after
60 years?
8. BIOLOGY Suppose a bacterium splits
into two bacteria every 15 minutes.
How many bacteria will there be in 3
hours?
Chapter 2
60
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Powers and Exponents
NAME ________________________________________ DATE ______________ PERIOD _____
2-9
Enrichment
7NS1.2, 7AF2.1
Solve the following puzzle by finding the correct path through the boxes. The
solution is a famous quote from United States history.
1
G
2
M
3
E
4
E
5
R
6
E
7
I
8
V
9
B
10
T
11
D
12
L
13
I
14
Y
15
R
16
E
17
E
18
E
19
O
20
G
21
T
22
A
23
M
24
V
25
I
Starting with Box 1, draw an arrow to the box next or diagonal to Box 1 with
the expression of the least value. The arrow cannot go to a box that has
already been used. The first arrow has been drawn to get you started.
When you have finished drawing your path through the boxes, write the box
numbers on the lines below. Put the numbers in the order in which they are
connected. Then use the chart at the right to convert each box number to a
letter.
1
2
53
6
7
11
8
12
16
8 3 18
Box Number
1
7
Letter
G
I
53 35
20
28 112
192
24
36 35
232
15
19
23
182
73
162 63
22
29 9 2
25 3 2
14
18
45 93
10
44
17
21
9
13
35
36 6 3
5
172
24 32
27
44 162
4
43 34
132
63
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3
25
212
23 7 2
Box Number
Letter
Chapter 2
H
61
Glencoe California Mathematics, Grade 7
Lesson 2-9
A-Mazing Exponents
NAME ________________________________________ DATE ______________ PERIOD _____
2-9
Scientific Calculator Activity
The Power Key
The power key on many calculators makes it easier to evaluate
expressions with exponents. It is usually labeled y x or
.
Example 1
Evaluate 54.
Enter: 5
ENTER
4 625
Therefore, 54 625.
Example 2
Evaluate 25 43.
Enter: 2
5
4
ENTER
3 2048
Therefore, 25 43 2,048.
Exercises
1. 38
2. 524
3. 2 63
4. 43 27
5. 3 25 45
6. 53 42 25
7. 54 33
8. 2 43 34
9. 3 53 4 27
10. 5 23 3 23
11. (4 5)2 63 25
12. (35 25) 55
13. CHALLENGE 10 73 6 23 34 5 43
Chapter 2
62
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Evaluate each expression.
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading Guide
2-10
7NS1.1
Scientific Notation
Get Ready for the Lesson
Read the introduction at the top of page 130 in your textbook.
Write your answers below.
Expression
Expression
Product
1.
8.7 102 8.7 100
1
8.7 101 8.7 10
1
8.7 102 8.7 100
8.7 103 8.7 8.7 103 8.7 8.7 101 8.7 10
87
Product
0.87
2. If 8.7 is multiplied by a positive power of 10, what relationship exists between the
decimal point’s new position and the exponent?
Read the Lesson
4. How can you tell that a number is in standard form?
Identify each positive number as either very large or very small.
5. 9,245,000
6. 0.00083986
7. 0.0000003
8. 1,000,000,000
For each pair of numbers, determine how many places the decimal
has moved and whether the exponent of the original would be
positive or negative in scientific notation.
9. 0.00037 → 3.7
10. 185,000 → 1.85
Write each number in scientific notation.
11. 8,790,000
12. 0.0000125
13. 0.00899
14. 402,500,000
Remember What You Learned
15. Work with a partner. One person should explain how to write a very large
number in scientific notation. The other person should explain how to
write a very small number in scientific notation.
Chapter 2
63
Glencoe California Mathematics, Grade 7
Lesson 2-10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. When 8.7 is multiplied by a negative power of 10, how does the new position of the
decimal point relate to the negative exponent?
NAME ________________________________________ DATE ______________ PERIOD _____
2-10
Study Guide and Intervention
7NS1.1
Scientific Notation
A number in scientific notation is written as the product of a factor and a power of ten.
Example 1
Write 8.65 107 in standard form.
8.65 107 8.65 10,000,000
86,500,000
Example 2
107 10 10 10 10 10 10 10 or 10,000,000
Move the decimal point 7 places to the right.
Write 9.2 10–3 in standard form.
9.2 0.001
1
10
1
1
or 0.001
103 1,000
0.0092
Move the decimal point 3 places to the left.
9.2 10–3 9.2 13
10
Example 3
103 3
Write 76,250 in scientific notation.
76,250 7.625 10,000
7.625 104
Example 4
The decimal point moves 4 places.
The exponent is positive.
0.00157 1.57 0.001
1.57 10–3
The decimal point moves 3 places.
The exponent is negative.
Exercises
Write each number in standard form.
1. 5.3 101
2. 9.4 103
3. 7.07 105
4. 2.6 103
5. 8.651 102
6. 6.7 106
Write each number in scientific notation.
7. 561
9. 56,400,000
8. 14
10. 0.752
11. 0.0064
12. 0.000581
Chapter 2
64
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write 0.00157 in scientific notation.
NAME ________________________________________ DATE ______________ PERIOD _____
2-10
Skills Practice
7NS1.1
Scientific Notation
1. 6.7 101
2. 6.1 104
3. 1.6 103
4. 3.46 102
5. 2.91 105
6. 8.651 107
7. 3.35 101
8. 7.3 106
9. 1.49 107
10. 4.0027 104
11. 5.2277 103
12. 8.50284 102
Write each number in scientific notation.
13. 34
14. 273
15. 79,700
16. 6,590
17. 4,733,800
18. 2,204,000,000
19. 0.00916
20. 0.29
21. 0.00000571
22. 0.0008331
23. 0.0121
24. 0.00000018
Chapter 2
65
Glencoe California Mathematics, Grade 7
Lesson 2-10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write each number in standard form.
NAME ________________________________________ DATE ______________ PERIOD _____
2-10 Practice
7NS1.1
Scientific Notation
Write each number in standard form.
1. 9.03 102
2. 7.89 103
3. 4.115 105
4. 3.201 106
5. 5.1 102
6. 7.7 105
7. 3.85 104
8. 1.04 103
Write each number in scientific notation.
9. 4,400
10. 75,000
11. 69,900,000
12. 575,000,000
13. 0.084
14. 0.0099
15. 0.000000515
16. 0.0000307
17. Which number is greater: 3.5 104 or 2.1 106?
19. POPULATION The table lists the populations
of five countries. List the countries from
least to greatest population.
Country
Australia
Brazil
Egypt
Luxembourg
Singapore
Population
2.0 107
1.9 108
7.7 107
4.7 105
4.4 106
Source: The World Factbook
20. SOLAR SYSTEM Pluto is 3.67 109 miles from the Sun. Write this number
in standard form.
21. MEASUREMENT One centimeter is equal to about 0.0000062 mile. Write
this number in scientific notation.
22. DISASTERS In 2005, Hurricane Katrina caused over $125 billion in damage
in the southern United States. Write $125 billion in scientific notation.
Chapter 2
66
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
18. Which number is less: 7.2 107 or 9.9 105?
NAME ________________________________________ DATE ______________ PERIOD _____
2-10
Word Problem Practice
7NS1.1
1. MEASUREMENT There are about
25.4 millimeters in one inch. Write this
number in scientific notation.
2. POPULATION In the year 2000, the
population of Rahway, New Jersey, was
26,500. Write this number in scientific
notation.
3. MEASUREMENT There are 5,280 feet in
one mile. Write this number in
scientific notation.
4. PHYSICS The speed of light is about
1.86 105 miles per second. Write this
number in standard notation.
5. COMPUTERS A CD can store about
650,000,000 bytes of data. Write this
number in scientific notation.
6. SPACE The diameter of the Sun is about
1.39 109 meters. Write this number
in standard notation.
7. ECONOMICS The U.S. Gross Domestic
Product in the year 2004 was
1.17 1013 dollars. Write this number
in standard notation.
8. MASS The mass of planet Earth is
about 5.98 1024 kilograms. Write this
number in standard notation.
Lesson 2-10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Scientific Notation
Chapter 2
67
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2-10 Enrichment
7NS1.1
Scientific Notation and Space
What travels faster than jets, spaceships, and sound waves? Light does. The speed of light
is about 3 108 meters per second (3 105 kilometers per second). Because distances in
space are so large, they are often discussed in terms of light years, or the distance a
photon of light would travel in a year.
1 light year speed of light in meters per second number of seconds in a year.
There are 365 24 60 60 31,536,000 3.15 107 seconds in a year.
1 light year (3 108) (3.15 107) 9.45 1015 meters 9.45 1012 kilometers
When performing operations with numbers in scientific notation, it is often helpful to
consider the decimal part and the power of ten separately.
(2.3 103) (1.4 102) (2.3 1.4) (103 102)
3.22 (10 10 10) (10 10)
3.22 105
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Distance
from Sun
(km)
Diameter
(km)
5.7 107
1.07 108
1.5 108
2.3 108
7.8 108
1.4 109
2.9 109
4.5 109
5.9 109
5.9 103
1.2 104
1.3 104
6.8 103
1.43 105
1.2 105
5.1 104
5.0 104
2.4 103
Distance
from Earth
Object
(lightyears)
Alpha Centauri
4.27
Sirius (Dog star)
8.7
Arcturus
36
Pleiades Cluster
400
Betelgeuse
520
Deneb
1,600
Crab Nebula
4,000
Center of Milky Way
38,000
Source: pbs.org
Source: wikipedia.com
1. How long does it take a photon of light to travel from the Sun to Earth?
2. How long does it take a photon of light to travel from the Sun to Pluto?
3. How far is Alpha Centauri from Earth in kilometers?
4. The Pleiades Cluster is about how many times as far from Earth as Alpha Centauri?
5. If you see Sirius in the night sky, how long ago was that light emitted from the star?
6. The diameter of Jupiter is how many times the diameter of Earth?
Chapter 2
68
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use the information above and the following tables to answer Exercises 1–6 below.
NAME ________________________________________ DATE ______________ PERIOD _____
2
Student Recording Sheet
Read each question. Then fill in the
correct answer.
A
B
C
D
2.
F
G
H
J
3.
A
B
C
D
4.
F
G
H
J
5.
A
B
C
D
6.
F
G
H
J
7.
A
B
C
D
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.
8.
F
G
H
J
9.
A
B
C
D
10.
F
G
H
J
11.
A
B
C
D
12.
F
G
H
J
Assessment
Use this recording sheet with pages 140-141 of the Student Edition.
Pre-AP
Record your answers for Question 13 on
the back of this paper.
Chapter 2
69
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2
Rubric for Scoring Pre-AP
(Use to score the Pre-AP question on page 141 of the Student Edition.)
General Scoring Guidelines
• If a student gives only a correct numerical answer to a problem but does not show how he or she
arrived at the answer, the student will be awarded only 1 credit. All extended response questions
require the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of the
question. For example, if a question has three parts, the correct response to one or two parts of the
question that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing that
the answer checks or is correct is not considered a complete response for full credit.
Exercise 13 Rubric
Score
4
Specific Criteria
A complete explanation of how to determine the number of blocks needed to fill the
999
container is given. The expression is given and correctly simplified to
333
3
The explanation is essentially correct, but not complete. The expression is correct
and is correctly simplified. OR
The explanation is completely correct and the correct expression is given, but the
expression is not simplified correctly.
2
The explanation is flawed, but the expression is correct. OR
The explanation is completely correct, but the expression is not correct.
1
An incomplete explanation is given and the expression is not given or is incorrect.
OR
No explanation is given, but the expression is correct.
0
Response is completely incorrect.
Chapter 2
70
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
determine 27 blocks are needed.
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Quiz 1
SCORE _____
(Lessons 2-1, 2-2 and 2-3)
Write each fraction or mixed number as a decimal.
1. 1
1.
2. 45
8
2.
9
Write each decimal as a fraction or mixed number
in simplest form.
3.
4. 7.3
3. 0.8
4.
Replace each with , , or to make a true sentence.
5. 4 2
5
3
6. 4.4 42
7. 2.9
3
2.93
5
5.
6.
7.
Multiply. Write in simplest form.
8. 1 3
8.
4
9. 5 3
12
9.
10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. 12 22
3
Assessment
3
10.
5
NAME ________________________________________ DATE ______________ PERIOD _____
2
SCORE _____
Chapter 2 Quiz 2
(Lessons 2-4 and 2-5)
Divide. Write in simplest form.
1. 3 9
4
10
1.
2. 41 23
8
4
2.
Add or subtract. Write in simplest form.
3. 4 7
9
9
4. 23 77
8
3.
8
4.
5. GEOMETRY Find the perimeter of the
triangle.
1
3 5 in.
3
1 5 in.
5.
3
3 5 in.
Chapter 2
71
Glencoe California Mathematics, Grade 7
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Quiz 3
SCORE _____
(Lessons 2-6 and 2-7)
Add or subtract. Write in simplest form.
1. 5 1
8
1.
3
2. 85 11
6
4
2.
Solve each equation. Check your solution.
3. m 1.42 5.36
3.
4. f 5 2
4.
9
3
5. MULTIPLE-CHOICE Four textbooks are stacked one
on top of the other. How tall is the pile if the books are
15
3
1
17 inches, inches, inches, and 1 inches thick?
16
A. 51 in.
16
4
B. 51 in.
2
2
C. 59 in.
16
D. 53 in.
4
5.
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Quiz 4
SCORE _____
(Lessons 2-8, 2-9 and 2-10)
For Questions 1–3, evaluate each expression.
1. 24
1.
2. 32 42
2.
3. 53
3.
4. PAPER A sheet of paper is approximately 0.003 inch thick.
Write this number in scientific notation.
4.
5. Identify the pattern and list the next three terms of the given
sequence 4, 15, 26, 37, ___, ___, ___
Chapter 2
72
5.
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Mid-Chapter Test
SCORE _____
(Lessons 2-1 through 2-5)
Write the letter for the correct answer in the blank at the right of each question.
1. Write 6 as a decimal.
11
B. 1.83
C. 0.5
4
D. 0.54
1.
45
J. 2.
as a fraction in simplest form.
3. Write 0.7
7
A. B. 7
C. 13
77
D. 3.
4. Which is a true statement?
F. 2 0.5
G. 4 5
H. 11 1.29
J. 61 6.3
4.
C. 1
D. 1
5.
A. 1.83
2. Write 0.45 as a fraction in simplest form.
41
F. 41
G. 9
H. 20
2
9
10
3
5
100
90
7
8
99
8
3
5
5. 5 2
6
A. 21
B. 7
12
11
3
3
6. 31 33
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5
4
G. 93
H. 12
20
75
7. Divide 2 8 . Write in simplest form.
3
9
2
16
B. 3
C. A. 9
4
27
8. Add 35 11 . Write in simplest form.
7
7
4
G. 46
H. 24
F. 2
7
7
7
64
F. 6.
D. 11
7.
J. 46
8.
20
11
J. 3
7
9. Order the numbers 8.9, 81, 87, and 8.9
from least to greatest. 9.
9
8
15
10. ALGEBRA Evaluate the expression xz if x 13 and z .
5
16
Write the answer in simplest form.
10.
11. What is 71 divided by 5?
11.
12. WORD PROCESSING An English project is to be typed and
divided into 3 columns. If the page is 71 inches wide, how
2
wide should each column be?
12.
13. SEWING Amy’s mother decided to sew new curtains for
Amy’s bedroom windows. She needs 41 yards of fabric for
8
one window and 65 yards for a second window. How many
8
yards of fabric does she need to buy?
13.
2
Chapter 2
22
73
Glencoe California Mathematics, Grade 7
Assessment
Multiply. Write in simplest form.
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Vocabulary Test
SCORE _____
bar notation
multiplicative inverses
scientific notation
base
power
terminating decimal
dimensional analysis
rational number
unlike fractions
exponent
reciprocals
like fractions
repeating decimal
1. The process of including units of measurement when you
compute is called __________ .
1.
2. A number that is expressed using an exponent is called
a(n) __________ .
2.
3. Repeating decimals can be expressed exactly using
__________ .
3.
4. Fractions with the same denominator are called __________ .
4.
5. The numbers 5 and 12 are __________ or ___________ since
5.
7
5
their product is 1.
6. In the expression 53, the number 3 is called the __________ .
6.
7. A number expressed as the product of a number that is at least
1 but less than 10 and a power of 10 is said to be
in __________ .
7.
8. The numbers 1.51, 7, 21, and 6.5
are examples of
11
8.
4
__________ .
9. To add or subtract __________, you must first rewrite each
fraction with a common denominator.
9.
10. In the expression 75, the number 7 is called the __________ . 10.
Define each term in your own words.
11. terminating decimal
12. repeating decimal
Chapter 2
74
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Choose from the terms above to complete each sentence.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 2 Test, Form 1
2
SCORE _____
Write the letter for the correct answer in the blank at the right of each question.
12
1. Write as a decimal.
25
A. 0.52
C. 2.083
B. 12.04
D. 0.48
1.
536
J. 2.
D. 4 0.5
7
3.
2. Write 5.36 as a mixed number in simplest form.
F. 59
536
H. 36
G. 5
25
100
100
1,000
3. Which of the following is a true statement?
A. 5 4
6
B. 4.3 43
9
4
C. 135 13.625
8
7
4. Which set of rational numbers is ordered from least to greatest?
F. 4.06, 41, 41, 4.3
G. 0.1
, 2, 2, 0.27
H. 61, 6.3
, 6.34, 65
4
8
13 12
J. 7.8
6
, 7.86
, 7
, 7
4
3 9
15
4.
13
Multiply or divide. Write in simplest form.
5. 6 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7
3
12
A. 21
B. 4
7
C. 4
11
D. 1
5.
G. 3
H. 22
J. 21
6.
B. 9
C. 2
D. 1
7.
G. 15
H. 1
J. 21
8.
9.
5
21
6. 22 11
5
4
F. 27
10
20
10
7. 3 3
8
4
A. 35
9
32
2
8. 2 6
7
F. 7
12
7
21
Add or subtract. Write in simplest form.
9. 8 4
9
9
A. 4
9
B. 11
C. 2
D. 2
G. 13
H. 22
J. 22
3
9
3
10. 34 12
7
F. 15
7
Chapter 2
7
7
0
75
7
10.
Glencoe California Mathematics, Grade 7
Assessment
5
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 2 Test, Form 1
2
(continued)
11. 82 41
3
9
A. 41
B. 47
6
9
C. 45
D. 127
9
11.
9
12. HOMEWORK Maria spent 3 of an hour studying on Wednesday and 11 hours
4
3
studying on Thursday. How much total time did she spend studying during
the two days?
F. 21 hours
12
G. 14 hours
7
H. 11 hours
J. 1 hour
4
12.
For Questions 13–15, solve each equation. Check your solution.
13. r 4.1 1.9
A. 6
B. 2.2
C. 0.46
D. 7.79
13.
G. 1
11
H. J. 11
14.
15. 3.4 1.7t
A. 5.1
B. 1.7
C. 2
D. 0.5
15.
16. Evaluate 63.
F. 18
G. 186
H. 216
J. 729
16.
B. 16
C. 1
D. 8
17.
14. 1 x 4
5
F. 31
5
5
20
20
17. Evaluate 42.
A. 1
16
8
18. WATER A pail of water is leaking. After 30 seconds the level has dropped
8 inches, after 1 minute the water has dropped 16 inches, and after
2 minutes the water level has dropped 32 inches. If the water in the pail
was originally 4 feet tall, how long will it take for the pail to drain?
F. 3 minutes
H. 2 minutes 30 seconds
G. 5 minutes
J. 4 minutes 30 seconds
18.
19. Write 3.471 105 in standard form.
A. 347,100
B. 3,471,000
D. 0.00003471
19.
20. TIME In one 24-hour day, there are 86,400 seconds. Write this number in
scientific notation.
F. 8.64 104
G. 864 102
H. 8.64 104
J. 864 102
20.
C. 0.0003471
Bonus Compute and express the value in scientific notation.
(13,000)(5,100)
300
Chapter 2
76
B:
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 2A
2
SCORE _____
Write the letter for the correct answer in the blank at the right of each question.
1. Write 43 as a decimal.
16
A. 4.1875
B. 4.316
D. 4.3
1.
11
J. 2.
C. 42 43
D. 11.3
9
11.39
3.
H. 1
J. 4
4.
C. 4.3
2. Write 0.5
as a fraction in simplest form.
55
F. G. 1
100
H. 5
2
9
20
3. Which of the following is a true statement?
A. 5 5
11
9
B. 0.1
5
3
20
3
5
F. 4
G. 0.3
13
3
11
Multiply or divide. Write in simplest form.
5. 5 8
12
15
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A. 1
9
B. 2
C. 2
D. 1
5.
G. 161
H. 91
J. 83
6.
B. 2
3
C. 5
75
D. 7.
G. 5
H. 14
J. 53
8.
9
3
4
6. 42 41
3
2
F. 21
3
15
7. 5 8
16
1
A. 1
2
6
5
16
128
8. 33 21
4
12
F. 12
3
9
5
4
Add or subtract. Write in simplest form.
9. 24 12
5
A. 32
5
5
B. 41
C. 21
D. 12
9.
G. 3
H. 6
19
J. 10.
5
5
5
10. 5 1
8
6
F. 5
48
Chapter 2
7
14
77
24
Glencoe California Mathematics, Grade 7
Assessment
4. Which number is the greatest?
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Test, Form 2A
(continued)
11. 24 11
9
3
A. 15
B. 11
6
C. 35
9
D. 37
12
9
11.
12. HEIGHT Marni is 483 inches tall, and Suzanna is 475 inches. How much
8
8
taller is Marni than Suzanna?
F. 3 in.
G. 11 in.
4
H. 13 in.
4
J. 1 in.
4
4
12.
For Questions 13–15, solve each equation. Check your solution.
13. 5 m 1
6
3
A. 1
2
14. 0.24t 1.68
F. 0.4032
B. 5
C. 11
D. 21
13.
G. 1.92
H. 1.44
J. 7
14.
B. 4.68
C. 2.7
D. 0.308
15.
G. 324
H. 432
J. 648
16.
B. 36
C. 81
D. 18
17.
18
6
2
15. r 1.2
A. 5.1
16. Evaluate 24 33.
F. 216
17. Evaluate 92.
A. 1
81
18. CONSTRUCTION The Phillip Company is constructing a new building.
After 5 days the building is 10 feet tall. In 10 days the building is 20
feet tall. In 15 days the building is 30 feet tall. How many days will
it take for the building to be 70 feet tall?
F. 4 days
G. 20 days
H. 35 days
J. 70 days
18.
19. Write 3.161 107 in standard notation.
A. 3,161,000
C. 31,610,000
B. 0.0000003161
D. 0.00000003161
19.
20. LANDMARKS The Statue of Liberty weighs 450,000 pounds. Write this
number in scientific notation.
F. 4.5 105
G. 4.5 104
H. 4.5 104
J. 4.5 105
20.
13
1
Bonus The sum of two numbers is 27
. One number is 5.
14
2
B:
Find the other number.
Chapter 2
78
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3.9
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Test, Form 2B
SCORE _____
Write the letter for the correct answer in the blank at the right of each question.
1. Write 75 as a decimal.
11
5
B. 7.4
A. 7.2
C. 7.45
D. 7.2
1.
J. 11
2.
C. 29 2.9
D. 2 0.4
3.
H. 23
J. 2.49
4.
2. Write 0.8
as a fraction in simplest form.
F. 8
G. 4
9
22
H. 5
25
8
3. Which of the following is a true statement?
A. 7 7
9
B. 1.2 11
11
6
10
5
F. 22
G. 2.67
3
5
Multiply or divide. Write in simplest form.
5. 7 4
12
21
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A. 2
9
B. 31
C. 1
D. 1
5.
G. 162
H 61
17
J. 3
6.
B. 1
C. 6
23
D. 1
7.
J. 11
8.
9.
16
3
9
6. 81 22
3
5
F. 20
15
2
36
10
7. 5 9
3
A. 38
9
6
27
8. 31 21
4
6
F. 11
G. 2
24
3
H. 71
24
2
Add or subtract. Write in simplest form.
9. 45 15
6
10
A. 5
6
6
B. 55
C. 62
D. 32
G. 62
H. 5
23
J. 6
3
3
10. 5 1
6
8
F. 3
7
Chapter 2
3
48
79
24
10.
Glencoe California Mathematics, Grade 7
Assessment
4. Which number is the greatest?
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Test, Form 2B
(continued)
11. 41 21
3
2
A. 15
6
B. 21
C. 25
6
D. 65
6
6
11.
12. CARPENTRY A carpenter has a 143-inch piece of molding. How much
4
1
remains after she cuts off a 5-inch piece?
4
F. 191 in.
G. 20 in.
H. 91 in.
2
2
J. 10 in.
12.
For Questions 13–15, solve each equation. Check your solution.
13. 1 k 3
10
5
A. 1
B. 7
C. 1
D. 1
13.
14. –3.6 0.9c
F. 4
G. 2.7
H. 4.5
J. 3.24
14.
B. 0.73
C. 0.4
D. 2.6
15.
G. 225
H. 759,375
J. 675
16.
B. 1
C. 1
D. 125
17.
6
10
2
2
15. m 1.1
16. Evaluate 52 33.
F. 864
17. Evaluate 53.
A. 15
15
125
18. CONSTRUCTION The Phillip Company is constructing a new building.
After 5 days the building is 10 feet tall. In 10 days the building is
20 feet tall. In 15 days the building is 30 feet tall. How tall will
the building be in 50 days?
F. 40 feet
G. 75 feet
H. 50 feet
J. 100 feet
18.
19. Write 4.297 108 in standard notation.
A. 429,700,000
C. 0.00000004297
B. 42,970,000
D. 0.000000004297
19.
20. SCIENCE The volume of a drop of liquid is 0.00005 liter. Write this number
in scientific notation.
F. 5.0 104
G. 5.0 105
H. 5.0 104
J. 5.0 105
20.
Bonus A ribbon is cut in half, and 1 is used. Then 1 of the
3
B:
4
remaining ribbon is cut off and used. The piece left is
15 inches long. How long was the ribbon originally?
Chapter 2
80
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.5
A. 1.65
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Test, Form 2C
SCORE _____
10
1. Write as a decimal.
1.
33
Write each decimal as a fraction or mixed number in
simplest form.
2. 1.4
2.
3. 0.66
3.
For Questions 4 and 5, replace each with , , or to
make a true sentence.
4. 23 25
4.
8
5. 1.04 11
5.
25
6. Order the numbers 5, 0.79, 0.85, and 4 from least
6
5
6.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
to greatest.
Multiply or divide. Write in simplest form.
7. 31 21
6
3
7.
9
18
5
8. 8.
9. 7 2
9.
25
9
3
10. 161 21
10.
11. 4 (8)
11.
3
3
3
For Questions 12–15, add or subtract. Write in simplest
form.
12. 8 1
15
15
12.
13. 15 31
7
Chapter 2
13.
7
81
Glencoe California Mathematics, Grade 7
Assessment
5
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Test, Form 2C
14. 5 5
6
18
(continued)
14.
15. 41 21
3
15.
2
16. COOKING A recipe for waffles calls for 21 cups of flour.
16.
4
How much flour is needed to double the recipe?
17. GARDENING Laurie needs 31 pounds of fertilizer for her
4
17.
lawn. She has 11 pounds. How much more fertilizer does
3
she need?
18. a 2 1
18.
19. 0.74 p 3.69
19.
20. 71y 51
20.
5
2
3
4
For Questions 21 and 22, evaluate each expression.
21. 42 52
21.
22. 72
22.
23. CONSTRUCTION The Phillip Company is constructing a new
building. After 5 days the building is 15 feet tall. In 10 days
the building is 30 feet tall. In 15 days the building is 45 feet
tall. How tall will the building be in 21 days?
23.
24. Write 5.297 103 in standard notation.
24.
25. Write 65,290 in scientific notation.
25.
2 1
2
Bonus Simplify . Write your answer in simplest form.
1
1
3
4
Chapter 2
82
B:
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation. Check your solution.
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Test, Form 2D
SCORE _____
1. Write 4 as a decimal.
1.
15
Write each decimal as a fraction or mixed number in
simplest form.
2. 3.58
2.
3. 6.7
3.
4. 1.33 11
4.
5. 52 54
5.
4
3
5
6. Order the numbers 18, 17, 1.93, and 1.89 from least to
9
10
6.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
greatest.
Multiply or divide. Write in simplest form.
7. 44 25
7
7.
8
8
16
3
8. 8.
9. 7 2
9.
27
12
3
10. 20 22
10.
11. 55 31
11.
5
6
2
For Questions 12–15, add or subtract. Write in simplest
form.
12. 27 15
12.
13. 13 61
13.
8
5
Chapter 2
8
5
83
Glencoe California Mathematics, Grade 7
Assessment
For Questions 4 and 5, replace each with , , or to
make a true sentence.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 2 Test, Form 2D
2
(continued)
14. 5 7
9
14.
18
15. 43 21
4
8
15.
16. CARS Sean uses 51 quarts of oil each time he changes the
4
16.
oil in his car. How much oil does Sean use for 3 oil changes?
17. FOOD Antonio bought 11 pounds of chicken and 21 pounds
3
4
17.
of hamburger for his picnic. How many pounds of meat did
he buy?
18. w 4.6 2.7
18.
19. 7 t 3
19.
20. c 5.7
20.
10
5
2.3
For Questions 21 and 22, evaluate each expression.
21. 24 32
21.
22. 82
22.
23. CONSTRUCTION The Phillip Company is constructing a new
building. After 5 days the building is 10 feet tall. In 10 days
the building is 20 feet tall. In 15 days the building is 30 feet
tall. How many more days will they have to work to finish
a 42-foot tall building?
23.
24. Write 1.698 104 in standard notation.
24.
25. Write 0.0021 in scientific notation.
25.
5 1
5
Bonus Simplify . Write in simplest form.
1
1
2
3
Chapter 2
84
B:
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation. Check your solution.
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Test, Form 3
SCORE _____
1. Write 54 as a decimal.
1.
33
Write each decimal as a fraction or mixed number in
simplest form.
2. 2.18
2.
3. 5.5
3.
4. 21 2.19
4.
5. 73 7.6
5.
6. STATISTICS If you order a set of numbers from least to
greatest the middle number is the median. Find the median
6.
5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5
of 16.31, 171, 16.36, 169, and 15.93.
3
10
7. Find the product of 1, 5, and 4.
5 6
7.
9
8. ALGEBRA Evaluate abc if a 2, b 9, and c 12.
3
10
3
8.
Multiply or divide. Write in simplest form.
9. 31 42
5
9.
5
10. 4 61
10.
3
8
11. 1 7
5
12. 52 24
3
Chapter 2
15
11.
12.
85
Glencoe California Mathematics, Grade 7
Assessment
For Questions 4 and 5, replace each with , , or to
make a true statement.
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Test, Form 3
(continued)
For Questions 13–16, add or subtract. Write in simplest form.
10
15
13. 17
13.
17
14. 6 21
5
14.
15. 41 21
15.
14
7
16. 1
2
16.
3
15
2
10
17. NEWSPAPERS The length of the page of the school newspaper
is 17 inches. The top and bottom margins are both 11 inches.
4
17.
18. CONSTRUCTION The Phillip Company is constructing a new
building. After 5 days the building is 10 feet tall. In 10 days
the building is 20 feet tall. In 15 days the building is 30 feet
tall. Will the company be able to complete a 50 foot tall
building in 30 days? Explain.
18.
Solve each equation. Check your solution.
19. r 4.75
19.
20. 3x 21
20.
1.08
4
2
For Questions 21 and 22, evaluate each expression.
21. 32 82
21.
22. 24 52
22.
23. ALGEBRA Evaluate p3 q2 if p 2 and q 4.
23.
24. Write 2.013 105 in standard notation.
24.
25. Write 9,610,300,000 in scientific notation.
25.
Bonus The closest Venus comes to Earth is 3.8 107 kilometers.
The closest Mercury comes to Earth is 7.7 107 kilometers.
How much closer to Earth does Venus come? Write this
number in standard notation.
B:
Chapter 2
86
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
What is the length of the page inside the margins?
NAME ________________________________________ DATE ______________ PERIOD _____
2
Chapter 2 Extended-Response Test
SCORE _____
Demonstrate your knowledge by giving a clear, concise solution to
each problem. Be sure to include all relevant drawings and justify
your answers. You may show your solution in more than one way or
investigate beyond the requirements of the problem. If necessary,
record your answer on another piece of paper.
1. For a school bake sale, each student has been asked to bring 6 dozen
cookies. Help Eva plan for the bake sale by completing the exercises.
b. Explain how to write your answer to part a as a decimal. Then
express the number of recipes that Eva should make as a decimal.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
c. Each recipe calls for 11 cups of flour. Explain how to use your answer
4
from part a to determine how much flour Eva will need for her
cookies. How much flour will she need?
d. The cookies will be sold in packages of one-half dozen cookies. The
equation 1x 6 can be used to find the number of packages of cookies
2
Eva will make. Explain how to solve the equation and then solve the
equation to find the number of packages.
2. Now help Jaime plan for the bake sale.
a. Jaime has chosen one recipe that makes 31 dozen cookies. Now he is
3
looking for a second recipe for the rest of the cookies. Explain how
Jaime can find the number of dozens of cookies the second recipe should
make so that he has a total of 6 dozen cookies. Then find how many
dozens the second recipe needs to make. Express the answer as a
fraction or mixed number in simplest form.
b. Express your answer to part a as a decimal. In what way does this
decimal differ from your answer to Exercise 1b?
c. After choosing a second recipe, Jaime finds that he needs 13 cups of
4
flour for one recipe and 2 cup of flour for the other recipe. Explain
3
how to find the total amount of flour that Jaime needs. Then find the
amount. Express the answer as a fraction or mixed number in
simplest form.
Chapter 2
87
Glencoe California Mathematics, Grade 7
Assessment
a. Eva has chosen a recipe that makes 21 dozen cookies. The expression
2
6 21 can be used to find the number of recipes that she should make.
2
Explain how to evaluate the expression. Then evaluate the expression
to find the number of recipes Eva should make. Express the answer
as a fraction or mixed number in simplest form.
NAME ________________________________________ DATE ______________ PERIOD _____
2
Standardized Test Practice
SCORE _____
(Chapter 2)
Part 1: Multiple Choice
Instructions: Fill in the appropriate circle for the best answer.
1. Which sentence is true? (Lesson 1-3)
A |2| 2
C 6 7
B 21 25
D –8 15
1.
A
B
C
D
2. Simplify |10| 6 (3) 10. (Lessons 1-4, 1-5)
F 29
G 9
H 9
J 29
2.
F
G
H
J
3.
A
B
C
D
4.
F
G
H
J
5.
A
B
C
D
6.
F
G
H
J
D 86
7.
A
B
C
D
8. If m 2.5 5.1, what is m? (Lesson 2-7)
F 7.6
G 5.1
H 3.6
J 2.6
8.
F
G
H
J
9. Evaluate 43 52. (Lesson 2-9)
A 120
B 200
D 1,600
9.
A
B
C
D
10.
F
G
H
J
3. Which equation has a solution of 8? (Lessons 1-9, 1-10)
A y 8 16
C y 2
4
B –16y 2
D y (4) 4
4. Which fraction is less than 5? (Lesson 2-2)
11
F 1
G 2
4
H 7
3
J 5
9
6
13 centimeters. (Lesson 2-3)
8
A 19 cm2
57
B 1
cm2
64
64
C 23 cm2
4
D 51 cm2
2
6. BAKING José needs 12 cup of flour for a cake recipe. How many
3
cakes can he make for the school carnival if he has 15 cups of
flour? (Lesson 2-4)
G 162
F 25
3
H 131
J 9
3
7. Find –43 – 43 . Write in simplest form. (Lesson 2-5)
5
A 91
5
5
B. 0
C. 11
5
5
C 400
10. The diameter of a grain of sand is about 0.0014 meter.
Write this number in scientific notation. (Lesson 2-10)
F 1.4 103 G 1.4 103 H 14 103 J 14 103
Chapter 2
88
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. GEOMETRY Find the area of a square with sides that measure
NAME ________________________________________ DATE ______________ PERIOD _____
Standardized Test Practice
2
(continued)
11. Evaluate ⏐p⏐⏐q⏐ if p 27 and q 10. (Lesson 1-4)
A 37
B 37
C 17
D 17
11.
A
B
C
D
H 14
J 224
12.
F
G
H
J
13.
A
B
C
D
14.
F
G
H
J
15.
A
B
C
D
16.
F
G
H
J
17.
A
B
C
D
18.
F
G
H
J
12. Find 56 (4). (Lesson 1-6)
F 224
G 14
13. Order the following integers from least to greatest {5,-7, 10, 0}
A {5, 0, 7, 10}
B {7, 10, 0, 5}
C {10, 7, 5, 0}
D {10, 7, 0, 5}
14. ALLOWANCE Marianne received her monthly allowance. She
gave $10 to her sister for movie tickets, $5 to her brother for
his birthday, and put half of what she had left in the bank.
She was left with $15 to spend at the mall. How much did
she earn for monthly allowance? (Lesson 1-8)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
F $60
G $45
H $30
J $22.50
11
15. Write the multiplicative inverse of . (Lesson 2-4)
7
11
7
A C 7
11
7
B D 77
11
16. Solve 12.7 + n = 15.4. (Lesson 2-7)
F 28.1
G 12.7
H 2.7
J 2.7
17. Write 37 as a decimal. (Lesson 2-1)
20
A 3.07
B 3.35
C 3.70
D 3.72
18. Evaluate 52. (Lesson 2-9)
1
25
F 25
H 1
25
J 25
G Chapter 2
89
Glencoe California Mathematics, Grade 7
Assessment
(Lesson 1-3)
NAME ________________________________________ DATE ______________ PERIOD _____
2
Standardized Test Practice
(continued)
Part 2: Short Response
Instructions: Write your answers in the space provided.
19. WEATHER The average temperature in St. Paul during July
is 75 warmer than the average temperature during
November. Define a variable and write an expression
for the temperature in July. (Lesson 1-7)
19.
20. The product of a number and 6 is 90. Write and solve
an equation to find the number. (Lesson 1-10)
20.
21. HOMEWORK Elise wants to be finished with her homework
in order to watch T.V. at 5:30. She has 1 hour of science,
30 minutes of math, half an hour of language arts, and
45 minutes of social studies. What time does she need to
start her homework in order to be done on time? (Lesson 1-8)
21.
3
4
22. Write 15 as a decimal. (Lesson 2-1)
3
8
23. Add . (Lesson 2-6)
23.
24. Solve 9.6 n 4.1 (Lesson 2-7)
24.
25. FOOD The school cafeteria had 10 pounds of spaghetti to
serve at the open house night. After 50 people had eaten,
there were 8 pounds of spaghetti left. After 100 people had
eaten, there were 6 pounds of spaghetti left, and after 150
people had eaten, there were 4 pounds of spaghetti left.
If this pattern continued, how many people was the cafeteria
able to feed spaghetti? (Lesson 2-8)
25.
26. JOGGING The jogging trail in Eastgate Park is 11 miles long.
4
a. How far did Mariah jog if she went around the trail once and then
jogged another 7 mile back home? How did you find your answer?
8
(Lesson 2-6)
b. How far did Jeremy jog if he went around the trail 31 times? How did
2
you find your answer? (Lesson 2-3)
Chapter 2
90
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2
5
22.
Chapter 2
Before you begin Chapter 2
Algebra: Rational Numbers
Anticipation Guide
A1
D
8. To subtract two fractions with a common denominator, subtract
the numerators and then the denominators.
After you complete Chapter 2
12. Any number written as a product of a number and a power of
10 is written in scientific notation.
11. Any number to the zero power equals 1.
10. The equation 0.7 x 2.4 would be solved by addition.
Chapter 2
7
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
D
A
A
A
D
7. To divide by a fraction, multiply by its opposite.
9. A common denominator must be found before adding or
subtracting fractions with different denominators.
A
A
5. Before multiplying two mixed numbers, rewrite both as
improper fractions.
1
6. 12 and are multiplicative inverses of each other.
2
D
4. When multiplying two fractions, first find a common
denominator, and then multiply numerators and denominators.
D
D
4
4
3. is greater than because 7 is greater than 5.
7
5
2. To write a fraction as a decimal, divide the numerator into the
denominator.
3
5
A
1
2
STEP 2
A or D
1. 3, , 0.4, and 2 are all examples of rational numbers.
Statement
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an
example of why you disagree.
Step 2
STEP 1
A, D, or NS
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree,
write NS (Not Sure).
Step 1
2
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter Resources
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1
2
7NS1.3, 7NS1.5
2
5
1
4
4
4
4
4
Rational number: 3
b
Chapter 2
9
Glencoe California Mathematics, Grade 7
A ratio between most integers can be written as a rational
number.
4
Ratio: 3
numbers, which can be written in the form a or a:b.
7. Notice that the first five letters of the word rational is the word ratio.
Explain what a ratio is. If this term is not familiar to you, look it up in
the dictionary. Write a ratio and a rational number. Explain how they are
related. Sample answer: A ratio is a comparison of two
Remember What You Learned
Sample answer: In the decimal 2.57
only the 7 repeats, so
2.57
2.5777… . In the decimal 2.5
7
both the 5 and the 7
repeat, so 2.5
7
2.575757… .
6. Explain the difference between the numbers 2.57
and 2.5
7
.
4
Sample answer: The expression 43 denotes addition, 4 3,
4
4
while the expression 43 denotes multiplication, 4 3.
5. Explain the difference in meaning between the expressions 43 and 4 3 .
Read the Lesson
4. What fraction of the humpback viewing sites are in Mexico? 3. At what fraction of the sites might you see gray whales? 2. What fraction of the sites are in Canada? 1
5
1. What fraction of the sites are in the United States?
Read the introduction at the top of page 84 in your textbook. Write
your answers below.
Get Ready for the Lesson
Rational Numbers
3-1
2-1
2-1 Lesson Reading Guide
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Anticipation Guide and Lesson 2-1)
Lesson 2-1
Chapter 2
Rational Numbers
Study Guide and Intervention
7NS1.3, 7NS1.5
4
Write 3 as a decimal.
Simplify.
0.16 is 16 hundredths.
Write 0.16 as a fraction.
Write 8.2
as a mixed number.
A2
Simplify.
9
Divide each side by 9.
3
7. 62 6.6
8
3. 7 0.875
25
11
8. 43
16
4. 2
Chapter 2
9. 0.8
4
5
Glencoe California Mathematics, Grade 7
10
1
9
11. 0.1
Glencoe California Mathematics, Grade 7
12. 1.7
1
7
9
4.2
7
2.64
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3
20
10. 0.15 Write each decimal as a fraction or mixed number in simplest form.
9
6. 12 1.2
3
10
5. 2 0.6
5
0.3
2. 3
Write each fraction or mixed number as a decimal.
1. 2 0.4
Exercises
The decimal 8.2
can be written as 82.
9N
74
9
9
N 82
9
10N 82.222…
1N 8.222… N 1N
9N 74
10N 1N 9N
Subtract.
Then 10N 82.222… .
Let N 8.2
or 8.222… .
Example 3
The decimal 0.16 can be written as 4.
25
25
4
100
16
0.16 Example 2
3
means 3 4.
4
The fraction 3 can be written as 0.75, since 3 4 0.75.
4
Example 1
To express a fraction as a decimal, divide the numerator by the denominator.
2-1
3-1
NAME ________________________________________ DATE ______________ PERIOD _____
Rational Numbers
Skills Practice
0.1
5
5
11
12. 73
15
10. 24
9
2.26
3.45
7.2
7
8. 7 0.7
20
6. 39
4. 4 0.8
8
2. 1 0.125
7NS1.3, 7NS1.5
3
25
Chapter 2
7
9
23. 6.7
6
21. 0.1
1
9
7
20
19. 2.35 2
17. 1.12 1
21
25
9
10
15. 0.84 13. 0.9
1
20
4
9
11
Glencoe California Mathematics, Grade 7
24. 8.4
8
8
9
22. 4.8
4
17
20
20. 8.85 8
18. 5.05 5
23
25
7
10
16. 0.92 14. 0.7
Write each decimal as a fraction or mixed number in simplest form.
33
11. 5
6
4.36
0.42
9. 11 1.16
25
7. 49
50
21
5. 4
0.1
3. 3 0.75
10
1. 1
Write each fraction or mixed number as a decimal.
3-1
2-1
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-1)
Lesson 2-1
Chapter 2
Rational Numbers
Practice
3
8. 4 4.375
8
1
7. 3 3.2
5
11
12. 9 9.36
30
5
9. 0.1
5
33
9
6. 0.28125
32
9
3. 0.45
20
7NS1.3, 7NS1.5
A3
9
16
12
1
1
10
1
16
1
3
Fraction of Total
Population
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
in.
Source: U.S. Census Bureau
Hispanic
African American
Asian
Race
23. Write the width of the jellybean as a decimal. 0.5625
Chapter 2
4
18. 4.4
4
9
7
20
15. 1.35 1
Population of California by Race
22. Write the width of the jellybean as a fraction. MEASUREMENTS For Exercises 22 and 23,
use the figure at the right.
19. Express the fraction for Asian as a
decimal. 0.1
20. Find the decimal equivalent for the
fraction of the population that
is African American. 0.0625
21. Write the fraction for Hispanic as a
decimal. Round to the nearest
thousandth. 0.333
For Exercises 19–21, refer
to the table at the right.
POPULATION
5
17. 1.5
1
9
8
16. 0.8
9
11
25
14. 0.44 13. 0.8 4
5
Write each decimal as a fraction or mixed number in simplest form.
11
11. 8 8.61
18
11
5. 0.6875
16
37
4. 0.74
50
7
10. 0.7
9
5
2. 0.625
8
3
1. 0.6
5
Write each fraction or mixed number as a decimal.
2-1
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Rational Numbers
Chapter 2
52
6
or 6.24 students per faculty
215
member
7. COLLEGES AND UNIVERSITIES Recently, a
small college had an enrollment of
1,342 students and a total of 215
faculty. What was the student-faculty
ratio for this college? Write your
answer as both a mixed number in
simplest form and a decimal rounded to
the nearest hundredth.
33
3
or 3.7 students per
47
computer
5. EDUCATION A local middle school has
47 computers and 174 students. What
is the number of students per computer
at the school? Write your answer as
both a mixed number in simplest form
and a decimal rounded to the nearest
tenth.
11
L
20
3. WEIGHTS AND MEASURES One pint is
about 0.55 liter. Write 0.55 liter as a
fraction in simplest form.
19
50
13
Glencoe California Mathematics, Grade 7
658
; 0.601
1,095
8. BASKETBALL In the 2004–2005 season,
Shaquille O’Neal made 658 field goals
out of 1,095 attempts. What was
Shaquille O’Neal’s ratio of successful
field goals to attempts? Write your
answer as both a fraction in simplest
form and a decimal rounded to the
nearest thousandth.
5
; 0.556
9
6. BASEBALL In the 2005 season, the
Atlanta Braves won 90 out of 162
games. What was the ratio of wins to
total games? Write your answer as both
a fraction in simplest form and a
decimal rounded to the nearest
thousandth.
5
252 mm
4. WEIGHTS AND MEASURES One inch is
25.4 millimeters. Write 25.4
millimeters as a mixed number in
simplest form.
39
50
7NS1.3, 7NS1.5
2. ENERGY Nuclear power provided 78% of
the energy used in France in 2005.
Write 0.78 as a fraction in simplest
form.
Word Problem Practice
1. ASTRONOMY The pull of gravity on the
surface of Mars is 0.38 that of Earth.
Write 0.38 as a fraction in simplest
form.
2-1
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-1)
Lesson 2-1
Chapter 2
0.384615
A4
3
Chapter 2
0.0625 1
0.8125
5
9
0.428571
1
30
0.318
0.25
1
4
0.333
Glencoe California Mathematics, Grade 7
0.03
3
7
0.5
13
16
14
0.05
1
2
5
13
3
8
0.2
3
4
1
7
1
8
0.75
1
9
0.375
0.142857
0.6363
0.125
7
8
7
11
1
20
Glencoe California Mathematics, Grade 7
1
6
0.05
0.11
2
3
0.083
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7
22
1
16
0.5
1
12
0.666
1
18
0.166
1
5
0.875
1
5
1
3
1
1
5
9
10
4
1 10 5
5
8. 4, 9
11
Chapter 2
15
10
9
Glencoe California Mathematics, Grade 7
have the same numerator, the one with the bigger
denominator is the smaller number.
3 3 3 3 3
, , , , ; Sample answer: When two positive fractions
11 8 7 5 4
a rule that helps you compare two positive fractions with the same
numerator.
7 5 8 4
9. Order the numbers 3, 3, 3, 3, and 3 from least to greatest. Then write
Remember What You Learned
0
5 3
7. 1, 1
For Exercises 7 and 8, graph each pair of rational numbers on a
number line. Then identify the lesser number.
answer: Graph both numbers on a number line. The number
further to the left is the lesser number.
6. Read Example 4 on page 93. Explain how to use a number line to
determine which of two rational numbers is the lesser number. Sample
Read the Lesson
2
No; the numbers are being compared to 1, not to each other.
5. Using this estimation method, can you order the rates from least to
greatest?
cans, scrap tires
4. Which items have a recycle rate greater than one half? aluminum
3. Which items have a recycle rate less than one half? paper, glass
More; 5 is greater than half of 8 or 4.
2. Do we recycle more or less than half of the aluminum cans? Explain.
Less; 5 is less than half of 11 or 5.5.
1. Do we recycle more or less than half of the paper we produce? Explain.
0
7NS1.1
Comparing and Ordering Rational Numbers
Lesson Reading Guide
Read the introduction at the top of page 91 in your textbook. Write
your answers below.
3-1
2-2
Get Ready for the Lesson
7NS1.3
Connect each pair of equivalent rational numbers with a straight line
segment. Although you will draw only straight lines, the finished
design will appear curved!
Enrichment
NAME ________________________________________ DATE ______________ PERIOD _____
A Triangular Line Design
2-1
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 2-1 and 2-2)
Lesson 2-2
Chapter 2
7NS1.1
Comparing and Ordering Rational Numbers
Study Guide and Intervention
Replace with , , or to make 4
5
7
a true sentence.
10
from
Order the set of rational numbers 3.25, 31, 32, and 3.25
3
5
least to greatest.
A5
3
3
10
6
10
5
8. 41 4.16
15
5
5
Chapter 2
5
4
24, 2.7, 2.28, 21
4
14. 21, 2.28, 2.7, 24
5 5
0.7, 3, 1, 0.25
5
12. 1, 0.7, 0.25, 3
0.1, 1, 0.5, 2
4
3
4 3
10. 0.5, 0.1, 1, 2
10
6
3
9
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
6
4.6, 42, 45, 5.3
3
3
15. 42, 45, 4.6, 5.3
9
12, 1.45, 12, 1.67
3
13. 12, 12, 1.45, 1.67
16
7
9. 4.58
4.5
8
19, 2.13, 2.4, 24
10
7
9
8
6. 23 24 11. 2.4, 24, 2.13, 19
7
9
3. 1 1 Order each set of rational numbers from least to greatest.
8
7. 2.6 25 5
5. 37 34 3
4. 2 7
6
13
2. 4 1. 5 2 Replace each with , , or to make a true sentence.
Exercises
5
32, 31, 3.25
, and 3.25.
3.25
3.25, the numbers from least to greatest are
Since 3.4 3.3
3
5
1
, so 31 3.3
.
0.3
3
3
2
2
0.4, so 3 3.4.
5
5
Write 31 and 32 as decimals.
Example 2
4
42
8
or 5
52
10
7
71
7
or 10
10 1
10
8
7 4
Since , 7.
10
10 5
10
Write as fractions with the same denominator. The least common denominator is 10.
Example 1
When comparing two or more rational numbers, either write the numbers as fractions with the same
denominator or write the numbers as decimals.
2-2
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6
3
7
8
9
12
11
9
14. 114 11.4
15
11. 27 2.45 8. 4 5
4
6
5. 3 9
3
2. 1 1 7
10
9
11
16
20
Chapter 2
57, 5.81, 59, 5.93
20
11
11
24. 59, 5.93, 57, 5.81
15
5.3, 67, 6.9, 6
8
16
8
15
22. 67, 6
, 6.9, 5.3
10
2.21, 21, 2.09, 1
9
11
10
20. 2.21, 2.09, 21, 1
19, 21, 2.7, 3.13
10 7
18. 2.7, 21, 3.13, 19
0.2, 2, 0.3, 1
9
3
3 9
16. 0.3, 0.2, 1, 2
3
4
4
4
8
6
8
3
3
17
4
8
11
8
4
Glencoe California Mathematics, Grade 7
11
41, 4.05, 3.65, 34, 31
25. 31, 41, 3.65, 34, 4.05
3
51, 5.3, 4.19, 41
23. 41, –4.19, –5.3, 51
3
3.1, 2, 17, 2.75
21. 3.1, 2.75, 17, 2
4
13, 1.7, 0.2, 1
19. 1, 1.7, 0.2, 13
3
6
15. 1.2
7
1.27
12. 5.25 5.2
5
9
5
9. 5 0.55 8
12, 1.55, 12, 1.67
5
10
6. 3 2 17. 12, 12, 1.55, 1.67
5
5
3. 2 3
Order each set of rational numbers from least to greatest.
13. 1.62 15 13
10
10. 4.72 4
7. 5 6 9
4. 2 1 4
1. 1 3 2
7NS1.1
Comparing and Ordering Rational Numbers
Skills Practice
Replace each with , , or to make a true sentence.
2-2
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-2)
Lesson 2-2
Chapter 2
3
5
5
7
5
13
10
27
3
8
7
8
10. 2
5
6
7
11. 7. 8 8.3 1
9
3. 3 3 5
21
6. 0.25 5
11
2
11
4
9
2. 8
17
2
9
9
11
12. 8
30
8. 4 4.3 7
15
4. 5 5 4
11
5
13
A6
3
5
3
5
1
9
0
1
9
1
4
P
1
2
1
11
Q
3
4
1, 1.1, 1, 1.01
4
5
3
4
Chapter 2
Glencoe California Mathematics, Grade 7
1
Glencoe California Mathematics, Grade 7
SR
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
18
middle number is the median. Find the median of 43.7, 41.3, 44.5,
42, and 43. 43.7
1
11
20. 1.01, 1.1, 1, 1
22. STATISTICS If you order a set of numbers from least to greatest, the
21. Which point on the number line is
the graph of 0.875? S
5.81, 5, 5.69, 5
3
4
19. 5.81, 5, 5, 5.69
3
4
Order each set of rational numbers from least to greatest.
11
7
11
18. Which is greatest: , 0.778, 0.7
8
, , or 0.787? 9
13
13
17. Which is least: , 0.4, , 0.035
, or ? 0.35
3
8
13. 4.5 4.55 14. 6.14 6.15 15. 3.57 3.5 16. 1.9 1.99 9. 8
13
5. 0.2 2
11
1. 7NS1.1
Comparing and Ordering Rational Numbers
Practice
Replace each with <, >, or = to make a true sentence.
2-2
NAME ________________________________________ DATE ______________ PERIOD _____
7NS1.1
7
Chapter 2
the faster time? Christina
8
was 837 seconds. Which runner had
7. SPORTS Christina ran one lap in 83.86
seconds, while Della’s time for one lap
19
5
54
4
8
Glencoe California Mathematics, Grade 7
5
53, 57, 5.9, and 54.
8. STATISTICS The median of a set of
numbers can be found by first putting
the numbers in order from least to
greatest, then choosing the middle
number. Find the median of 5.79,
12
apple weighed 6.65 ounces. Which
apple weighed more? Carla’s
day did Rob run faster? Tuesday
5
weighed 67 ounces, while Carla’s
6. FOOD Hector and Carla both gave
apples to their teacher. Hector’s apple
averaged 34 laps per minute. On which
5. EXERCISE On Monday, Rob averaged
3.75 laps per minute. On Tuesday, he
125 in.
8
larger?
Which beaker has the smaller amount
of water? Beaker B
8
and 123 inches. Which circumference is
5
yard have circumferences of 125 inches
3
B contains 43 fluid ounces of water.
10
4. NATURE The two trees in Opal’s back
Central
Which team had the better record?
53
of its games last year, while
78
55
Southern’s team won of its games.
81
41 fluid ounces of water, while beaker
3. MEASUREMENT Beaker A contains
12
Percy; 7 4
free throws. Which player has the
better free throw record?
the same period, Tariq made 4 of his
7
12
Percy made 7 of his free throws. For
2. SPORTS Central’s baseball team won
Comparing and Ordering Rational Numbers
Word Problem Practice
1. BASKETBALL In the last ten games,
2-2
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-2)
Lesson 2-2
Chapter 2
Enrichment
G
1
H
2
2
A7
1
A
4
2
G
3
A
3
2
R
3
4
2
3
6
H
1
E
6
4
P
0
6
A
3
1
R
I
G
2
3
R
I
Chapter 2
astronauts in space.
4. Why are these three people famous?
6
S
1
S
20
O
M
D
0
5
2
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
They were the first three
3
11
1
5
, point O at , and point I at 3. point G at 21, point M at 1, point S at 5, point S at 11, point R at
2
S
4
point H at 5, and point P at 1
2. point R at 1, point E at 3, point S at 2, point D at 3, point A at 1,
0
G
3
3
13
2
point I at , and point A at 2
3
3
10
1
2
6
1
1. point R at , point A at 1, point N at 4, point G at , point G at ,
Graph each set of points on the number line. When you are finished,
the letters will spell the last names of some famous people.
point H is at 3.
2
The number line above shows the graph of two points. Point G is at 1 and
0
N
7NS2.5
A number line can be used to graph a mixed number or an improper fraction.
A Famous Line-Up
2-2
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5
15
2
8
5
3
15
4
b. 2 2 4
5
20
3
c. 1 3 3
5
8
d. 2 4 Chapter 2
21
exchange rate to get the number in Euros.
y dollars
Glencoe California Mathematics, Grade 7
x Euros
rate as a fraction, , and then multiply the $50 by the
9. If you were to visit Europe, you may need to exchange some of your
money for Euros. The exchange rate tells you how many dollars equals
how many Euros. How would you use dimensional analysis to compute
the number of Euros you would get from $50? Set up the exchange
Remember What You Learned
computation and divided out like common factors to yield
the correct units for the answer.
8. How is dimensional analysis used in Example 5 on page 98 in your
textbook? Sample answer: Units are included in the
Dimensional analysis is the process of including units of
measurement when you compute.
7. How is dimensional analysis defined on page 98 in your textbook?
Numerators and denominators are divided by their greatest
common factors to simplify the product.
6. How is the greatest common factor used when multiplying fractions?
common factor of two numbers is the biggest number that is
a factor of both numbers.
5. What is the greatest common factor of two numbers? The greatest
Read the Lesson
the factors equals the denominator of the product.
4. What is the relationship between the denominators of the factors and the
denominator of the product? The product of the denominators of
factors equals the numerator of the product.
3. What is the relationship between the numerators of the factors and the
numerator of the product? The product of the numerators of the
4
3
a. 3 1 2. Use an area model to find each product. See students’ models.
3
2
1. What is the product of 1 and 2? Complete the Mini Lab at the top of page 96 in your textbook.
Write your answers below.
15
7NS1.2, 7MG1.3
Multiplying Positive and Negative Fractions
Lesson Reading Guide
Get Ready for the Lesson
2-3
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 2-2 and 2-3)
Lesson 2-3
Chapter 2
1
Simplify.
Multiply the numerators and denominators.
5
A8
6
5
15
42
5
82
5
76
1
3
18
7 41
2
7
9
18
5
6
5
Chapter 2
10. 17 22
8
5
5
2
Glencoe California Mathematics, Grade 7
22
17
3
20
2
18
8
10
6
21
8
21
Glencoe California Mathematics, Grade 7
12. 22 23
3
7
7
3
9. 33 25 9
7
6. 4 2
7
3. 1 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. 13 21
4
5
3
8. 31 11 5
8
7
3
2. 4 3 2
7. 22 1 5
5
5. 5 4
3
5
3
4. 9 2 10
3
2
1. 2 3 4
Write the result as a mixed number.
Simplify.
Multiply the numerators and denominators.
Divide 18 and 3 by their GCF, 3.
Multiply. Write in simplest form.
Exercises
3
21 33
Example 2
Find 21 33. Write in simplest form.
3
5
18
1
7 3
18
7 2 , 3 3
3 5
5
3
5
To multiply mixed numbers, first rewrite them as improper fractions.
31
2 11
3
22
2
Divide 8 and 4 by their GCF, 4.
Find 3 4. Write in simplest form.
8 11
9
Multiplying Positive and Negative Fractions
4
3 4
3
11
8 11
8
Example 1
2-3
7
3
7
3
5
6
7
11
7
35
8
7
36
4
8
3
2
4
12
1
3
4
14. 22 21
6
3
11. 21 12 3
5
8
1
8. 4 43 3
9
5. 2 3
9
2. 2 7 5
5
22
5
6
5
8
5 5 15. 4 4
4
15
2
9
20. rst 17. st 1
2
21. rtv 5
18
18. rs Chapter 2
22. ad 5
12
2
15
23. bc 23
16
25
Glencoe California Mathematics, Grade 7
2
27
24. abc 5
1
2
3
ALGEBRA Evaluate each expression if a , b , c , and d .
9
5
3
4
1
5
19. stv 16. rv 8
9
3
12. 19 24 4
16
15
1
3
7
9. 2 55 9
11
6. 3 5
6
3. 5 3
5
1
4
3
ALGEBRA Evaluate each expression if r , s , t , and v .
6
3
5
4
7
13. 31 12
5
10. 13 11 1
4
35
6
1
7. 13 2 1
10
4. 4 3
8
1. 1 2 1
12
Multiply. Write in simplest form.
Multiplying Positive and Negative Fractions
7NS1.2, 7MG1.3
Skills Practice
7NS1.2, 7MG1.3
Study Guide and Intervention
To multiply fractions, multiply the numerators and multiply the denominators.
2-3
NAME ________________________________________ DATE ______________ PERIOD _____
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-3)
Lesson 2-3
Chapter 2
2
5
1
3
1
1
2
1
5
1
5,
11. 2 2 2 11
1
1
8. 1 1
4
5
2
3
A9
7
8
1
4
2
14. ab 15
7
15. abc 60
3
4
1
16. abd 10
3
cup
4
2
3
1
6
1
5
Chapter 2
19. efh2 4
4
5
1
4
20. e2h2 2
24
1
3
22. 2ef(gh) 17
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
25
1
21. f 2g 1
8
27
ALGEBRA Evaluate each expression if e 1, f 2, g 2, and h 1.
1
4
1
18. FARMING A farmer has 6 acres of land for growing crops. If she plants corn on
2
9
3
of the land, how many acres of corn will she have? 3 acres
5
10
1
need to make of the recipe?
3
17. COOKING A recipe calls for 2 cups of flour. How much flour would you
7
13. bc 12
4
5
12. 10 8.56 42
1
2
2
1
9. 2 3
4
2
3
1
8
ALGEBRA Evaluate each expression if a b , c , and d .
1
1
5
4
10. 7
15
4
21
1 1 1
7. 1 4 5 4
6. 78 17 3
10
5. 285 1156
2 1
3 5
3
15 4
4. 16 5
4
3
10
3. 6
7
1 3
2 7
2. 4 1
5 5
1. 1
4
7NS1.2, 7MG1.3
Multiplying Positive and Negative Fractions
Practice
Find each product. Write in simplest form.
2-3
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9
4
2
Chapter 2
3
81 c
amount, how much heavy cream should
he use?
wants to make 21 times the normal
3
for 31 cups of heavy cream. If Steve
7. COOKING A recipe for ice cream calls
25
4
Glencoe California Mathematics, Grade 7
4
31 inches
5
bracelet in the photograph?
10
is 53 inches, what is the length of the
8. ADVERTISING A jewelry advertisement
shows a bracelet at 6 times its actual
size. If the actual length of the bracelet
2
31 in2
8
115 gal
9
and a width of 15 inches?
rectangle with a length of 21 inches
6. GEOMETRY The area of a rectangle is
found by multiplying its length times
its width. What is the area of a
8
17 c
much flour should she use?
4
to make 3 of a batch of cookies, how
2
calls for 21 cups of flour. If she wants
4. COOKING Enola’s recipe for cookies
voters in Afton voted for the incumbent
mayor. If 424 people voted in Afton in
the last election, how many voted for
the incumbent mayor? 159 people
many gallons of gas did it take to cross
Arizona?
2
tank on her car holds 151 gallons. How
a tank of gas to cross Arizona. The gas
5. TRANSPORTATION Hana’s car used 3 of
32 in.
3
model of a race car. If the tires on the
actual car are 33 inches in diameter,
what is the diameter of the tires on the
model?
3. HOBBIES Jerry is building a 1 scale
4
2011 Calories
fat. How many Calories in the granola
bar come from fat?
states that 7 of the Calories come from
8
2. ELECTIONS In the last election, 3 of the
8
7NS1.2, 7MG1.3
Multiplying Positive and Negative Fractions
Word Problem Practice
1. NUTRITION Maria’s favorite granola bar
has 230 Calories. The nutrition label
2-3
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-3)
Lesson 2-3
Chapter 2
A10
2
3
2
4 2
6
4
4
6
8
10
n
4
6 n
O
4
2
12
b
8
4
5
2
8
20
15
O
8
4
10
4
12
4
10
4
4
2
2
5
4. 0
16
12
d
8
2
9
d
4
6
4
6
16
4
4
.
8
15
6
20
n
Chapter 2
Glencoe California Mathematics, Grade 7
16
n
Glencoe California Mathematics, Grade 7
12
n
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
26
Possible counterexample is (0, 0).
coordinate system using the ordered pair (a, b). All ordered pairs on the
same line stand for equivalent rational numbers. Answers will vary.
b
6. Show that this generalization is false: A rational number a is shown on a
coordinate system using the ordered pair (a, b). Using this model,
all lie on the same line.
equivalent rational numbers will
5. Complete this generalization: A rational number a is shown on a
6
2
3
3. 2
4
2
0
8
4
3
12
2. 4 8 12
8
6
6
d
16
4
d
8
2
1. 1 2 3 4
Graph the rational numbers as ordered pairs.
2
numerator and the vertical axis for the denominator.
0
4
shows the number 1. The horizontal axis is used for the
3
7NS1.2, 7MG1.3
Dividing Positive and Negative Fractions
Lesson Reading Guide
1
2
4
8
8
11
7. 13 7
7
25
8. 34 9
50
11
Chapter 2
27
Glencoe California Mathematics, Grade 7
See students’ work. Sample answer: When you divide
fractions, you invert the divisor and multiply.
12. Look up the word invert in the dictionary. Draw a simple picture and then
invert it. Explain how this helps you remember how to divide fractions.
Remember What You Learned
5
5
number by 21? Multiply the number by .
11. Look at your answers for Exercises 6 and 10 above. How do you divide a
multiply by its multiplicative inverse.
9
9. 55 10. Explain how to divide by a fraction. To divide by a fraction,
5
6. 21 5
11
For Exercises 6–9, write the multiplicative inverse of each mixed
number.
improper fraction. Then switch the numerator and
denominator of that fraction.
5. Describe the process for finding the multiplicative inverse of a mixed
number. Sample answer: First write the mixed number as an
Read the Lesson
4
multiplying by 1? They are the same.
4. What can you conclude about the relationship between dividing by 4 and
3. Compare the values of 110 4 and 110 1. They are the same.
4
2. Find the value of 110 1. 27
1. Find the value of 110 4. 27.5
Read the introduction at the top of page 102 in your textbook.
Write your answers below.
2-4
Get Ready for the Lesson
d
7AF3.3
If you think of a rational number as an ordered pair, it
can be located on a coordinate system. The example graph
Enrichment
NAME ________________________________________ DATE ______________ PERIOD _____
Rational Numbers as Ordered Pairs
2-3
2-1
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 2-3 and 2-4)
Lesson 2-4
Chapter 2
7NS1.2, 7MG1.3
Dividing Positive and Negative Fractions
Study Guide and Intervention
Write 23 as an improper fraction.
4
Write the multiplicative inverse of 23.
2
6
Simplify.
A11
5
13
5
3
6. 12
3
2. 8
9
3
5
9
8
6
4
3
Chapter 2
15. 6 (4)
11
7
13. 31 32
6
9
7
3
22
6
1
11. 5 3 1
3
9. 1 1 2
Divide. Write in simplest form.
5. 23
5
1. 3
5
7
28
16. 5 21
3
9
4
8. 71
4
4. 1
6
4
29
6
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
21
7
2
9
15
14. 4 2 5
10
8
12. 11 21 5
5
27
10
7
10. 2 4 7. 52
5
3. 1
10
Write the multiplicative inverse of each number.
16
7
8
1
6
6
Divide 6 and 3 by their GCF, 3.
8
7
7
3
7
Multiply by the multiplicative inverse of 6, which is 7.
8
Find 3 6. Write in simplest form.
3 7
Exercises
3
6
8
7
Example 2
To divide by a fraction or mixed number, multiply by its multiplicative inverse.
4
4
4
11
4
3
4
Since 1, the multiplicative inverse of 2 is .
4
11
4
11
11
23 Example 1
Two numbers whose product is 1 are multiplicative inverses, or reciprocals, of each other.
2-4
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7
12
39
11
6
14
10
3
Chapter 2
9
7
27. 24 62
5
3
18
3
31
7
3
2
25. 91 53 1
5
2
23. 4 3 6
7
2
10
21. 34 11
4
9
7
19. 13 21 5
4
7
9
17. 4 8 8
5
5
15. 5 3 7
5
13. 3 3 15
11. 48
13
7
4
16
15
68
7
7
3
9
15
5
4
29
5
7
17
5
2
41
5
28
Glencoe California Mathematics, Grade 7
9
6
10
3
28. 111 31 3
3
26. 123 25
15
11
2
6
5
7
24. 34 42 11
2
10
22. 5 10
22
20. 23 13
11
5
7
14
17
12
9. 23 17
14
6. 12
3. 1
12. 53 9
18. 2 4 9
14
16. 7 1
14. 2 6 13
35
9
8. 13
35
5. 9
7
2. 4 Divide. Write in simplest form.
11
10. 36
7. 15 7
1
22
2
4. 22 3
3
1. 2 7NS1.2, 7MG1.3
Dividing Positive and Negative Fractions
Skills Practice
Write the multiplicative inverse of each number.
2-4
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-4)
Lesson 2-4
Chapter 2
4 5
5 4
7 12
12 7
2. 3
4
A12
1
3
3
4
1
4
18. 8 3 2
3
44
8
43
24
25
1
2
1
3
89 13
16
1
2
19. 10 2 4
13
18
5
6
16. 4
5
13. 2
7
7
8
2
3
Chapter 2
Glencoe California Mathematics, Grade 7
3
4
30
Glencoe California Mathematics, Grade 7
4
11 16
23. m n if m and n 9
12 33
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7
7
22. r s if r and s 20
15
ALGEBRA Evaluate each expression for the given values.
in a single stack if each box is foot tall? 10 boxes
3
4
21. STORAGE The ceiling in a storage unit is 7 feet high. How many boxes may be stacked
clip? 1 times
1
2
inches long. How many times longer is the jumbo paper clip than the regular paper
20. OFFICE SUPPLIES A regular paper clip is 1 inches long, and a jumbo paper clip is 1
17. 4 1 2
1
5
2
25
2
9
2
3
15. 10
5
25
3
5
14. 12
5
36
4
5
2
5
6
11
3
4
12. 8 11. 10 6
7
6 11
11 14
10. 3 1
16
3
8
9. 6 8. 4 3
5 8
3
7
5 12
6 25
2
5
3
10
3
8
4. 5 7. 6. 1
5
5. 1 4
4 5
1
20
3. 20 Find each quotient. Write in simplest form.
1. 7NS1.2, 7MG1.3
Dividing Positive and Negative Fractions
Practice
Write the multiplicative inverse of each number.
2-4
NAME ________________________________________ DATE ______________ PERIOD _____
11 pots
3
Chapter 2
4 pictures
Glencoe California Mathematics, Grade 7
13 passes
on each pass. How many passes will
Leon need to finish the lawn?
beside each other within the frame?
3
mower makes a cut that is 12 feet wide
3
which is 212 feet wide. His lawn
2
that are 33 inches wide can be placed
8
8. YARD WORK Leon is mowing his yard,
12 ft
7
What is the width of the rectangle?
7
is 131 inches wide. How many pictures
7. HOBBIES Dena has a picture frame that
3
22 in.
inches. What is the width of the
rectangle?
square feet and a length of 32 feet.
length. A rectangle has an area of 45
3
length. A rectangle has an area of 62
square inches and a length of 21
2
6. GEOMETRY Given the length of a
rectangle and its area, you can find the
width by dividing the area by the
31
4
side. How many paving stones placed
end-to-end are needed to make a path
that is 21 feet long? 12 stones
paving stones that are 13 feet on each
4. HOME IMPROVEMENT Lori is building a
path in her backyard using square
wide. How many CDs will fit on one
shelf? 26 CDs
for storing CDs. Each CD is 3 inch
8
2. MUSIC Doug has a shelf 93 inches long
5. GEOMETRY Given the length of a
rectangle and its area, you can find the
width by dividing the area by the
2
61 bowls
cereal are in one box?
5
22 ounces of cereal, how many bowls of
5
153 ounces of cereal. If a bowl holds
3. SERVING SIZE A box of cereal contains
3
quart?
4
How many clay pots can be filled from
one bag of potting soil if each pot holds
potting soil contains 81 quarts of soil.
4
4
7NS1.2, 7MG1.3
Dividing Positive and Negative Fractions
Word Problem Practice
1. CONTAINER GARDENING One bag of
2-4
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-4)
Lesson 2–4
Chapter 2
Enrichment
Notice that each fraction must
have a numerator of 1 before the
process is complete.
A13
1
12
1
1
1 1
3
3 1
1
17
4. 6
11
17
2. 1
Chapter 2
5. 1 1
1
2
1 1
1
8
5
6. 1 1
1
3
32
1 1
1
11
7
1
5
1
1
5
1 1
1
17
11
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
7. 1 5
1
7NS2.2
1 1
9
1
1
1 1
1
2
1 1
1
Write each continued fraction as an improper fraction.
25
3. 13
10
13
1. 1
1
Change each improper fraction to a continued fraction.
Exercises
4
4 4 1
1
4
4
72
4 17
17
1
4 17
The expression at the right is an example of a
continued fraction. The example shows how to
change an improper fraction into a continued
fraction.
72
Example
Write as a continued fraction.
Example
17
Continued Fractions
2-4
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Adding and Subtracting Like Fractions
Lesson Reading Guide
7NS1.2
8 8
6. 5, 7 yes
7
7
7. 4, 5 yes
9
5
5
8
8
2
1
12. 5 7 1
9
9
1
3
13. 5 2 7
7
7
1
14. 4 5 Chapter 2
33
Glencoe California Mathematics, Grade 7
work. Students should state that in the lesson, like means
the same denominator.
15. Talk with a partner about the word like. What does it usually mean? How
is this different from the way it is used in the lesson? See students’
Remember What You Learned
5
4
11. 3 1 Add or subtract. Write in simplest form.
like fractions, subtract the numerators, and write the
difference over the denominator.
10. Explain how to subtract like fractions. Sample answer: To subtract
fractions, add the numerators, and write the sum over the
denominator.
3
8. 5, 2 no
9. Explain how to add like fractions. Sample answer: To add like
5 7
5. 3, 3 no
For Exercises 5–8, determine whether each pair of fractions are like
fractions.
Like fractions are fractions with the same denominator.
4. Define like fractions.
Read the Lesson
2
No; the total amount of ingredients is 4 c.
3
3. Can you combine these ingredients in a 4-cup mixing bowl? Explain.
3
2. How many 1 cups are there? 5
1. What is the sum of the whole-number parts of the amounts? 3 c
Read the introduction at the top of page 108 in your textbook.
Write your answers below.
Get Ready for the Lesson
2-5
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 2-4 and 2-5)
Lesson 2-5
Chapter 2
Adding and Subtracting Like Fractions
Study Guide and Intervention
7NS1.2
5
1 (4)
5
3
or 3
5
5
5
Simplify.
Add the numerators. The denominators are the same.
Find 1 4 . Write in simplest form.
9
9
11
2
or 1
9
9
9
9
9
11
2
Rename as 1.
Subtract the numerators. The denominators are the same.
A14
7
7
2
3
5
2
5
Chapter 2
7
7
1
7
10. 35 23 6
5
7. 4 3 1
6
3
5
Glencoe California Mathematics, Grade 7
8
34
1
4
13
13
12
9
1
2
9
11
5
4
5
Glencoe California Mathematics, Grade 7
5
4
11
12. 43 24 1
4
9. 21 11 3
11
9
6. 5 4
9
4
3. 5 1 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8
1
2
11. 35 13 2
13
8
8. 9 6
8
10
5. 3 7 6
7
4. 1 5 7
2. 1 5
7
6
1. 4 2 10
7
64
1
Rewrite as 9.
Add the numerators. The denominators are the same.
Write the mixed numbers as improper fractions.
Add or subtract. Write in simplest form.
Exercises
7
Find 23 65. Write in simplest form.
17
47
23 65 7
7
7
7
17 47
7
64
1
or 9
7
7
Example 3
To add or subtract mixed numbers, first write the mixed numbers as improper fractions. Then add or
subtract the improper fractions and simplify the result.
9
9
Find 4 7. Write in simplest form.
4 7
4 7 Example 2
To subtract like fractions, subtract the numerators of the fractions and write the difference over the
denominator.
1
4
5
5
Example 1
Fractions that have the same denominator are called like fractions. To add like fractions, add the
numerators of the fractions and write the sum over the denominator.
2-5
NAME ________________________________________ DATE ______________ PERIOD _____
4
5
1
2
7
7
Chapter 2
8
7
13
4
7
8
1
4
13
11
4
3
22. 43 27 7
7
19. 56 32 2
13
11
16. 3 7
16
1
4
13. 2 6 16
12
10. 9 3
12
4
7. 7 5
4
5
4. 1 3 5
1. 1 3 4
9
9
9
12
7
9
35
2
31
5
7
23. 52 24 2
12
7
5
1
20. 67 31
7
15
4
3
1
17. 23 12 3
15
8
14. 4 7
8
9
1
11. 5 3 9
9
7
9
8. 1 4
9
9
5. 4 8 9
2. 2 5 11
5
4
5
11
96
Glencoe California Mathematics, Grade 7
5
11
5
54
24. 81 42 3
11
15
5
9
21. 25 71
15
9
7
11
3
7
7
19
18. 14 48
9
19
15. 1 4
19
7
13
6
12. 7
7
9. 5 3
7
10
11
7NS1.2
6. 5 2 11
3. 7 3
Adding and Subtracting Like Fractions
Skills Practice
Add or subtract. Write in simplest form.
2-5
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-5)
Lesson 2-5
Chapter 2
1
4
3 1
4 2
3
4
1
2
2
1
7
8
9
7
9
3
4
18 3
5
4
5
4
5
3
5
11. 4 5 10
9
10
7
10
8. 5 9 15
7 1
11
5. 12 3
12
3
8
2. 10
11
5
6
5
6
5
9
12. 8 3 5
4
9
1
3
A15
1
2
1
7
57 1
7
1
12
11
12
5
9
7
9
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
36
7
9
Chapter 2
2
5
5
12
18. b c if b 2 and c 9 6
2
5
7
12
17. r s if r 8 and s 3 5
4
5
16. 7 4 9 7
5 1 in.
8
4 3 in.
8
ALGEBRA Evaluate each expressions for the given values.
15. 5 2 3 7
4
7
Simplify each expression.
3
triangle. 12 in.
8
2 7 in.
8
the fabric will remain at the store after Naomi buys her fabric? 3 yd
14. GEOMETRY Find the perimeter of the
8
9
9. 7 3 3
2
7
6. 15
15
game. The fabric store has 6 yards of the fabric she wants. How much of
1
4
2
11
3. 8
11
7NS1.2
13. SEWING Naomi needs 2 yards of fabric to make a banner for a football
10. 1 4 6
8
9
7. 4 6 11
3
4
5
4
4. 7
7
1. 1
2
Adding and Subtracting Like Fractions
Practice
Add or subtract. Write in simplest form.
2-1 2-5
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3
3
Chapter 2
3
in.
5
much longer is Tom’s foot than
Randy’s?
5
right foot measures 94 inches. How
5
measures 102 inches, while Randy’s
7. HUMAN BODY Tom’s right foot
2
191 years
the sum of the ages of the sisters?
12
sister Yoki is 85 years old. What is
12
5. AGE Nida is 111 years old, while her
3
81 oz
How much juice is left in the bottle?
glass from a 212 ounce bottle of juice.
3
3. MEASUREMENTS Tate fills a 131 ounce
3
and a width of 31 inches. 16 in.
rectangle with a length of 42 inches
37
7NS1.2
8
8
10
10
10
8
8
9
3
Glencoe California Mathematics, Grade 7
51 megabytes
What will be the size of the resulting
file?
while the other file is 38 megabytes.
9
combine. One file is 14 megabytes,
8. COMPUTERS Trey has two data files on
his computer that he is going to
41 in.
8
What is the perimeter of the triangle?
8
11 inches, 13 inches, and 15 inches.
6. GEOMETRY A triangle has sides of
10
Yes; 47 51 10
feet wide. Will the two posters fit beside
each other on a wall that is 10 feet
wide? Explain.
is 47 feet wide and the other is 51
4. DECORATING Jeri has two posters. One
2
111 lb
does Hunter weigh?
and Hunter is 1377 pounds. How much
pounds. The combined weight of Pat
the scale and reads her weight as 1263
2. PETS Pat wants to find out how much
her dog Hunter weighs. Pat steps on
Adding and Subtracting Like Fractions
Word Problem Practice
1. GEOMETRY Find the perimeter of a
2-5
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-5)
Lesson 2-5
Chapter 2
Enrichment
7MR1.1
2
1
4
4
4
2
1
8
8
8
8
4
2
1
16
16
16
16
1
1
2
4
1
1
1
2
4
8
1
1
1
1
2
4
8
16
Row 2:
Row 3:
Row 4:
15
16
7
8
3
4
1
2
A16
27
9
3
1
81
81
81
81
1
1
1
1
3
9
27
81
1
1
121
1
1
1
81
27
9
3
1
3
9
243
27
81
243
243
243
243
243
243
Row 4:
Row 5:
Chapter 2
Glencoe California Mathematics, Grade 7
16
64
38
256
1,024
Glencoe California Mathematics, Grade 7
4,096
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
6. CHALLENGE Find this sum: 1 1 1 1 1 1. 1,365
4,096
13
27
9
3
1
27
27
27
1
1
1
27
3
9
Row 3:
40
81
4
9
3
1
9
9
1
1
3
9
Row 2:
1
3
1
3
1
3
Row 1:
5. Now complete the following pattern.
63 511
; 64 512
4. What would be the fraction at the end of Row 6? Row 9?
1
1
1
16
31
1
1
8
4
2
1
2
4
8
32
32
16
32
32
32
32
32
3. In the space below, write Row 5 of the pattern.
one.
2. What is the relationship between the numerators of the fractions in the
second column? Each numerator is divided by 2 to get the next
next one.
1. What is the relationship between the denominators of the fractions in the
first column? Each denominator is multiplied by 2 to get the
1
2
1
2
Row 1:
When examining the solution of a problem, good problem solvers look for ways
to extend the problem. The questions on this page show you a way to examine
and extend the following pattern.
Extending Problems
2-5
NAME ________________________________________ DATE ______________ PERIOD _____
7NS1.2, 7NS2.2
Adding and Subtracting Unlike Fractions
Lesson Reading Guide
2
8
6. 4, 6 12
8 12
10. 5, 7
24
7
7
10
11. 4, 5 7
7. 5, 10
9
3
12. 5, 2 9
8. 9, 12 36
2
7 1
14 14
8
14
1
10
5
10
2
5
7
8
6
8
7
8
5
8
21
35
15
35
1
35
18. 3 3 ; 1
4
15. 3 7 ; 1
8
12
3
19. 5 7
9
6
9
39
Glencoe California Mathematics, Grade 7
often means “the opposite of.” Unlike fractions are the opposite
of like fractions because their denominators are different.
Chapter 2
1
9
15
14 1
; 24
24 24
5
9
16. 5 2 ; 20. Describe what the prefix un- usually means when it appears in front of a
word. How does this meaning relate to unlike fractions? The prefix un-
Remember What You Learned
7
17. 4 1 ; 5
14. 3 1 ; 1
6
10
Rewrite each sum or difference in terms of like fractions. Then add
or subtract. Write in simplest form.
subtract unlike fractions, rewrite the fractions with a common
denominator and then add or subtract as like fractions.
13. Explain how to add or subtract unlike fractions. Sample answer: To add or
5 7
9. 3, 3 35
Find the LCD of each pair of fractions.
5. 2, 3 6
Find the LCM of each pair of numbers.
least common multiple; the LCM of two or more numbers is the
smallest number that is a multiple of each number; LCD stands for
least common denominator; the LCD of two or more fractions is the
LCM of the denominators of the fractions.
4. What do LCM and LCD stand for? Give a definition for each. LCM stands for
Read the Lesson
3. Find the missing value in 1 ?.
4
8
2. What is the least common multiple of the denominators?
1. What are the denominators of the fractions? 4, 8
Read the introduction at the top of page 114 in your textbook.
Write your answers below.
Get Ready for the Lesson
2-6
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 2-5 and 2-6)
Lesson 2-6
Chapter 2
7NS1.2, 7NS2.2
Adding and Subtracting Unlike Fractions
Study Guide and Intervention
5
6
A17
6
Simplify.
Add the numerators. The denominators are the same.
2
6
2 3
6
21
11
6
6
21 11
6
32
16
1
or or 5
6
3
3
11
7 3 10
9
20
Chapter 2
5
4
10. 11 21 3
10
7. 7 1
1
5
17
12
7
10
2
4. 3 5
4
6
5
1. 2 3
9
40
3
11. 24 11
5
8. 21 13 3
4
8
8
9
5. 4 1
5
3
9
9
11
12
15
Simplify.
21
9
7
18
5
3
14
15
12. 33 22 5
9. 33 11 2
4
3
12
6. 12 4
3
9
9
6
3. 5 1
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
Subtract the numerators.
5
2. 1 2 3
3 or 6.
Rename 7 using the LCD.
2
The LCD is 2
Write the mixed numbers as improper fractions.
Add or subtract. Write in simplest form.
Exxercises
2
2
3 or 15.
Rename each fraction using the LCD.
The LCD is 5
Find 31 15. Write in simplest form.
11
31 15 7 Example 2
3
Find 3 2. Write in simplest form.
3
2
3 3
2 5
5
3
5 3
3 5
10
9 15
15
9 10
15
19
4
or 1
15
15
Example 1
Fractions with unlike denominators are called unlike fractions. To add or subtract unlike fractions,
rename the fractions using the least common denominator. Then add or subtract as with like fractions.
2-6
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2
3
2
21
12
8
19
20
3
4
35
7
Chapter 2
9
3
23. 102 31
3
4
21. 32 42
5
9
135
21
20
7
19. 21 33 5
3
8
5
12
11
15
17. 51 32 8
4
4
15. 23 63
6
3
13. 31 41 7
5
3
12
11. 32 21 5
7
6
9
14
9. 3 2 1
4
14
8
7
7. 1 5 7
4
5. 6 3
8
1
3. 7 1 1
2
1. 1 1 6
7NS1.2, 7NS2.2
7
20
7
5
10
3
5
3
41
3
15
37
9
81
Glencoe California Mathematics, Grade 7
5
6
71
2
12
27
41
24. 21 54
22. 57 21
9
6
3
10
3
14
14
11
20. 21 45
3
18. 33 9
4
16. 51 22
2
14. 11 11
2
2
12. 55 31 9
7
4
7
15
10. 4 1
5
3
12
8. 3 1 5
3
7
9
6. 4 1 4
3
5
4. 3 2 1
9
2. 4 1 Adding and Subtracting Unlike Fractions
Skills Practice
Add or subtract. Write in simplest form.
2-6
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-6)
Lesson 2-6
Chapter 2
1
5
3
4
19
20
5
9
2
9
1
5
3
5
9
10
3
5
11. 4 5 10
1
2
9
10
3
5
7
10
1
6
5
12
3
4
2
3
14
15
12. 18 14 3
1
3
9. 7 5 12
5
24
6. 8. 1 5 3
6
5
23 1
12
7
8
2
15
A18
7
10
1
10
5
9
5
6
7
18
3 1 in.
3
23
24
5 1 in.
4
x in.
3
8
Glencoe California Mathematics, Grade 7
42
17.
3
8
Glencoe California Mathematics, Grade 7
1
4
17 3 in.
4
14 5 in.
8
perimeter 59 in. 16 in.
x in.
10 1 in.
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
perimeter 12 in. 4 in.
Chapter 2
16.
GEOMETRY Find the missing measure for each figure.
14. m n if m and n 10 1015. j k if j and k 4 5
3
5
ALGEBRA For Exercises 14 and 15, evaluate each expression using the given information.
19
countries? 30
population lives in India. What fraction of the world’s population lives in other
13. POPULATION About of the world’s population lives in China, and of the world’s
10. 3 4 8
2
3
7. 4 6 10 5. 3
4
2 17
5 45
1
3
3. 1
4
5
4. 7
9
5
59 18
2. 5
6
7 1
10 5
1. 1
2
7NS1.2, 7NS2.2
Adding and Subtracting Unlike Fractions
Practice
Add or subtract. Write in simplest form.
2-6
NAME ________________________________________ DATE ______________ PERIOD _____
3
What is the sum of the lengths of the
two line segments?
4
lengths of 31 inches and 11 inches.
2
5
Chapter 2
17
2
oz
20
the beaker?
4
101 ounces. How much water is left in
water from a beaker containing
7. MEASUREMENT Ned pours 72 ounces of
2
lb
3
second puppy weigh than the first?
6
51 pounds. How much more does the
2
45 pounds and the other puppy weighs
5. PETS Laura purchased two puppies
from a litter. One of the puppies weighs
16
Right hand; 1 in.
8
4
3
3
6
41 in.
Glencoe California Mathematics, Grade 7
What is the perimeter of the triangle?
6
11 inches, 11 inches, and 12 inches.
8. GEOMETRY A triangle has sides of
12
107 years
the sum of the ages of Alma and David?
brother David is 35 years old. What is
6
6. AGE Alma is 63 years old, while her
85 in.
8
must the frame be to fit both pictures?
the longer index finger? How much
longer is it?
2
frame. One is 31 inches wide and the
4. DECORATING Sugi has two pictures that
she wants to put beside each other in a
27 megabytes
18
larger is the second file than the first?
other is 51 inches wide. How wide
43
9
other file is 41 megabytes. How much
One file is 21 megabytes, while the
2. COMPUTERS The biology class has
created two data files on the computer.
measures 35 inches. Which hand has
16
while the index finger on his left hand
8
Pablo’s right hand measures 33 inches,
3. HUMAN BODY The index finger on
12
47 in.
7NS1.2, 7NS2.2
Adding and Subtracting Unlike Fractions
Word Problems Practice
1. GEOMETRY Two line segments have
2-6
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-6)
Lesson 2-6
Chapter 2
Enrichment
5
6
A19
1
3
1 13
1
16
3
4
3
1
1
14
7
12
5
12
2
3
1 23
2 23
1
12
1
2
11
12
1
13
3
21
1
3
1
5
6
1
6
2
2
3
1
4
1
12
1
6
1
4
5
12
2
3
7
12
3
4
Chapter 2
Other correct answers
are possible.
1
3
1
2
1
1 12
6. Arrange these numbers to make
a magic square.
4. 2
1. 5
1
2. 2
4
5
8
1
3
5
4
1
2
3
8
3
4
9
8
1
8
44
3
4
1
4
1
6
5
12
2
3
5. 2
Find the magic sum for each square in
Exercises 1–5. Then fill in the empty cells.
A magic square is an arrangement of numbers
such that the rows, columns, and diagonals all
have the same sum. In this magic square, the
magic sum is 15.
Magic Squares
2-6
1
1
4
1
2
7
12
1
12
5
8
11
16
7
8
Column
2
7
1
1
8
5
16
15
16
3. 0
13
16
1
1
4
1
16
1
2
Diagonal
9
5
8
6
3
16
9
16
7
8
2
1
3
8
7
16
1
1 2
0
1
12
Row
3
4
1
2
1
2
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
1
2
4
3
7NS1.2
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7AF1.1, 7NS1.2
Solving Equations with Rational Numbers
Lesson Reading Guide
30 s
_____ a
_____ c
12
3
e. Subtract 1.25 from each side.
d. Divide each side by 1.25.
c. Add 1.25 to each side.
8
Subtract 3 from each side and simplify.
Multiply each side by 3.2 and simplify.
Chapter 2
45
Glencoe California Mathematics, Grade 7
2. Identify the variables and the operators to use. 3. Write the equation
and substitute in any known values.
8. The description of a problem often has more information than you need to
design an equation and solve it. Describe the process of writing an
equation to solve a problem. Sample answer: 1. Write the equation in words.
Remember What You Learned
8
7. 3 v 7
3.2
6. y 1.1
5
b. Multiply each by 5.
a. Subtract 3 from each side.
Explain in words how to solve each equation.
3
1
f 5
2
r – 1.25 4.5
_____ b
_____ e
x 1.25 5.25
7
3
m 10
5
_____ d
1.25a 3.75
5. Match the method of solving with the appropriate equation.
Read the Lesson
Multiplying by the multiplicative inverse; it only takes one step.
4. Which method of solving the equation seems most efficient?
3. What is the speed of a grizzly bear? 30 mph
6
inverse of 5. Write the result.
2. Multiply each side of the original equation by the multiplicative
1. Multiply each side of the equation by 6. Then divide each side by 5. Write
the result. 150 5s; 30 s
Read the introduction at the top of page 119 in your textbook.
Write your answers below.
Get Ready for the Lesson
2-7
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 2-6 and 2-7)
Lesson 2-7
Chapter 2
7AF1.1, 7NS1.2
Solving Equations with Rational Numbers
Study Guide and Intervention
A20
2
2
✓
3
3
Simplify.
Replace x with 4.04.
3
4
Simplify.
6
Replace y with 5.
Write the original equation.
Simplify.
Multiply each side by 5.
Write the equation.
Chapter 2
3
4
8
9
10. 2 3t Glencoe California Mathematics, Grade 7
46
10.5
8
1
14
Glencoe California Mathematics, Grade 7
4
12. 13r 35 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2.5
11. w 4.2
5
4
15
9. 3x 6 10
5
8. 5.04 1.26d 4
3
3
3
8
7. 3.2c 9.6
4
6. 2 f 3 1
8
5. 5 x 1 1
3
9
9
2. b 4.22 7.08 11.3
4. h 4 7 1. t 1.32 3.48 2.16
Solve each equation. Check your solution.
5
3. 8.07 r 4.48 3.59
Write the original equation.
Simplify.
Add 2.73 to each side.
Write the equation.
Solve 4y 2. Check your solution.
1.31 1.31 ✓
2
3
5 2
4 3
y 5
6
4
2
y 5
3
4 5
2
5 6
3
4
y 5
5 4
y 4 5
Exercises
Check
x 4.04
x 2.73 1.31
4.04 2.73 1.31
Example 2
Check
x 2.73 1.31
Solve x 2.73 1.31. Check your solution.
x 2.73 2.73 1.31 2.73
Example 1
The Addition, Subtraction, Multiplication, and Division Properties of Equality can be used to solve
equations with rational numbers.
2-7
NAME ________________________________________ DATE ______________ PERIOD _____
10
18
2
9
5
Chapter 2
3
8
9
1
3
23. 7.5g 62 5
12.96
21. 22f 31 1
1.8
19. x 7.2
17. 2.11 w (5.81) 7.92
15. 5.1 1.7r 3
3
11
13. 2 3t 2
9
1
2
0.5
2
11
11. 4 8a 9. 12.8y 6.4
7. 3.4c 6.8
3
5. 5 x 1 3. 3.38 r 9.76 6.38
1. x 2.62 6.37 3.75
6
7AF1.1, 7NS1.2
5
8
9
10
22
8
23
3
2
47
5
3
Glencoe California Mathematics, Grade 7
5
1
4
1
2
24. 21 c 4
8
8
22. 1.5d 3 4
9.1
20. 21y 33 1
2.6
18. w 3.5
16. z (3.2) 3.69 0.49
11
15
19
14. 4w 5
12. 2s 4
4
10. 3x 9 12
8. 1.56 0.26w 6
10
1
4
6. 4 z 1
8
4. s 5 7 2. y 3.16 7.92 11.08
Solving Equations with Rational Numbers
Skills Practice
Solve each equation. Check your solution.
2-7
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-7)
Lesson 2-7
Chapter 2
13
16
13
40
8.4 1.4y 6
A21
f
2.4
23
27
2
3
Chapter 2
48
64.5 s 79.4; 14.9 thousand seats
18. Let s equal the number of additional seats
that the Pittsburgh Steelers’ stadium needs
to equal the number of seats in Kansas City
Chiefs’ stadium. Write and solve an addition
equation to determine the number of seats
that the Steelers’ stadium needs to equal
the number of seats in the Chiefs’ stadium.
FOOTBALL For Exercise 18, refer to the table.
65.7
79.4
64.5
71.3
(thousands)
Seats
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
Source: stadiumsofnfl.com
Dallas Cowboys
Kansas City Chiefs
Pittsburgh Steelers
San Diego Chargers
Stadium
NFL Stadiums
Seating Capacity
4
Chapter 2
123 mph
4
the average speed s of the bus. What
was the average speed of the bus?
3
equation 1s 41 can be used to find
3
and the ride took 1 of an hour. The
4
The distance she traveled was 41 miles
7. SPEED Ella rode the bus to work today.
9
47 yd
1
4
francs. 1d 15; $12
3
length of the truck?
9
equation 24 21. What is the
truck can be found by solving the
3
is 21 yards long. The length of the
5. AUTOMOBILES The bed of Julian’s truck
$2.88 per gallon
premium gasoline?
p
2.40. What is the price of the
1.2
3. ENERGY PRICES Suppose regular
unleaded gasoline costs $2.40 per
gallon. The price p of premium gasoline
can be found using the equation
9.62 m
equation to find the number of U.S. dollars that would equal 15 Swiss
1
2
15. 8 1.3
g 6
p
6.25
12. 3.6 22.5
The currency in Switzerland is called a franc. On a certain day,
1
3
14. 4.5w 8 1
11. 7.5 18
9. 2.94 0.42a 7
7.87
6. 2.5 n (5.37)
3
5
3. d 7AF1.1, 7NS1.2
49
3
2
2
3
22 in.
Glencoe California Mathematics, Grade 7
find the width w of the rectangle. Solve
the equation.
The equation 62 21w can be used to
3
4
62 square inches and length 21 inches.
8. GEOMETRY A rectangle has area
3
t 9
4
of Ted’s time. Using t for Ted’s time,
write a multiplication equation to
represent the situation.
Leo’s time was 9 minutes, which was 3
6. SPORTS Leo and Ted both ran in a race.
4. DRIVING TIME Sam went for a drive last
Sunday. His average speed was 46
miles per hour and he drove 115 miles.
The equation 115 46t can be used to
find the time t that he spent driving.
Solve the equation. 2.5 h
$41.41
2. SHOPPING Kristen went shopping and
spent $84.63 on books and CDs. The
equation 84.63 b 43.22 can be used
to determine the amount b that she
spent on books. Solve the equation.
Solving Equations with Rational Numbers
Word Problem Practice
1. NATURE The height of a certain tree is
12.85 meters. The length of its longest
branch can be found using the equation
3.23 12.85. Solve the equation.
2-7
NAME ________________________________________ DATE ______________ PERIOD _____
1
one U.S. dollar equaled 1 Swiss francs. Write and solve a multiplication
4
17. MONEY
13. 2.5x 10.
3
8. v 27 63
7
5
8
7. k 25 40
h (6.3) 8.12 1.82
5.
2. t 2.89 9.15 12.04
11
7
1
4. b 4
16
16
1. m 0.88 1.64 0.76
5 7
6 30
7AF1.1, 7NS1.2
Solving Equations with Rational Numbers
Practice
Solve each equation. Check your solution.
2-7
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Answers (Lesson 2-7)
Lesson
Lesson X–1
2-7
Chapter 2
Enrichment
7AF1.2
A22
Chapter 2
2
3
7
0.4
n
12
14
3
2
2
Glencoe California Mathematics, Grade 7
Glencoe California Mathematics, Grade 7
2
3
15 5 n5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
50
20
100
1.5
5.5
66 3
75n 50
n
0.3
n 4.5 10
0.2
11
2
3
7
9
2
6n 5 1
2
3
29.2 36.2 n
40
5n 2
9
2
0.1 0
9n
n
2
5.2 n 3.7
1.5
n 11 16
End
40 40 n
6n
3 4.5 n
9
2
2
3
5
0
1
3
40
14 0.5n 6
n
4
21 12n 13
Start Here
4
3.3
0.7n 4 0.9
43 n 41.5
90 32 n 30
1.1
1.5
11
3.3n 36.3
19 n 17.9
n 3.7 7
To solve the maze, start with the number in the center. This number
must be the solution of the equation in the next cell. The number in
the new cell will then be the solution to the equation in the next cell.
At each move, you may only move to an adjacent cell. Each cell is
used only once.
Equation Hexa-Maze
2-7
NAME ________________________________________ DATE ______________ PERIOD _____
x (4)
7
6
[TEXT] Done
(
(
)
4
)
c
.)
ENTER
[QUIT]
(
38.3
(
)
4
)
b
c
7
ENTER
3
17
40
51
11
6. 9.1 1.4t 18.9
20
Glencoe California Mathematics, Grade 7
7. The volume of a cylinder is given by the formula V = r2h, where r
is the radius of the base and h is the height of the cylinder. The
volume of a cylinder is 21.21 cubic centimeters. If the cylinder
has a height of 27 centimeters, what is its radius? Round to the
nearest hundredth. 0.50 cm
4
2. 6.9 c 2.6 4.3
4. p (17.1) 28.3 11.2 5. 5 g 8
1. 4x 24.9 6.225
3. 423 114k 3 15
The calculator displays 4.9, which matches the left side of the equation. So the
result is correct.
D
2nd
F
Solve each equation. Check your solution.
Chapter 2
b
CLEAR
Check the result. Evaluate the right side of the equation with the value 38.3 x for x.
Read the value of x in the second row.
x 38.3
ENTER
In the Solve row, choose x. (Ignore any current value shown for x.)
7
ENTER
4.9
2nd
Enter the equation. (If an equation is already there, press
MATH
menu to solve equations quickly or to
Solve 4.9 . Check your solution.
Choose Equation Solver.
Exercises
Step 5
Step 4
Step 3
Step 2
Step 1
Example
MATH
Solving and Checking Equations
TI-73 Activity
Use the Equation Solver feature in the
check your solutions.
2-7
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-7)
Lesson 2-7
Chapter 2
7MR2.4, 7NS1.2
Problem-Solving Investigation: Look for a Pattern
Study Guide and Intervention
Select a strategy including a possible estimate.
Solve the problem by carrying out your plan.
Examine your answer to see if it seems reasonable.
Plan
Solve
Check
A23
Sixth Stop
13
35 + 13 = 48
people on
the train
Seventh Stop
15
48 + 15 = 63
people on
the train
Check your pattern to make sure the answer is correct.
At the seventh and final stop there were 63 people on the subway train.
Fifth Stop
11
24 + 11 = 35
people on
the train
2
3
Chapter 2
52
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
2. FUNDRAISER There were 256 people at a fundraiser. When the event was over, half of the
people who remained left every 5 minutes. How long after the event ended did the last
person leave? 90 minutes
cups of flour should be used when 4 cups of sugar are used? 15 cups of flour
1. COOKING A muffin recipe calls for 2 cups of flour for every cup of sugar. How many
1
2
Look for a pattern. Then use the pattern to solve each problem.
Exercises
Check
Fourth Stop
9
15 + 9 = 24
people on
the train
Second Stop
5
3+5=8
people on
the train
First Stop
3
3 people on
the train
Third Stop
7
8 + 7 = 15
people on
the train
Complete the information for the first, second, and third stops. Continue the
pattern to solve the problem.
Look for a pattern and use the pattern to find how many people boarded the
train in all.
Plan
Solve
You know that 3 people boarded the subway train at the first stop. At each
subsequent stop, 2 more people board the train than at the previous stop.
Explore
Three people board the subway train at the first stop. Five people board the train at the
second stop. Seven people board the train at the third stop. If this pattern continues and no
one gets off the train, how many people are on the subway train when it reaches the seventh
and final stop?
Example
Determine what information is given in the problem and what you need to find.
Explore
You may need to look for a pattern to solve a problem.
2-8
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7MR2.4, 7NS1.2
Problem-Solving Investigation: Look for a Pattern
Skills Practice
Chapter 2
and 45 minutes
53
Glencoe California Mathematics, Grade 7
6. HOT TUBS A hot tub holds 630 gallons of water when it is full. A hose fills the tub at a
rate of 6 gallons every five minutes. How long will it take to fill the hot tub? 8 hours
5. GEOMETRY Find the perimeters of the next two figures in the pattern. The length of
each side of each small square is 3 feet. 60 feet; 72 feet
4. CHEERLEADING The football cheerleaders will arrange themselves in rows to form a
pattern on the football field at halftime. In the first five rows there are 12, 10, 11, 9,
and 10 girls in each row. They will form a total of twelve rows. If the pattern continues,
how many girls will be in the back row? 5 girls
3. HONOR STUDENTS A local high school displays pictures of the honor students from each
school year on the office wall. The top row has 9 pictures displayed. The next 3 rows
have 7, 10, and 8 pictures displayed. The pattern continues to the bottom row, which
has 14 pictures in it. How many rows of pictures are there on the office wall? 11 rows
2. BIOLOGY Biologists place sensors in 8 concentric circles to
track the movement of grizzly bears throughout Yellowstone
National Park. Four sensors are placed in the inner circle.
Eight sensors are placed in the next circle. Sixteen sensors
are placed in the third circle, and so on. If the pattern
continues, how many sensors are needed in all? 512
1. YARN A knitting shop is having a huge yarn sale. One skein sells for $1.00, 2 skeins sell
for $1.50, and 3 skeins sell for $2.00. If this pattern continues, how many skeins of yarn
can you buy for $5.00? 9 skeins
Look for a pattern. Then use the pattern to solve each problem.
2-8
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-8)
Lesson 2-8
Chapter 2
40
60
50
20
30
d.
b.
A24
Distance Fallen
16 feet
48 feet
80 feet
112 feet
1
8
Chapter 2
minutes.
Glencoe California Mathematics, Grade 7
54
Glencoe California Mathematics, Grade 7
Multiplication and addition;
5 2 2 4 18; 18 years
6. U.S. PRESIDENTS President Clinton
served 5 two-year terms as governor of
Arkansas and 2 four-year terms as
President of the United States. How
many total years did he serve in these
two government offices?
Division; 570 0.06 9,500;
Alaska is 9,500 times larger.
5. MOVIES The land area of Alaska is
about 570 thousand square miles. The
land area of Washington, D.C., is about
0.06 thousand square miles. How many
times larger is Alaska than Washington,
D.C.?
For Exercises 5 and 6, select an
appropriate operation to solve the
problem. Justify your solution and
solve the problem.
Select the Operation
280 pages
4. READING Ling read 175 pages by 1:00
P.M., 210 pages by 2:00 P.M., and 245
pages by 3:00 P.M. If she continues
reading at this rate, how many pages
will Ling have read by 4:00 P.M.?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
have enough time? No, he needs 42
minutes to mow of the yard, will he
3
4
yard every 7 minutes. If he has 40
3. YARD WORK Denzel can mow of his
• Use the four-step plan.
• Look for a pattern.
PROBLEM-SOLVING STRATEGIES
Use any strategy to solve Exercises 3
and 4. Some strategies are shown
below.
Time Period
1st second
2nd second
3rd second
4th second
2. ANALYZE TABLES A falling object
continues to fall faster until it hits the
ground. How far will an object fall
during the fifth second? 144 ft
c.
10
1. GEOMETRY Draw the next two angles in
the pattern.
For Exercises 1 and 2, look for a
pattern. Then use the pattern to solve
the problem.
a.
7MR2.4, 7NS1.2
Problem-Solving Investigation: Look for a Pattern
Practice
Mixed Problem Solving
2-8
NAME ________________________________________ DATE ______________ PERIOD _____
7MR2.4, 7NS1.2
Problem-Solving Investigation: Look for a Pattern
Word Problem Practice
Chapter 2
12 white daisies and 10 yellow
daisies
5. GARDENING Marial was planting
daisies in her garden. She planted 2
white daisies and 5 yellow daisies in
the first row, 4 white daisies and 6
yellow daisies in the second row, and 6
white daisies and 7 yellow daisies in
the third row. If she continues the
pattern, how many white and yellow
daisies will she plant in the sixth row?
3. SAVINGS Jordan saved $1 the first
week, $2 the second week, $4 the third
week, and $8 the fourth week. If this
pattern continues, how much will she
save the eighth week? $128
55
The cost increases by $0.10 less
for each additional person in the
group.
1. Describe the pattern used to calculate
the cost for a group.
Number of Total Cost
People in
per Group
Group
1
$1.00
2
$2.00
3
$2.90
4
$3.70
5
$4.40
old
Glencoe California Mathematics, Grade 7
6. BIOLOGY A newborn seal pup gains 4
pounds the first week, 8 pounds the
second week, 16 pounds the third week,
and 32 pounds the fourth week. If this
growth pattern continues, how many
weeks old will the seal pup be before it
weighs over 100 pounds? 6 weeks
4. AGRICULTURE In a vegetable garden,
the second row is 8 inches from the
first row, the third row is 10 inches
from the second row, the fourth row is
14 inches from the third row, and the
fifth row is 20 inches from the fourth
row. If the pattern continues, how
far will the eighth row be from the
seventh row?
50 inches
$5.90
2. If the pattern continues, what would
the cost be for a group of 8 skaters?
ENTERTAINMENT For Exercises 1 and 2, use the information
at the right, which shows the ticket prices at a skating rink.
Look for a pattern. Then use the pattern to solve each problem.
2-8
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-8)
Lesson 2-8
Chapter 2
Powers and Exponents
Study Guide and Intervention
A25
11. 95 59,049
13. 28 256
cccccccc
9. c8
Chapter 2
56
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
negative exponent gives a positive rational number.
Write a true sentence using the terms negative exponent, power, positive,
and rational. Sample answer: A positive power with a
4
14. Notice that 43 13 . A power with a negative exponent is not negative.
12. 63 216
99999
8. 95
Remember What You Learned
10. 54 625
Evaluate each expression.
5555
7. 54
Rewrite each expression using multiplication instead of an exponent.
6. Explain in words what 54 means. 54 is the product of 4 factors of 5.
5. x8 base: x; exponent: 8; power: x8
4. 72 base: 7; exponent: 2; power: 72
3. 54 base: 5; exponent: 4; power: 54
For Exercises 4–6, identify the base, exponent, and power in each
expression.
that is multiplied. An exponent tells how many times the
base appears as a factor. A power is a number expressed
using an exponent.
2. Define the terms base, exponent, and power. A base is a number
Read the Lesson
1. How many 2s are multiplied to determine the number of great
grandparents? great-great grandparents? 3; 4
Write p p p q q using exponents.
7NS1.2, 7NS2.1, 7AF2.1
Simplify.
Chapter 2
57
Glencoe California Mathematics, Grade 7
14. 34 72 3,969
13. 3–4 1
81
12. 24 52 400
10. 23 32 72
8. 53 125
6. s w w s s s s4 w2
4. g g g g g g g g7
2. 4 4 4 4 44
Simplify.
Definition of negative exponents
Evaluate 5–3.
5–3 13
¬ 5
1
¬ 125
Example 4
11. 8–2 1
64
9. 132 169
7. 42 16
Evaluate each expression.
5. 5 5 9 9 5 9 5 5 55 93
3. a a a a a a a6
1. 8 8 8 8 8 85
Write each expression using exponents.
Exercises
36
Definition of exponents
Evaluate 62.
62 6 6
Example 3
Any nonzero number to the zero power is 1. Any nonzero number to the negative n power is the
multiplicative inverse of nth power.
Since p is used as a factor 3 times and q is used as a factor 2 times, p p p q q p3 q2.
Example 2
Since 7 is used as a factor 5 times, 7 7 7 7 7 75.
Write 7 7 7 7 7 using exponents.
Example 1
2-9
Expressions containing repeated factors can be written using exponents.
7NS1.2, 7NS2.1, 7AF2.1
Read the introduction at the top of page 126 in your textbook.
Write your answers below.
Powers and Exponents
Lesson Reading Guide
NAME ________________________________________ DATE ______________ PERIOD _____
Get Ready for the Lesson
2-9
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Answers (Lesson 2-9)
Lesson 2-9
Chapter 2
A26
64
32
1
2,401
58
Chapter 2
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Glencoe California Mathematics, Grade 7
24. 74 1
64
23. 82 22. 23 1
8
20. 26 62 2,304
19. 42 34 1,296
21. 33 73 9,261
18. 23 52 200
16. 54 625
14.
17. 28 256
15. 83 512
13.
43
25
12. y x x y x y y x3 y4
11. m n n n m n m2 n4
Evaluate each expression.
10. a a b a b a a a5 b2
9. 8 8 2 2 2 2 8 24 83
8. 4 4 4 4 6 6 6 44 63
7. 5 5 5 3 3 53 32
4. x x x
x3
6. s s s s s s s s7
76
7NS1.2, 7NS2.1, 7AF2.1
5. c c c c c c5
3. 7 7 7 7 7 7
1. 2 2 2 2 24
2. 9 9 92
Powers and Exponents
Skills Practice
Write each expression using exponents.
2-9
NAME ________________________________________ DATE ______________ PERIOD _____
Powers and Exponents
Practice
1
72
1 1
1
5 25 125
22. x5 y, if x 2 and y 8 256
20. m2 n3, if m 6 and n 2 288
Chapter 2
59
Glencoe California Mathematics, Grade 7
25. EPIDEMICS At the beginning of an epidemic, 50 people are sick. If the
number of sick people triples every other day, how many people will be
sick at the end of 2 weeks? 109,350 people
24. MONEY Suppose $100 is deposited into an account and the amount doubles
every 8 years. How much will be in the account after 40 years? $3,200
1, , , ,
189
625
18. 7 33 54 1
125
14. 53 10. 23 52 200
23. Complete the following pattern.
54 625, 53 125, 52 25, 51 5, 50 ? , 51 ? , 52 ? , 53 ?
21. f 4 g5, if f 3 and g 1 81
19. r3 s, if r 5 and s 4 500
ALGEBRA Evaluate each expression.
16. 32 6 102 5,40017. 32 23 15. 7 22 52 700
1
81
13. 92 9. 22 62 144
12. 83 1
512
8. 53 125
53 82 x 3 y 4
11. 34 1
81
7. 24 16
Evaluate each expression.
2 52 72 r4 s2
6. x 8 y x 5 x 5 y 8 y y 5
4. g 7 7 g h 7 h 7 3 g 2 h 2
3. p 9 3 q p 9 3 92 p 2 q
5. 2 5 r 7 s r 5 r 7 r s
2. 2 d 5 d d 5 2 52 d 3
7NS1.2, 7NS2.1, 7AF2.1
1. 3 3 m 32 m
Write each expression using exponents.
2-9
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-9)
Lesson 2-9
Chapter 2
A27
Chapter 2
7. BANKING Suppose that a dollar placed
into an account triples every 12 years.
How much will be in the account after
60 years? $243
1,000,000 mm
5. MEASUREMENT There are 106
millimeters in a kilometer. Write the
number of millimeters in a kilometer.
60
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
8. BIOLOGY Suppose a bacterium splits
into two bacteria every 15 minutes.
How many bacteria will there be in 3
hours? 4,096 bacteria
6. NATURE Suppose a certain forest fire
doubles in size every 12 hours. If the
initial size of the fire was 1 acre, how
many acres will the fire cover in
2 days? 16 acres
signatures
4. ACTIVISM A petition drive is being held
in 10 cities. In each city, 10 people have
collected 10 signatures each. The
expression 103 denotes the number of
signatures that have been collected
altogether. Find this number. 1,000
32
3. MONEY An apartment complex has 3
buildings. Each building has 3
apartments. There are 3 people living
in each apartment, and each person
pays 3 dollars per month for pool
maintenance. The expression 34
denotes the amount paid each month
for pool maintenance. Find this
amount. $81
7NS1.2, 7NS2.1, 7AF2.1
2. GEOMETRY The volume of a box can be
found by multiplying the length, width,
and height of the box. If the length,
width, and height of the box are all 5
inches, write the volume of the box
using an exponent. 53 in3
Powers and Exponents
Word Problem Practice
1. SPORTS In the first round of a local
tennis tournament there are 25
matches. Find the number of matches.
2-9
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enrichment
Letter
O
Box Number 19
G
Letter
232
83 18
35
27
132
1
22
17
12
7
2
Box Number
2 9 92
3 6 63
44 162
63
53
Chapter 2
21
16
11
6
1
3
E
8
V
36 35
162 63
44
24 32
43 34
M
2
24
19
14
9
4
E
6
25
20
15
10
L
I
12 13
212
192
73
2 5 32
172
5
B
9
E
4
23 72
28 112
5 3 35
182
4 5 93
R
5
R
G
I
V
61
E
M
E
E
A
V
I
24
25
T
T
H
Y
Glencoe California Mathematics, Grade 7
D
M
23
A
T
22
G
21
19
20
E
O
18
E
E
16
17
R
15
I
Y
13
14
L
12
T
D
11
B
9
10
E
6
I
R
5
V
E
4
8
E
3
2
7
10 14
15 20 25 24 18 23 17 11 16 22 21
I
7
23
18
13
8
3
When you have finished drawing your path through the boxes, write the box
numbers on the lines below. Put the numbers in the order in which they are
connected. Then use the chart at the right to convert each box number to a
letter.
Starting with Box 1, draw an arrow to the box next or diagonal to Box 1 with
the expression of the least value. The arrow cannot go to a box that has
already been used. The first arrow has been drawn to get you started.
G
M
1
7NS1.2, 7AF2.1
Solve the following puzzle by finding the correct path through the boxes. The
solution is a famous quote from United States history.
A-Mazing Exponents
2-9
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-9)
Lesson 2-9
Chapter 2
The Power Key
Scientific Calculator Activity
Evaluate
5
43.
4
A28
598
Chapter 2
Glencoe California Mathematics, Grade 7
209
659,375
Glencoe California Mathematics, Grade 7
12. (35 25) 55
6,998
62
34
10. 5 23 3 23 16
8. 2 43
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. CHALLENGE 10 73 6 23 34 5 43
11. (4 5)2 63 25 6,993
9. 3 53 4 27 887
7.
33
6. 53 42 25 64,000
5. 3 25 45 98,304
54
4. 43 27 8,192
2. 524 7,311,616
ENTER
3 2048
Therefore, 25 43 2,048.
Enter: 2
25
3. 2 63 432
1. 38 6,561
ENTER
4 625
Therefore, 54 625.
Enter: 5
Evaluate 54.
Evaluate each expression.
Exercises
Example 2
Example 1
The power key on many calculators makes it easier to evaluate
expressions with exponents. It is usually labeled y x or
.
2-9
NAME ________________________________________ DATE ______________ PERIOD _____
Scientific Notation
Lesson Reading Guide
8.7 10
Product
1
8.7 8.7 0.87
10
1
2
8.7 10 8.7 0.087
100
1
8.7 103 8.7 0.0087
1,000
8,700
870
87
7NS1.1
101
8. 1,000,000,000 very large
4; negative
10. 185,000 → 1.85 5; positive
14. 402,500,000 4.025 108
13. 0.00899 8.99 103
Chapter 2
63
Glencoe California Mathematics, Grade 7
15. Work with a partner. One person should explain how to write a very large
number in scientific notation. The other person should explain how to
write a very small number in scientific notation. See students’ work.
Remember What You Learned
12. 0.0000125 1.25 105
11. 8,790,000 8.79 106
Write each number in scientific notation.
9. 0.00037 → 3.7
For each pair of numbers, determine how many places the decimal
has moved and whether the exponent of the original would be
positive or negative in scientific notation.
6. 0.00083986 very small
5. 9,245,000 very large
7. 0.0000003 very small
Identify each positive number as either very large or very small.
There are no exponents.
4. How can you tell that a number is in standard form?
Read the Lesson
opposite of the exponent gives the number of places the decimal point
moves to the left in the product.
3. When 8.7 is multiplied by a negative power of 10, how does the new position of the
decimal point relate to the negative exponent? When the power is negative, the
the number of the exponent gives the number of places the decimal
point moves to the right in the product.
2. If 8.7 is multiplied by a positive power of 10, what relationship exists between the
decimal point’s new position and the exponent? When the power is positive,
8.7 103 8.7 1,000
8.7 102 8.7 100
8.7 101
Read the introduction at the top of page 130 in your textbook.
Write your answers below.
Expression
Expression
Product
1.
Get Ready for the Lesson
2-10
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 2-9 and 2-10)
Lesson 2-10
Chapter 2
Scientific Notation
Study Guide and Intervention
7NS1.1
Write 8.65 107
10
A29
The exponent is positive.
The decimal point moves 4 places.
1.57 10–3
The exponent is negative.
The decimal point moves 3 places.
6. 6.7 106 0.0000067
5. 8.651 102 0.08651
64
Chapter 2
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
12. 0.000581 5.81 104
10. 0.752 7.52 101
11. 0.0064 6.4 103
9. 56,400,000 5.64 107
7. 561 5.61 102
8. 14 1.4 101
4. 2.6 103 0.0026
3. 7.07 105 707,000
Write each number in scientific notation.
2. 9.4 103 9,400
1. 5.3 101 53
Write each number in standard form.
Exercises
Move the decimal point 3 places to the left.
Write 0.00157 in scientific notation.
7.625 104
0.00157 1.57 0.001
Example 4
1
10
1
1
or 0.001
103 1,000
103 3
Write 76,250 in scientific notation.
0.0092
9.2 0.001
76,250 7.625 10,000
Example 3
Move the decimal point 7 places to the right.
107 10 10 10 10 10 10 10 or 10,000,000
in standard form.
Write 9.2 10–3 in standard form.
9.2 10–3 9.2 13
Example 2
86,500,000
8.65 107 8.65 10,000,000
Example 1
A number in scientific notation is written as the product of a factor and a power of ten.
2-10
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Scientific Notation
Skills Practice
Chapter 2
23. 0.0121 1.21 102
21. 0.00000571 5.71 106
19. 0.00916 9.16 103
17. 4,733,800 4.7338 106
15. 79,700 7.97 104
13. 34 3.4 101
8. 7.3 106 0.0000073
6. 8.651 107 86,510,000
4. 3.46 102 346
2. 6.1 104 61,000
7NS1.1
12. 8.50284 102 0.0850284
10. 4.0027 104 0.00040027
65
Glencoe California Mathematics, Grade 7
24. 0.00000018 1.8 107
22. 0.0008331 8.331 104
20. 0.29 2.9 101
18. 2,204,000,000 2.204 109
16. 6,590 6.59 103
14. 273 2.73 102
Write each number in scientific notation.
11. 5.2277 103 0.0052277
9. 1.49 107 0.000000149
7. 3.35 101 0.335
5. 2.91 105 291,000
3. 1.6 103 1,600
1. 6.7 101 67
Write each number in standard form.
2-10
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-10)
Lesson 2-10
Chapter 2
0.000077
6. 7.7 105
7,890
2. 7.89 103
9.9 103
14. 0.0099
7.5 104
10. 75,000
5.15 107
15. 0.000000515
11. 69,900,000
6.99 107
0.000385
7. 3.85 104
411,500
3. 4.115 105
A30
Source: The World Factbook
Country
Australia
Brazil
Egypt
Luxembourg
Singapore
Population
2.0 107
1.9 108
7.7 107
4.7 105
4.4 106
3.07 105
16. 0.0000307
5.75 108
12. 575,000,000
0.00104
8. 1.04 103
3,201,000
4. 3.201 106
7NS1.1
Chapter 2
$1.25 1011
Glencoe California Mathematics, Grade 7
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
66
22. DISASTERS In 2005, Hurricane Katrina caused over $125 billion in damage
in the southern United States. Write $125 billion in scientific notation.
21. MEASUREMENT One centimeter is equal to about 0.0000062 mile. Write
this number in scientific notation. 6.2 106 mile
20. SOLAR SYSTEM Pluto is 3.67 109 miles from the Sun. Write this number
in standard form. 3,670,000,000 miles
Singapore, Australia, Egypt, Brazil
19. POPULATION The table lists the populations
of five countries. List the countries from
least to greatest population. Luxembourg,
18. Which number is less: 7.2 107 or 9.9 105? 9.9 105
17. Which number is greater: 3.5 104 or 2.1 106? 2.1 106
8.4 102
13. 0.084
4.4 103
9. 4,400
Write each number in scientific notation.
0.051
5. 5.1 102
903
1. 9.03 102
Write each number in standard form.
Scientific Notation
2-10 Practice
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 2
$11,700,000,000,000
7. ECONOMICS The U.S. Gross Domestic
Product in the year 2004 was
1.17 1013 dollars. Write this number
in standard notation.
6.5 108 bytes
5. COMPUTERS A CD can store about
650,000,000 bytes of data. Write this
number in scientific notation.
3. MEASUREMENT There are 5,280 feet in
one mile. Write this number in
scientific notation. 5.28 103 ft
2.54 101 mm
Scientific Notation
67
7NS1.1
Glencoe California Mathematics, Grade 7
8. MASS The mass of planet Earth is
about 5.98 1024 kilograms. Write this
number in standard notation.
5,980,000,000,000,000,000,000,000 kg
1,390,000,000 m
6. SPACE The diameter of the Sun is about
1.39 109 meters. Write this number
in standard notation.
186,000 mi per s
4. PHYSICS The speed of light is about
1.86 105 miles per second. Write this
number in standard notation.
2. POPULATION In the year 2000, the
population of Rahway, New Jersey, was
26,500. Write this number in scientific
notation. 2.65 104
Word Problem Practice
1. MEASUREMENT There are about
25.4 millimeters in one inch. Write this
number in scientific notation.
2-10
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 2-10)
Lesson 2-10
Chapter 2
7NS1.1
A31
Diameter
(km)
5.9 103
1.2 104
1.3 104
6.8 103
1.43 105
1.2 105
5.1 104
5.0 104
2.4 103
Distance
from Sun
(km)
5.7 107
1.07 108
1.5 108
2.3 108
7.8 108
1.4 109
2.9 109
4.5 109
5.9 109
Distance
from Earth
(lightyears)
Alpha Centauri
4.27
Sirius (Dog star)
8.7
Arcturus
36
Pleiades Cluster
400
Betelgeuse
520
Deneb
1,600
Crab Nebula
4,000
Center of Milky Way
38,000
Source: pbs.org
Object
Chapter 2
11 times
68
Glencoe California Mathematics, Grade 7
Answers
Glencoe California Mathematics, Grade 7
6. The diameter of Jupiter is how many times the diameter of Earth?
8.7 yr
5. If you see Sirius in the night sky, how long ago was that light emitted from the star?
About 94 times as far
4. The Pleiades Cluster is about how many times as far from Earth as Alpha Centauri?
4.035 1013 km
3. How far is Alpha Centauri from Earth in kilometers?
≈19,667 s, or 5 hr, 27 min, 47 s
2. How long does it take a photon of light to travel from the Sun to Pluto?
500 s
1. How long does it take a photon of light to travel from the Sun to Earth?
Source: wikipedia.com
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Planet
Use the information above and the following tables to answer Exercises 1–6 below.
(2.3 103) (1.4 102) (2.3 1.4) (103 102)
3.22 (10 10 10) (10 10)
3.22 105
When performing operations with numbers in scientific notation, it is often helpful to
consider the decimal part and the power of ten separately.
1 light year (3 108) (3.15 107) 9.45 1015 meters 9.45 1012 kilometers
There are 365 24 60 60 31,536,000 3.15 107 seconds in a year.
1 light year speed of light in meters per second number of seconds in a year.
What travels faster than jets, spaceships, and sound waves? Light does. The speed of light
is about 3 108 meters per second (3 105 kilometers per second). Because distances in
space are so large, they are often discussed in terms of light years, or the distance a
photon of light would travel in a year.
Scientific Notation and Space
2-10 Enrichment
NAME ________________________________________ DATE ______________ PERIOD _____
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Answers (Lesson 2-10)
Chapter 2 Assessment Answer Key
1.
0.125
2.
4.5
3.
4
5
71
3
4.
5.
6.
7.
8.
9.
1
4
1
8
10.
4
Quiz 3 (Lesson 2-6 through 2-8)
Page 72
1.
2.
23
24
1.
C
101
2.
G
3.
A
4.
F
5.
D
6.
H
7.
B
8.
F
12
3.
3.94
4.
1
9
5.
Mid-Chapter Test
Page 73
A
9.
Quiz 2 (Lesson 2-4 and 2-5)
Page 71
5
6
1.
2.
3.
4.
5.
Chapter 2
11
2
1
3
Quiz 4 (Lesson 2-9 and 2-10)
Page 72
1.
16
2.
144
3.
1
125
4.
3.0 103 in.
101
4
82 in.
5
10.
11.
12.
13.
5.
81, 87, 8.9, 8.9
9
8
11
2
33
21 in.
2
103 yd
4
Add 11; 48,
59, 70
A32
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Quiz 1 (Lesson 2-1 through 2-3)
Page 71
Chapter 2 Assessment Answer Key
Vocabulary Test
Page 74
1. dimensional analysis
2.
power
3.
bar notation
4.
like fractions
5.
multiplicative inverses;
reciprocals
6.
exponent
Form 1
Page 75
1.
D
2.
F
3.
C
4.
F
Page 76
11.
D
12.
F
13.
B
14.
H
15.
C
16.
H
17.
A
18.
F
19.
D
20.
F
7. scientific notation
9.
5.
B
unlike fractions
10.
6.
G
7.
D
8.
H
base
Sample answer: a
number whose
remainder is 0
when the division
ends in converting
from a fraction to a
decimal
11.
Sample answer: a
decimal in which
it is impossible to
12. write all the digits
9.
A
10.
J
B:
Chapter 2
A33
Answers
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8. rational numbers
2.21 105
Glencoe California Mathematics, Grade 7
Chapter 2 Assessment Answer Key
1.
A
2.
H
Page 78
11.
12.
Form 2B
Page 79
D
1.
B
2.
F
F
3.
C
3.
C
4.
J
4.
G
5.
13.
C
14.
J
B
5.
15.
6.
7.
B
8.
H
9.
B
10.
J
Chapter 2
16.
H
17.
A
18.
H
19.
B
20.
J
B:
223
7
11.
A
12.
H
13.
B
14.
F
15.
A
16.
J
17.
C
18.
J
19.
A
D
B
F
Page 80
6.
F
7.
B
8.
J
9.
C
10.
J
20.
G
B: 120 in.
A34
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Form 2A
Page 77
Chapter 2 Assessment Answer Key
Form 2C
Page 81
Page 82
0.3
0
1.
14
14.
15.
65
6
50
16.
17.
4.
5.
0.85, 5, 4, 0.79
6
5
18.
7.
8.
9.
77
18
11
6
7
11.
1
6
12.
13.
20.
2
5
10.
19.
7
15
2
111
lb
12
1
15
4.43
7
10
21.
400
22.
1
49
23.
63 feet
24.
0.005297
25.
6.529 104
13
7
B:
Chapter 2
41 c
A35
42
7
Glencoe California Mathematics, Grade 7
Answers
33
3.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9
9
2.
6.
11
Chapter 2 Assessment Answer Key
Form 2D
Page 83
2.
3.
0.26
29
3 50
7
6 9
14.
15.
16.
17.
4.
5.
17,18,1.89,1.93
10 9
6.
18.
19.
7.
12
8.
2
9
9.
10.
11.
12.
13.
Chapter 2
7
8
17
18
25
8
15 3 qt
4
3 7 lb
12
1.9
13
10
20.
13.11
21.
144
22.
1
64
23.
6 more days
24.
16,980
25.
2.1 103
8 1
3
12
3
41
2
43
5
B:
A36
66
25
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1.
Page 84
Chapter 2 Assessment Answer Key
Form 3
Page 85
5.1
2
13.
14.
2.
3.
2 9
50
5 5
9
15.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
16.
4.
5.
6.
16.36
7.
2
27
17.
9.
10.
12
19
11.
8
35
Chapter 2
3 4
5
15
6
23
30
141 in.
2
19.
5.13
31
3
1
142
25
12.
17
Yes, if they
continue the
pattern they can
build 60 feet in
30 days
18.
20.
8.
5
21.
576
22.
16
25
23.
2
24.
0.00002013
25.
9.6103 109
B:
39,000,000 km
21
2
A37
Glencoe California Mathematics, Grade 7
Answers
1.
Page 86
Chapter 2 Assessment Answer Key
Extended-Response Test, Page 87
Scoring Rubric
Specific Criteria
4
The student demonstrates a thorough understanding of the mathematics
concepts and/or procedures embodied in the task. The student has
responded correctly to the task, used mathematically sound procedures,
and provided clear and complete explanations and interpretations. The
response may contain minor flaws that do not detract from the
demonstration of a thorough understanding.
3
The student demonstrates an understanding of the mathematics concepts
and/or procedures embodied in the task. The student’s response to the
task is essentially correct with the mathematical procedures used and the
explanations and interpretations provided demonstrating an essential but
less than thorough understanding. The response may contain minor errors
that reflect inattentive execution of the mathematical procedures or
indications of some misunderstanding of the underlying mathematics
concepts and/or procedures.
2
The student has demonstrated only a partial understanding of the
mathematics concepts and/or procedures embodied in the task. Although
the student may have used the correct approach to obtaining a solution or
may have provided a correct solution, the student’s work lacks an essential
understanding of the underlying mathematical concepts. The response
contains errors related to misunderstanding important aspects of the task,
misuse of mathematical procedures, or faulty interpretations of results.
1
The student has demonstrated a very limited understanding of the
mathematics concepts and/or procedures embodied in the task. The
student’s response to the task is incomplete and exhibits many flaws.
Although the student has addressed some of the conditions of the task, the
student reached an inadequate conclusion and/or provided reasoning that
was faulty or incomplete. The response exhibits many errors or may be
incomplete.
0
The student has provided a completely incorrect solution or
uninterpretable response, or no response at all.
Chapter 2
A38
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Level
Chapter 2 Assessment Answer Key
Extended-Response Test, Page 87
Sample Answers
In addition to the scoring rubric, the following sample answers may be used as
guidance in evaluating extended response assessment items.
2. a. Subtract 31 from 6. First rewrite 31
1. a. To evaluate the expression, first
3
express the mixed number 21 as an
10
as an improper fraction, . Then
2
3
improper fraction, 5. Then multiply
rewrite 6 with the LCD of 3 to get
2
12
6 by 2, the reciprocal of 5, to get .
2
5
Finally, write as a mixed number, 22.
5
2
Eva should make 2 recipes.
5
subtracting 10 from 18 and writing
the difference, 8, over the
denominator, 3, to get 8. Finally,
3
b. To write the fraction 2 as a decimal,
5
write as a mixed number 22.
3
divide the numerator, 2, by the
denominator, 5, to get 0.4. Then add
0.4 to the whole-number part of the
mixed number, 2, to get 2.4.
The second recipe should make
22 dozen.
3
.
b. Expressed as a decimal, 22 is 2.6
Eva should make 2.4 recipes.
3
c. Multiply the number of recipes by
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
18
10
18
. Now subtract from by
3
3
3
the amount of flour per recipe to find
This is a repeating decimal, but the
decimal in Exercise 1b is a
terminating decimal.
c. Add the two amounts to find the
the total amount of flour. First write
the mixed numbers 22 and 11
5
4
12
5
as improper fractions, and
.
5
4
total amount of flour. First rewrite
13 as an improper fraction, 7. Then
4
4
rewrite both fractions with the
Multiply numerator by numerator
21
common denominator of 12, and
and simplify to get 3.
12
8
. Add the numerators to get 29 and
12
Eva needs 3 cups of flour.
29
get . Write as a mixed number,
and denominator by denominator
place this over the denominator 12 to
12
5
2.
12
d. To solve the equation, multiply each
side by 2, the multiplicative inverse
of 1. Then simplify each side to get
2
x 12.
Jaime needs 25 cups of flour.
12
Eva will make 12 packages.
Chapter 2
A39
Glencoe California Mathematics, Grade 7
Answers
5
3
Chapter 2 Assessment Answer Key
Standardized Test Practice
Page 88
1.
A
B
C
D
2.
F
G
H
J
A
B
C
F
G
H
J
5.
A
B
C
D
6.
F
G
H
J
7.
A
B
C
D
8.
F
G
H
J
9.
A
B
C
D
F
G
Chapter 2
H
A
B
C
D
12.
F
G
H
J
13.
A
B
C
D
14.
F
G
H
J
15.
A
B
C
D
16.
F
G
H
J
17.
A
B
C
D
18.
F
G
H
J
D
4.
10.
11.
J
A40
Glencoe California Mathematics, Grade 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3.
Page 89
Chapter 2 Assessment Answer Key
19.
t = November’s
temperature;
t 75
20.
n 6 90;
n 15
21.
2:45
22.
15.75
23.
31
40
24.
5.5
25.
250 people
26.
Answers
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Standardized Test
Page 90
1
1
7
2 mi; Add 1 and .
8
4
8
43 mi; Multiply
8
27.
Chapter 2
11 by 31.
4
2
A41
Glencoe California Mathematics, Grade 7
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