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3.1 Modeling Parts of a Whole • 95
Key Terms fraction
numerator
denominator
Learning GoalsIn this lesson, you will:
Determine equal parts of a whole.
Draw different representations of equal parts.
Did you know that the first United States flag had 13 stars on it? You
might have seen some historic flags with the 13 stars in a circle within a field
of blue, or maybe you saw the 13 stars in rows. Because there were no
government guidelines about how the flag’s stars were to be organized in the
blue field in the early days of the United States, the placement of stars varied.
Since 1776, the United States has grown to include 50 states, so, the current
flag has 50 stars. Do you remember what the 13 red and white stripes represent?
FlagsandFractionsModeling Parts of a Whole
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Problem 1 Part-Whole
In this chapter you will be adding to your knowledge of fractions. As you learned in
elementary school, a fraction represents a part of a whole object, set, or unit. A fraction is
written using two whole numbers separated by a bar. The number above the bar is the
numerator, and the number below the bar is the denominator. The denominator (bottom
number) indicates how many parts make up the whole, while the numerator (top number)
indicates how many parts are counted.
96 • Chapter 3 Fractions
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There are 10 total bowling pins and 3 of the pins are knocked
down.
You can represent this situation as:
3 ___ 10
→ numerator ____________ denominator
→ the number of bowling pins knocked down
_______________________________________ the total number of bowling pins
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3.1 Modeling Parts of a Whole • 97
The Student Bowler Association (SBA) is an organization of student bowlers in Grades 3
through 8. Each of the SBA bowling teams consists of two student bowlers. Each team is
asked to design two flags to represent the two players on the team. Each team flag must
be labeled and evenly divided into thirds, fourths, fifths, sixths, eighths, or twelfths. Each
flag has the same dimensions as shown.
1. Describe the dimensions and total area of the flag.
Team members Yvonne and Matthew each designed a flag and labeled them “Fourths”
and “Thirds.”
Matthew’s Flag
Fourths
Yvonne’s Flag
Thirds
If labels aren't provided,
use the word "unit"” to describe the
dimensions.
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They showed their flags to team members Dante and Miko. Dante looked at the flags and
said, “Your flags don’t seem correct. Look at our flags.”
Dante’s Flag
Fourths
Miko’s Flag
Thirds
Ashley looked at all four flags and said, “You are all correct! Each flag shows equal parts
of a whole.”
2. For each question, explain why Ashley’s statement is correct.
a. How are both Matthew’s and Dante’s flags of fourths correct? Explain your answer
by describing how each flag shows equal parts of the whole.
b. How are both Yvonne’s and Miko’s flags of thirds correct? Explain by describing
how each flag shows equal parts of the whole.
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3.1 Modeling Parts of a Whole • 99
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Let’s analyze another fractional representation.
3. A rectangular flag is divided into 24 equal parts, and 15 of those parts are shaded.
a. Represent the portion of the flag that is shaded as a fraction. Then describe what
each number of the fraction represents.
b. Does the shaded portion of the rectangular flag shown represent 15 ___ 24
?
Explain your reasoning.
c. Shade a different representation for 15 ___ 24
. Explain how you know you are correct.
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Fractions can be represented in different ways as long as they have the same equal
number of units dividing the whole. This means the way the model of the fraction looks
does not affect the value of the fraction.
4. Draw three different flags for each fraction. Show how you know you have equal parts
by writing how many square units are in each part. Then describe how you made your
flags. Extra grids are included for workspace.
a. Halves
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3.1 Modeling Parts of a Whole • 101
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b. Thirds
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c. Fourths
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3.1 Modeling Parts of a Whole • 103
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d. Sixths
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e. Eighths
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3.1 Modeling Parts of a Whole • 105
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f. Twelfths
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Problem 2 Who’s Correct? 1. Carmen designed a flag and shaded half of it. Did she correctly label her flag?
Explain your reasoning.
2. Katy wondered if she could make a flag using fifths. Katy had an idea and drew these
lines on her flag and said her flag was divided into fifths. Is she correct?
Explain your reasoning.
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3.1 Modeling Parts of a Whole • 107
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3. What do you think? Can you make fifths in the rectangular flag shown? If so, draw the
flag. Explain your reasoning.
4. Represent each fraction on the 10 3 10 grid by shading.
a. 1 __ 2
b. 1 __ 4
c. 3 __ 4
d. 1
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Problem 3 Think Backward
1. Use these flag pieces to answer each question.
A
B
C
D
a. If A 5 1, then B 5 , C 5 , D 5 .
b. If B 5 1, then A 5 , C 5 , D 5 .
c. If C 5 1, then A 5 , B 5 , D 5 .
d. If D 5 1, then A 5 , B 5 , C 5 .
As you answer each question, think
of the given shape as "one whole." Are the other shapes smaller or larger
than the whole?
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3.1 Modeling Parts of a Whole • 109
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Problem 4 Fractions of a Set
1. The seventh grade class is collecting books for the local children’s hospital library.
They have collected:
● 16 books about animals
● 8 books about sports
● 20 books about different cultures
● 10 biographies
● 6 mysteries
● 12 books about ancient civilizations
Represent each book type in the collection of books as a fraction.
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Problem 5 Fundraising Goals
The eighth-grade class at Carnegie Middle School decided to sell pom-poms at all the
sporting events. The money from the sales will be donated to the local children’s hospital.
Each homeroom set a different goal, displayed at the top of each thermometer. The total
money raised so far by each homeroom, including today’s donations, is shaded.
GOAL: $180 $120 $100 $80 $120
HR804 HR805 HR806 HR807 HR808
Yolanda is in charge of announcing the progress of the pom-pom fundraiser during the
morning announcements. She announces that Homeroom 805 (HR 805) has raised the
most money so far.
1. Do you think Yolanda is correct? Explain why or why not. If you think Yolanda is
incorrect, determine which homeroom has raised the most money.
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3.1 Modeling Parts of a Whole • 111
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2. Complete the table shown using the information from the fundraising thermometers.
Homeroom
FractionalPartoftheGoal
CompletedasofToday
MoneyRaised(indollars)
HR 804
HR 805
HR 806
HR 807
HR 808
a. Is it better to announce the fractional part of money raised or the actual amount of
money raised? Why?
b. If HR 804 raises 11 ___ 12
of their goal, how much money would they have raised?
c. If HR 807 raises 3 __ 5 of their goal, how much money would they have raised?
d. If HR 805 raises 7 ___ 12
of their goal, how much money would they have raised?
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112 • Chapter 3 Fractions
3. Let’s consider the same thermometers, but this time all the homerooms have the
same goal. How much money has each homeroom raised?
a. Homeroom 804
b. Homeroom 805
c. Homeroom 806
d. Homeroom 807
e. Homeroom 808
Be prepared to share your solutions
and methods.
Don't forget you just calculated the fractional part of
each thermometer's shaded region in the
previous table.
$300 $300 $300 $300 $300
HR804 HR805 HR806 HR807 HR808
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3.2 Fractional Representations • 113
Pattern blocks can be used to show fractions. Pattern blocks are a relatively
new mathematical model that was invented in the 1960s. You will use pattern
blocks in this lesson. What shapes are the pattern blocks? Have you ever used
pattern blocks before?
Learning GoalsIn this lesson, you will:
Create different fractional representations using pattern blocks.
Write fractional statements for different representations given the whole.
Determine fractional representations given the whole.
Determine fractional representations given parts of the whole.
YouMeanThreeCanBeOne?Fractional Representations
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Problem 1 Hexagonal Fractions
1. Complete the table shown. Use your yellow hexagon to represent the whole, or 1.
Yellow
ShapeNameofShape
FractionalPartofWhole
Number of Fractional Parts to
Make a Whole
red
blue
green
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3.2 Fractional Representations • 115
2. Create different representations for the yellow hexagon.
Follow the example shown.
● Start with the yellow hexagon.
● Cover the yellow hexagon with other pattern blocks.
● Record your designs.
● Write a fraction sentence to describe your design.
● Repeat the process to create as many representations as possible.
You can place different pattern blocks on top of the yellow
hexagon to create another representation for the whole. For
example, you can create the design shown.
red
green
green green
As you saw from the table you completed, a red trapezoid
covers 1 __ 2
of the hexagon, and a green triangle covers 1 __ 6
of
the trapezoid. So, in this example, the red trapezoid
covers 1 __ 2
of the hexagon, and 3 triangles cover 1 __ 2
of the
hexagon. The fraction sentence for this representation would
be 1 5 1 __ 2 1 1 __
6 1 1 __
6 1 1 __
6 .
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3.2 Fractional Representations • 117
3. How did you know you had determined all the combinations?
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118 • Chapter 3 Fractions
Problem 2 You Mean Three Can Be One?
Recall the title of this lesson: “You Mean Three Can Be One?” You will now determine the
parts of a whole when the whole is more than one hexagon.
1. The three hexagons shown represent the whole, or 1. Determine what fractional part
each pattern block shape represents. Explain your reasoning.
a.
Yellow 1 hexagon
Keep in mind, these 3 hexagons
represent the whole. Are the new figures given smaller or larger than
the whole?
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3.2 Fractional Representations • 119
b.
red 1 trapezoid
c.
blue 1 rhombus
d.
green 1 triangle
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2. Complete each statement.
a.
If red 5 1, then Yellow 5 .
green 5 .
blue 5 .
b.
If blue
5 1, then Yellow 5 .
green
5 .
red
5 .
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3.2 Fractional Representations • 121
c.
If
green
5 1, then Yellow 5 .
blue
5 .
red 5 .
d.
green
Yellow If 5 1, then Yellow 5 .
green
5 .
red
5 .
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e.
If
green
green
5 1, then Yellow 5 .
green5 .
red
5 .
f.
red
blue
If 5 1, then Yellow 5 .
green
5 .
red
5 .
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3.2 Fractional Representations • 123
3. Build and sketch each representation for the description given.
a. A triangle that is two-thirds red, one-ninth green, and two-ninths blue.
b. A parallelogram that is three-fourths blue and
one-fourth green.
c. A trapezoid that is two-thirds blue and one-third green.
Now, think in reverse. What will the whole look for each description?
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d. A parallelogram that is one-half red and one-half blue.
e. A triangle that is one-third green and two-thirds red.
f. Create a puzzle for your partner to solve using three pattern block types. Make
sure it is possible to create.
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3.2 Fractional Representations • 125
4. Determine each fractional representation by drawing a model.
a.
If is 1, what is 3 __ 4
?
b.
If is 1, what is 3 __ 4
?
c. If is 1, what is 3 __ 4
?
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d.
If is 2 __ 3
, what is 1?
e.
If is 1 1 __ 2 , what is 1?
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3.2 Fractional Representations • 127
f.
If is 1
1
__
2
, what is 1?
g. If is 1 1 __ 2
, what is 1?
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h.
If is 2, what is 1 __ 2
?
Talk the Talk
1. Describe a method for determining the value of a fractional part of any set.
Be prepared to share your solutions and methods.
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3.3 Dividing a Whole into Fractional Parts • 129
Key Terms unit fraction
equivalent fractions
Learning GoalsIn this lesson, you will:
Create equal parts of a whole.
Determine if fractions are equal.
Graph fractions on a number line.
Is there more news in a newspaper or are there more advertisements? In
addition to supplying news stories, newspapers routinely sell advertisement space
on each page. With your partner, take a section from a newspaper and measure
the size of each article in the section’s first four pages. Then, measure the size of
each advertisement in the first four pages. What do you notice?
RocketStripsDividing a Whole into Fractional Parts
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Problem 1 Newspaper Column Preparation
You signed up to participate in the school newspaper club. During the first meeting, faculty
advisors Ms. Foster and Ms. Shu showed everyone copies of last year’s publication of the
Rocket. The teachers have already planned out the sections for this year’s Rocket.
Matthew volunteered to create the “Random Acts of Kindness” section. The section
will appear along the right side of the paper’s back page. The newspaper is printed on
8 1 __ 2 -inch by 11-inch paper.
Matthew plans to put a box in each homeroom and ask students to nominate classmates
for the monthly recognition of random kindness acts. Students must tell what nice act their
nominee performed on a nomination slip. In preparation for completing his section, help
Matthew plan the layout of the column; do not worry about the top or bottom margin of
the page.
1. To begin, cut eight strips of paper the length
of a newspaper page. Remember, the
Rocket is printed on 8 1 __ 2 -inch by 11-inch
paper. Each strip of paper should be 1 inch
wide. The strip represents one whole column.
Do not fold the first strip, and label it as 1 whole.
2. Take one of your paper strips and fold it carefully in half to divide the
strip into two equal parts like the one shown. Label each folded part
of the paper strip with the appropriate fraction, and draw a line to
mark your fold. The strip shown will represent a column that
recognizes two students.
12
12
The strips are provided for
you at the end of this lesson.
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3.3 Dividing a Whole into Fractional Parts • 131
3. Take another paper strip and fold it carefully in half two times. Unfold and draw lines to mark
your folds. Then, label each folded part of the paper strip with the appropriate fraction.
How many students can be recognized in this column?
4. Take another paper strip and fold it in half three times. Be very careful to fold
accurately. Unfold and draw lines to mark your folds. Then, label each folded part of
the paper strip with the appropriate fraction.
How many students can be recognized in this column?
5. Take another paper strip and fold it very carefully in half, four times. Unfold and draw
lines to mark your folds. Then, label each folded part of the paper strip with the
appropriate fraction.
How many students can be recognized in this column?
6. Take another paper strip and fold it carefully into three equal sections. Unfold and
draw lines to mark your folds. Then, label each folded part of the paper strip with the
appropriate fraction.
How many students can be recognized in this column?
7. Take the next paper strip and fold it into thirds, and then fold the strip in half. Unfold
and draw lines to mark your folds. Then, label each folded part of the paper strip with
the appropriate fraction.
How many students can be recognized in this column?
8. Finally, take your last paper strip and fold it into thirds. Then, fold in half, and then fold
in half once more. Unfold and draw lines to mark your folds. Then, label each folded
part of the paper strip with the appropriate fraction.
How many students can be recognized in this column?
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Arrange your strips in a column so that all of the left edges are lined up and the strips are
ordered from the strip with the smallest parts to the strip with the largest parts.
9. As the number of students who can be recognized in the column increases, describe
what happens to the space for each student.
A unitfraction is a fraction that has a numerator of 1 and a denominator that is
a positive integer.
10. List the unit fractions for each strip you
created in ascending order.
11. Explain how understanding the size of a
unit fraction helps you determine the size of
the whole.
To list a set in ascending order
means to list the set from least to greatest.
To list a set in descending order means to list the set from
greatest to least.
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3.3 Dividing a Whole into Fractional Parts • 133
If you folded the paper strips carefully, you will notice that some of the folds line up with
each other. Fractions that represent the same part-to-whole relationship are equivalent
fractions.
12. Show that 1 __ 2
is equivalent to 6 ___
12 . Draw on the paper strips to represent halves and
twelfths. Then, shade the strips to represent 1 __ 2 and 6 ___
12 .
13. Make a collection of equivalent fractions using your fraction strips. Then, complete
the graphic organizer by writing all the equivalent fractions for each.
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2__3
1
1__2
3__4
EquivalentFractions
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3.3 Dividing a Whole into Fractional Parts • 135
14. What do you notice in the collection of equivalent fractions? Give an example to
justify your answer.
Talk the Talk
1. What do you notice about the numerator and denominator of the equivalent
fractions?
2. What do you need to do to both the numerator and the denominator of a fraction in
order to write another equivalent fraction?
Be prepared to share your solutions and methods.
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3.5 Equivalent Fractions • 153
Key Terms Multiplicative Identity Property
simplest form
Learning GoalsIn this lesson, you will:
Determine equal portions of a whole.
Determine equivalent fractions.
Calculate equivalent fractions using
a form of 1.
Simplify fractions.
Determine equivalent fractions
in context.
Order fractions.
What’sMyCut?Equivalent Fractions
Today, you can take your coins to the grocery store to have them counted by a
machine. You can exchange your coins for a cash voucher, gift cards, or you can
even donate your coins to charity.
Careful, though. Unless you’re donating your money, these machines usually take
a “cut” of about 10 cents for every one of your dollars that it counts.
One of the largest transactions recorded for one of these machines was in San
Dimas, California. A customer turned in over $8000 worth of coins! What was the
machine’s “cut”?
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Problem 1 Pizza Cuts
1. Coach Finley buys pizzas to share with everyone who participated in the volleyball
intramural program. She buys 21 pizzas to share among the 28 students who are
sitting at tables of four.
a. How many pizzas should each table receive if she wants each table to receive the
same amount of pizza? Explain your reasoning.
b. Coach Finley suggests dividing each pizza into fourths. Draw a diagram that
represents the problem. Then, explain her reasoning.
c. What fractional part of a pizza will each student receive?
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3.5 Equivalent Fractions • 155
d. Mario suggests dividing the pizzas in half. Will Mario’s method work? Why or why
not? If Mario’s suggestion is not possible, explain what he can do to make his
suggestion work. Draw a diagram that supports your explanation.
e. Sydney tries to divide his group’s pizzas into thirds. Will Sydney’s method work?
Why or why not? If Sydney’s method is not possible, explain what he can do to
make his method work. Draw a diagram that supports your explanation.
f. Natalie tries to divide her group’s pizzas into eighths. Will Natalie’s method work?
Why or why not? If it is not possible, explain what she can do to make her method
work. Draw a diagram that supports your explanation.
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156 • Chapter 3 Fractions
g. Name the student(s) whose method did not require your suggestion. Then, name
the fractional part of a pizza each student at the table will receive.
h. Juanita claims that dividing the pizzas into any number of equal-sized pieces will
work to divide the pizzas equally among the 4 students in her group. Is she correct?
Explain your reasoning and offer a solution if Juanita’s method does not work.
2. Casey and Jamal are talking about pizza parties they had in each of their classes.
Casey said, “In my class, four people shared three pizzas.” Jamal said, “In my class,
three people shared two pizzas.”
a. Which student’s classmates each got more pizza? Use a drawing or diagram to
explain your reasoning. Assume the pizzas are the same size.
All this talk of pizza
is making me hungry!
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3.5 Equivalent Fractions • 157
Problem 2 Equivalent Fractions
Throughout this chapter, you have encountered equivalent fractions. Recall that equivalent
fractions are fractions that represent the same part-to-whole relationship.
When determining equivalent fractions, you must multiply the numerator and the
denominator of a fraction by the same
number. This process is the same as
multiplying the given fraction by a
fraction with the same numerator and
denominator, such as 3 __ 3
.
Recall that any fraction whose
numerator and denominator are the
same number is equivalent to 1.
Multiplying any number by 1 does not
change that number.
1. Complete each number sentence with the correct fraction to make it true. Explain
your reasoning. Use your fraction strips if you need help determining the missing
fraction to make equivalent fractions.
a. 5 __ 6
3 ( )
_____ ( )
5 15 ___ 18
b. 3 __ 4
3 ( )
_____ ( )
5 15 ___ 20
c. 5 __ 8 3
( ) _____
( ) 5 15 ______
( ) d. 9 ___
27 3
( ) _____
( ) 5
( ) _____
27
To change a fraction to an equivalent
fraction with a larger numerator
and denominator, you multiply
the fraction by a form of 1.
For example,
5 __ 8
3 3 __ 3 5 15 ___
24 .
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2. You just multiplied each fraction by the same number. What number was it?
The MultiplicativeIdentityProperty states: a 3 1 5 a, where a is a nonzero number.
3. Complete each equation to make the fractions equivalent. Explain your reasoning.
Use your fraction strips if you need help determining equivalent fractions.
a. 1 __ 4
5 ( )
_____ 16
b. 2 __ 3
5 ( )
_____ 6
c. 7 ___ 16
5 ( )
______ 32
d. ( )
_____ 12
5 3 __ 4
e. 1 ___ 18
5 1 ______ ( )
4. Write the first 10 equivalent fractions of each using what you know about equivalent
fractions. The first example is done for you.
a. 1 __ 4
, 2 __ 8
, 3 ___ 12
, 4 ___ 16
, 5 ___ 20
, 6 ___ 24
, 7 ___ 28
, 8 ___ 32
, 9 ___ 36
, 10 ___ 40
b. 3 __ 5
,
c. 2 __ 3 ,
d. 5 __ 8 ,
e. How did you determine the order to list your equivalent fractions?
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3.5 Equivalent Fractions • 159
Whenever you determine an equivalent fraction whose numerator and denominator are
smaller than the original fraction’s numerator and denominator, the new fraction is simpler.
When a fraction cannot be simplified further, the fraction is in simplest form, or completely
simplified. Simplestform is a way of writing a fraction so that the numerator and
denominator have no common factors other than 1.
You can say a fraction is in a simpler form in several ways:
“ 1 __ 2 is simpler than 4 __
8 .”
“ 1 __ 2 is a simplified form of 4 __
8 .”
“ 4 __ 8 in simplest form is 1 __
2 .”
Sometimes it is read:
“ 1 __ 2 is the simplified form of 4 __
8 .”
“ 1 __ 2 is in lowest, or simplest, terms.”
5. Determine if each fraction is simplified completely. If the fraction is not simplified
completely, write the fraction in simplest form.
a. 9 ___ 24
5 9 4 3 _______ 24 4 3
5 3 __ 8
b. 6 ___ 12
5 6 4 3 _______ 12 4 3
5 2 __ 4
c. 18 ___ 27
5 18 4 3 _______ 27 4 3
5 6 __ 9
To change a fraction to an equivalent fraction with a smaller numerator and
denominator, you must divide the numerator and denominator by a form of 1.
For example, 15 ___ 24
4 3 __ 3
5 5 __ 8 .
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160 • Chapter 3 Fractions
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6. Circle the fractions that are simplified completely. How do you know?
9 ___13
10 ___ 32
9 ___ 12
12 ____ 144
7 ___ 12
33 ___ 55
Recall that the factors of a number are those numbers that divide into the number with
no remainder.
7. How can you use factors of a number to simplify fractions?
8. Write each fraction in simplest form.
a. 6 __ 9
b. 9 ___ 12
c. 8 ___ 24
d. 12 ___ 15
e. 18 ___ 36
f. 14 ___ 42
g. Explain how you simplified each fraction.
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3.5 Equivalent Fractions • 161
9. Ms. Glick asked her students to simplify 24 ___ 36
. Jose, Sara, and Clifton’s methods are
shown. Analyze each method and solution to determine if it is correct. If one of the
methods is incorrect, what would you tell the student to do to correct his or
her method?
Jose:
Isimplified24___36byfirstdividingboththenumeratoranddenominatorby2.Ithen
continueddividingby2untilthefractioncouldnotbeevenlydividedby2__2.
24___36=
24:_2______36:_2=
12___
18=
12:_2______18:_2=
6__9
Sara:
IdividedboththenumeratoranddenominatorbytheGCFof12and
gotaquotientof2__3.
24__36=24:_12______36:_12=
2__3
Clifton:
Iwrotetheprimefactorizationofthenumeratoranddenominator,andthenIdividedoutthecommonprimefactors.
24___36=2x2x2x3_________2x2x3x3=2__3
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10. Simplify each fraction using prime factorization.
a. 15 ___ 20
b. 8 ___ 24
c. 24 ___ 28
d. 20 ___ 24
e. 24 ___ 30
f. 8 ___ 15
11. Simplify each fraction using the GCF. State the GCF used.
a. 24 ___ 28
b. 45 ___ 56
c. 33 ___ 77
d. 16 ___ 32
e. 63 ___ 72
f. 72 ___ 99
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3.5 Equivalent Fractions • 163
Problem 3 Vegetable Lasagna Recipe
Shauna has invited three of her friends to come to her house to watch the big game. She
decides to make a pan of her famous vegetable lasagna for the four of them to enjoy. The
ingredients Shauna uses in her lasagna are shown.
1. The only measuring cups that Shauna owns are a 1 __ 8
-cup measuring cup and a 1-cup
measuring cup. How can Shauna use the 1 __ 8 -cup measuring cup for:
● the chopped green pepper?
● the chopped onion?
● the parmesan cheese?
VegetableLasagna
16 ounces lasagna noodles 52 ounces pasta sauce
1 cup fresh mushrooms 1 1 __ 3
teaspoon dried basil
3 __ 4
cup chopped green pepper 15 ounces ricotta cheese
1 __ 4
cup chopped onion 4 cups shredded mozzarella cheese
3 cloves of garlic 2 eggs
2 tablespoons vegetable oil 1 __ 2
cup parmesan cheese
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2. Shauna’s friend Gustavo brought two cheese quesadillas to share among the four
friends. Each quesadilla is cut into 8 pieces.
Shauna
If we divide the quesadillas evenly,
each of us will receive 4 __ 16 of the
total amount.
GustavoWe will each have 2 __
8 of the
quesadillas if we split them up
evenly.
Explain why both Shauna and Gustavo are correct.
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3.5 Equivalent Fractions • 165
Problem 4 Frac-O
Frac-O is played with two players. The object of the game is to be the first player to
arrange five fraction cards on the game board in ascending order. To begin, cut apart the
16 Frac-O fraction cards.
Directions:
1. Shuffle the fraction cards. Deal one card face down on each of the five spaces on
each player’s game board.
2. Put the remaining cards face down in a pile. Turn the top card over and place it in a
discard pile.
3. Each player turns over the five cards on his or her game board. You may NOT change
the order of the cards at any point during the game.
4. Players take turns as follows:
a. The first player takes either the top card from the face down pile or the top card
from the discard pile.
b. The player decides whether to keep the card or put it face up in the discard pile.
c. If the player keeps the card, he or she must replace one of the five cards on the
game board with the card drawn. The replaced card now goes face up on the
discard pile.
5. If all the facedown cards are used, then shuffle the discard pile and continue.
6. The winner is the first person to have all five cards in ascending order.
Good Luck!
Be prepared to share your solutions and methods.
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3.5 Equivalent Fractions • 167
3 __ 5
1 ___ 12
3 __ 4
1 __ 5
1 __ 3
11 ___ 12
4 __ 7
5 __
6
3 __ 8
1 __ 4
7 __ 9
2 __ 3
4 __ 9
3 __ 7
4 __ 5
5 __ 8
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3.5 Equivalent Fractions • 169
Fra
c-O
Gam
e B
oar
d
Clo
sest
to 0
Clo
sest
to 1
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