LE
SS
O
N
15
EXAMPLE A
1
Understanding Equivalent Fractions
2
4
Are __
​ 3 ​and __
​ 6 ​equivalent fractions?
2
Make a model to show __
​ 3 ​.
2
3
2
4
Make another model to show __
​ 6 ​.
The wholes must be the same size. 2
3
4
6
3
2
Compare the part that shows __
​ 3 ​
4
with the part that shows __
​ 6 ​.
The shaded part of each model is
the same size.
2
4
▸ The models show that __​ 3 ​and __​ 6 ​are
equivalent fractions.
106 Domain 3: Number and Operations—Fractions
M O DE L
1
2
Show that __
​ 3 ​ and __
​ 6 ​are equivalent
fractions.
Duplicating any part of this book is prohibited by law.
The models are the same size. EXAMPLE B
1
3
2
Are __
​ 4 ​and __
​ 6 ​equivalent fractions?
2
Draw a number line in fourths. Find __
​ 4 ​.
1
4
0
2
2
4
3
4
1
3
4
1
3
Make another number line in sixths. Find __
​ 6 ​.
1
4
0
0
1
6
2
4
2
6
3
6
4
6
3
5
6
1
Compare the locations of the
3
2
points for __
​ 4 ​and __
​ 6 ​.
2
The point for ​ __
4 ​lines up exactly
Duplicating any part of this book is prohibited by law.
3
with the point for __
​ 6 ​. M O DE L
2
3
Draw a model to show that __
​ 4 ​and __
​ 6 ​
are equivalent fractions.
2
▸ The number lines show that __​ 4 ​
3
and __
​ 6 ​are equivalent fractions.
Lesson 15: Understanding Equivalent Fractions 107
EXAMPLE C
1
What fraction with a denominator of 8 is equivalent to __
​ 2 ​? 
1
1
Think of the problem as __
​ 2 ​ 5 __
​ 8  ​.
1
Use a fraction strip to show __
​ 2 ​.  
1
2
2
1
Use __
​ 8 ​ fraction strips to match the
1
length of __
​ 2 ​. 
1
2
1
8
3
1
8
1
8
1
8
Write the equivalent fraction.
1
Four ​ __
8 ​ fraction strips are the same
1
length as __
​ 2 ​. 
1
4
​ 8 ​.
Four __
​ 8 ​ fraction strips show __
4
1
__
So ​ __
8 ​is equal to ​ 2  ​.
1
TRY
Use the fraction strips below. What fraction with a denominator
1
of 6 is equivalent to __
​ 2  ​?
1
2
1
6
108 Domain 3: Number and Operations—Fractions
1
6
1
2
1
6
1
6
1
6
1
6
Duplicating any part of this book is prohibited by law.
4
▸ ​ __8 ​ is equivalent to __​ 2 ​. 
EXAMPLE D
Name a fraction with a denominator of 3 that is equal to 1.
1
Think of the problem as 1 5 __
​ 3  ​.
Use a number line. The denominator is 3. Make 3 equal
parts from 0 to 1.
0
1
2
Label each mark with a fraction.
0
3
2
3
1
3
3
3
0
3
1
Write the equivalent fraction.
3
The fraction ​ __
3 ​names the same
point as 1.
3
▸ ​ __3 ​ is equivalent to 1.
C HE C K
Duplicating any part of this book is prohibited by law.
Shade the model below to check
1
that three __
​ 3 ​s  make 1 whole.
1
3
1
3
1
3
Lesson 15: Understanding Equivalent Fractions 109
Practice
Are the fractions equivalent? Write yes or no.
1.
2.
3.
3
4
1
2
1
3
2
8
2
4
H
IN
T
3
6
Are the shaded
parts equal?
Fill in the numerator to write equivalent fractions.
1
6
6.
110 5.
1
3
1
8
1
6
1
__
​ 3 ​ 5 ___
​  6   ​
1
4
REMEMBER Find how
many sixths are equal
to one third.
0
1
0
1
2
__
​ 3 ​5 ___
​  6   ​
Domain 3: Number and Operations—Fractions
1
4
1
8
1
8
1
4
1
8
1
8
1
8
3
__
​ 4 ​5 ___
​  8   ​
7.
0
1
0
1
1
__
​ 2 ​ 5 ___
​  6   ​
Duplicating any part of this book is prohibited by law.
4.
Use the models to write equivalent fractions.
8.
9.
5
5
Use the model to write a fraction for 1 whole.
10.
11.
12.
___
​   ​ 5 1
___
​   ​ 5 1
___
​   ​ 5 1
Choose the best answer.
Duplicating any part of this book is prohibited by law.
13. Which fraction is equivalent to 5?
14. Which fraction is equivalent to 8?
5
A. ​ __
5 ​
4
A. ​ __
4 ​
5
B. ​ __1  ​
8
B. ​ __
8 ​
1
C. ​ __
5  ​
1
C. ​ __
8 ​ 
1
D. ​ _1 ​
8
D. ​ __1 ​ 
Solve.
15. IDENTIFY Write a fraction that is
equivalent to 6. Explain why the
fraction is equivalent to 6.
16. DEMONSTRATE Use the number line
to show that 1 whole is equivalent
to a fraction with a denominator
of 8. Plot the point and label the
fractions.
0
1
Lesson 15: Understanding Equivalent Fractions 111