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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