Math 7 Chapter Two Homework
Lesson 2.1.1


2-8. How many tenths are in one whole? How many hundredths? Homework Help ✎
2-9. Convert the following fractions to decimals. Show your work. Homework Help ✎
a.
b.
c.




2-10. Mario ordered a pizza for dinner. When it arrived, Mario quickly ate
of the pizza. While
Mario was getting napkins, his pet poodle ate
of the pizza. Homework Help ✎
a. Draw a model of the pizza that shows the portion that has been eaten.
b. Write a numerical expression to show the fraction of the pizza that is left.
c. About what percent of the pizza is left?
2-11. Nicole has a machine that will produce a number from 1 through 50 when she pushes a
button. Explore by highlighting numbers on the 2-11 HW eTool (CPM). If she pushes the button, what
is: Homework Help ✎
a. P(multiple of 10)?
b. P(not 100)?
c. P(not a mutliple of 4)?
d. P(one-digit number)
2-12. Lyle and his study team are designing spinners. Homework Help ✎
a. If one half of the sections on a spinner are green and there are 14 sections, how many are green?
b. If three fourths of the sections on a different spinner have stripes and there are 24 sections, how
many sections have stripes?
2-13. Which of the fractions listed below will have repeating decimals and which will have terminating
decimals? Explain how you know. Homework Help ✎
a.
b.
c.
d.



2-14. Here are the lengths (in inches) of snakes in a reptile display at the zoo: 10, 31, 36, 36, 38, 42, 47,
48, 49, and 52. Find the mean and median of the lengths. 2-14 HW eTool (CPM). Homework Help ✎
2-15. Thomas has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. For each part below, if
the marble selected is replaced before the next marble is drawn, find the probability for the given draw.
Write your answer as a fraction, as a decimal, and as a percent. 2-15 HW eTool (CPM). Homework Help
✎
a. A red marble?
b. A red or a green marble?
c. An orange marble?
2-16. Finding patterns is an important problem-solving skill used in mathematics. You will use the
patterns in Diamond Problems to solve other problems later in the course. Can you discover a pattern for
the numbers in each of the four diamonds below? Homework Help ✎
Copy the Diamond Problems below and use the pattern you discovered to complete each of them.
a.
b.
c.

d.
2-17. Read the Math Notes box for this lesson. Then rewrite each number below as a single fraction
greater than one. Homework Help ✎
a.
b.
c.
Lesson 2.1.2

2-26. Which of the following fractions are repeating decimals and which are terminating? Show how
you made your decisions. Homework Help ✎
a.
b.
c.


d.
2-27. Copy the portions webs below and fill in the missing parts. Homework Help ✎
a.
b.

2-28. Lila is making a spinner game for her cousins to play. She has divided it into 8 equal sections and
has labeled each section with a symbol. When the spinner lands on a flower (
), her cousins will win
a prize. Create a spinner to explore your ideas! 2-28 HW eTool (CPM). Homework Help ✎
a. What is P( )? Express your answer as a fraction, as a decimal, and as a percent.
b. What is the probability of not getting ? Write your answer as a fraction, as a decimal, and as a
percent.
c. What is P( )? Write your answer as a fraction, as a decimal, and as a percent.
d. If Lila's cousins spin 100 times, about how many times would you expect them to spin a heart (


)?
2-29. Copy the graphs below onto your paper. Then complete the scale by labeling the remaining tick
marks. Homework Help ✎
2-30. Approximately 3 out of every 25 Americans live in California. About 3 out of every 50
Americans live in New York, and about 2 out of every 25 Americans live in Texas. Homework Help ✎
a. Which state has the largest population?
b. Which state has the smallest population?
c. About what percentage of Americans do not live in California, New York, or Texas?
Lesson 2.2.1



2-36. Read the Math Notes box in this lesson. Then use generic rectangles to complete the following
multiplication problems. Homework Help ✎
a. 54 ·32
b. 91 ·78
2-37. Below are some new distances with given lengths to help Cecil cross the tightrope. Find at least
two ways to get Cecil across. Write your solutions as numerical expressions. 2-37a HW eTool
(CPM). 2-37b HW eTool (CPM). Homework Help ✎
a. Span of tightrope: 6 feet
Given lengths: 1, 3, 4 feet
b. Span of tightrope: 8 feet
Given lengths: 2, 5, 7 feet
2-38. Simplify each of the following expressions to find the length of the tightrope. Homework Help ✎
A. 5 + 2 + 8
C. 7 + 3 + 2 + (−4)
B.
D.
4+9+3
8 + 6 + 2 + (−5)

2-39. Copy these incomplete number lines. Label the missing numbers on each of them. Homework
Help ✎

2-40. One of the topics you will review in this course is reading graphs. Look at the graph at right. This
graph shows positive and negative values on both axes. It divides the flat surface into four parts, or
quadrants, and is therefore called a four-quadrant graph. Homework Help ✎

a. The coordinates (the x- and y-values) for point A are (−3, 5). Explain how these numbers tell you
the position of point A using the graph.
b. Name the coordinates (x, y) for points B and C.
c. If Samantha moved point A 9 units down and 6 units to the right, at what point would she end
up?
2-41. Gracie loves to talk on the phone, but her parents try to limit the amount of time she talks. They
decided to keep a record of the number of minutes that she spends on the phone each day. Here are the
data for the past nine days: 120, 60, 0, 30, 15, 0, 0, 10, and 20. 2-41 HW eTool (CPM). Homework Help
✎
a. Find the mean and median for the information.
b. Which of the two measures in part (a) would give Gracie’s parents the most accurate information
about her phone use? Why do you think so?
Lesson 2.2.2

2-51. Write an expression to represent each of the following sketches. Then give the value of each
sketch. Homework Help ✎
a.
b.
c.
d.

2-52. Use the numbers 5, 6, and 7 and the operations of addition, subtraction, multiplication, and/or
division to create three different number expressions with three different values. One of the expressions
should have a value of 37. Homework Help ✎


2-53. Use a number line to show your work as you find the value of each expression. Homework Help
✎
a. −5 + 3.25
b. 3.18 + (−7)
2-54. Rewrite the following fractions as decimals and decide if they are terminating or repeating
decimals. Show your work and explain how you made your decision. Homework Help ✎
a.
b.
c.

d.
2-55. Evan's uncle gave him money for his birthday. Homework Help ✎
a. Evan plans to put half of the money in his savings account, spend
of the money on bubble
gum to share with his friends, and buy comic books with the money he has left. What portion of
the money will he spend on comic books?
b. Evan uses some of his comic-book money to buy a magazine for $4. If Evan’s uncle gave him
$30, what fraction of this money did he spend on the magazine?
Lesson 2.2.3

2-62. Sketch each expression using + and – tiles or draw it on a number line. Then find the
simplified value of each expression. 2-62a HW eTool (CPM). Homework Help ✎
a. −5 + 6 + 4
b. 7 + (−3) + (−4)
c.
d.



2-63. What happens if Cecil goes any number of feet in one direction and then goes the same number of
feet the other direction? Where does he end up? How do you know? Homework Help ✎
2-64. John has a bag of marbles that contains 12 red marbles, 20 green marbles, and 17 blue marbles. 264 HW eTool (CPM). Homework Help ✎
a. If John pulls one marble out of the bag, what is the probability that it will not be red? That is,
P(not red)?
b. What is the probability that he will draw a purple marble? That is, P(purple)?

2-65. Find the missing lengths in the problems below. Assume each line segment is subdivided into
equal segments. Show your work. Homework Help ✎)
a.
b.

2-66. On Saturday, Stella worked for two hours helping her mother around the house. She spent
of
her time doing laundry,
of her time cleaning, and the rest of her time working in the yard. How
much of her time was spent in the yard? Show all of your work. Use a diagram if it helps. Homework
Help ✎
Lesson 2.2.4

2-79. Find the value of each of the following expressions. Use a tile diagram or a number line to help
you, if you need it. Homework Help ✎
a. 3(4)
b. 4 + 11 + (–4)
c. 3.2(2)
d.
e.


f.
2-80. Use the Distributive Property to rewrite each of the following products as sums, and then calculate
the value, as shown in the example below. Homework Help ✎
Example: 4(307) = 4(300) + 4(7) = 1200 + 28 = 1228
a. 9(410)
b. 6(592)

2-81. Copy and complete each of the Diamond Problems below. The pattern used in the
Diamond Problems is shown at right. Homework Help ✎

2-82. Copy and complete each of the portions webs below. Homework Help ✎
a.


b.
2-83. Camille had a very fun birthday party with lots of friends and family attending. The party lasted
for 3 hours. She and her friends played games for
of the time, ate pizza and cake for 50% of the
time, and spent the remainder of the time opening presents. Draw a diagram and make calculations to
show the amount of time spent opening presents. Homework Help ✎
2-84. Jahna measured the heights of the sunflowers growing in her backyard. Here are the heights that
she found (in inches): 34, 48, 52, 61, 76, 76, 61, 84, 61, 39, 83, 61, 79, 81, 56, and 88. Find the mean
and median of the heights. 2-84 HW eTool (CPM). Homework Help ✎
a. Find the mean and median of the heights.
b. Create a histogram to represent this data. Your histogram should have four bins, each with a
width of 15.
Lesson 2.2.5

2-90. Frieda Friendly works for a local car dealership. She noticed that
of the cars are sedans and
that half of them are white. What fraction of the dealership’s cars are white sedans? Homework Help
✎
a. Use a unit rectangle to represent this situation. Label the parts carefully.
b. Write an equation or a sentence that describes the situation, and answer the question.
c. Write your answer from part (b) as a decimal and as a percent.

2-91. In parts (a) and (b) of problem 2-89, the rectangular models for
of
and
of
looked
different, but the answers were the same. Read the steps for the example given in the Math Notes box in
this lesson for how to calculate

of
. Then follow the steps and draw a similar rectangle to
show
of . Are the answers the same? Why or why not? Homework Help ✎
2-92. Simplify each expression. Homework Help ✎
a.


b.
c. −5.37 + 8.14 − 1.89
2-93. Do you think it matters what order you follow when performing math operations? Investigate this
by doing the following problems. Homework Help ✎
a. For the problem 9 + 2(3) do you get the same final answer if you add first as you do if you
multiply first?
b. For the problem (2 · 4) · 7 do you get the same final answer if you start with the first two
numbers as you do if you start with the last two numbers?
2-94. Multiple Choice: Which of the following numbers could not represent a probability? Write a
sentence explaining why they could not. Homework Help ✎
a.
b. 1
c. 1%
d. 0.1
Lesson 2.2.6


2-101. Multiply the mixed numbers. Homework Help ✎
a.
b.
c.
d.


2-102. Below is a fast mental-math technique to find
. Homework Help ✎
a. What is one sixth of 24?
b. What is five times that quantity?
. Remember that
c. What is
?
2-103. Use the above method to calculate mentally each product below. Write an equation for each
problem. Homework Help ✎
a.
b.
c.



2-104. While going on a field trip, a busload of 54 students will have to be split up into
three groups. Two thirds will go to lunch first, and one third will go visit the exhibits. How many will
go to lunch first? Write an equation to represent the problem. Homework Help ✎
2-105. Draw a coordinate grid. Make both the x-axis and y-axis go from –10 to 10. Then plot the
following points. Label each point with its letter. Homework Help ✎

a. (−2.2, 4.64)
b. (8.2, 7.59)
c.
,
d. (0.62, −5.1)
Lesson 2.3.1

2-115. Complete the scaling for each number line or set of axes. Homework Help ✎


2-116. Copy and complete each of the Diamond Problems below. The pattern used in the
Diamond Problems is shown at right. Homework Help ✎


2-117. Copy each expression and then simplify it without using a
calculator. Be sure to show all steps. Homework Help ✎
a.
b.

c.
2-118. Carmen is drawing a card from a standard deck of playing cards. Find each probability below. If
you need a reminder, you may reread the information about a standard deck of cards in problem
1-68. Homework Help ✎
a. What is the probability that she will draw a heart?
b. What is the probability that she will not draw a club?

2-119. Christina collected information about the ages of the players on her softball team. The ages were
10, 12, 14, 13, 12, 11, 13, 12, 11, 12, 12, and 13. Christina wants to describe the players’ ages in an
article for the school newspaper. She does not want to list all of the ages, so should she use the range
(difference between the highest and lowest values) or a measure of central tendency (mean, median) to
describe them? Justify your choice. Homework Help ✎

2-120.This problem is a checkpoint for multiple representations of portions. It will be
referred to as Checkpoint 2.
For each portion of a whole, write it as a percent, as a fraction, and as a decimal. Homework Help ✎


a. 0.43
b. nine tenths
c. 39%
d.
Check your answers by referring to the Checkpoint 2 materials located at the back of your book.
Ideally, at this point you are comfortable working with these types of problems and can solve them
correctly. If you feel that you need more confidence when solving these types of problems, then review
the Checkpoint 2 materials and try the practice problems provided. From this point on, you will be
expected to do problems like these correctly and with confidence.
Lesson 2.3.2

2-124. Troy is a fan of baseball, and his favorite player is Moe Jauer of the Minnesota Triplets. Troy
made a table displaying how many home runs Jauer hit during his first five seasons. Graph Troy’s
data. Homework Help ✎





2-125. Sara turned in the two graphs below for homework, but her teacher marked them wrong. Explain
to Sara what mistakes she made. Then choose one of her graphs to correct, copy it on your paper, and
correct it. Homework Help ✎
2-126. If a set of xy-axes has 20 grid units in each direction and the greatest value of the data to be
placed on the horizontal axis is 132, what would be an appropriate and convenient scale to use for this
axis? Explain. Homework Help ✎
2-127. Simplify each expression. Homework Help ✎
a.
b.
c.

d.
2-128. For each of the experimental results described, write the indicated probability. Homework Help
✎



a. A coin is flipped 80 times. It lands tails 47 times. What is the P(heads)? 2-128a HW
eTool (CPM).
b. A bag contains purple and orange marbles. Sam randomly takes out one marble and then returns
it to the bag. He does this 18 times, and 12 of those times an orange marble is pulled out. What
is P(green)? 2-128b HW eTool (CPM).
c. Sarah pulls a card from a standard deck and then replaces it. She does this 30 times, and 40% of
the time it is hearts. What is the probability that she does not get hearts? (Note: For more
information on standard card decks, refer to problem 1-68.) 2-128c HW eTool (CPM).
2-129. Use your reasoning about numbers to answer the following questions. Homework Help ✎
a. If multiplying by
makes a positive number smaller, then what does dividing by
do to the
value of the number? Explain your reasoning.
b. If multiplying by 1 does not change the value of a number, then what effect does multiplying
by
have? Explain your reasoning.
c. If you find 80% of a number, do you expect the answer to be greater or less than the
number? What if you find 120%? Explain your reasoning.
Chapter 2 Closure
 CL 2-130. Convert the following fractions to decimals and the decimals to fractions.
a.
b.
c. 0.204
d. 0.47
 CL 2-131. Suppose that Cecil, the tightrope walker, can only travel lengths of 5 feet, 6 feet, and 8 feet. He
can travel forward or backward and can go farther than his ladder and come back. Show two number
expressions that represent a way for Cecil to cross a tightrope of the following lengths. Make at least one of
your expressions for each length include a backward movement.
a.
b.
c.
d.
 16 feet
19 feet
13 feet
3 feet
 CL 2-132. Cecil started from Point A and moved according to the expression 8 + (−5) + 7 + 6 + (−7) + 5 +
(−8). What one additional step does Cecil need in order to return to the starting point?
 CL 2-133. Rewrite each of these products as an addition problem and then state the number that the
expression represents.
a. 5(3)
b. 3(−2)
 CL 2-134. George is playing a game, but the spinner is incomplete. Help him figure out what fraction is
missing.

CL 2-135. Multiply

. You may want to copy and complete the diagram at right to show your work.
CL 2-136. Mary has a bag of colored tiles. There are 8 red tiles, 7 blue tiles, 9 yellow tiles, and 12 green
tiles. If she reaches into the bag, what is the probability of picking a:
a. Yellow tile?
b. Green tile?
c. Purple tile?
 CL 2-137. Copy the incomplete axes and fill in the missing numbers so that the scaling is consistent.

a.
b.
 CL 2-138. Use the numbers 0, 1, 2, 2 , 3, 7, 7 , 9, and 10 to answer each of the following questions. Note
that you may use each number as many times as you like.
a. List five numbers with a mean of 5.
b. List five numbers with a mean of 5 and a median of 2 .
c. If a list of five numbers has a mean of 5, what is the largest median that this set of data can have?