Answer Key • Lesson 3: Find Equivalent Fractions
Student Guide
Find Equivalent Fractions
For Questions 1–9, use the fraction circle pieces and the Equivalent
Fractions Chart in your Student Activity Book. The red circle is the unit
whole.
1. Frank looked at his Equivalent Fractions Chart. He made a list of all the
1
fractions that are equivalent to ⫺
3 .
1 =—
2 =—
4
—
—
3 6 12
Frank knew that equivalent fractions have the same value. He decided to
1
1
10
find other fractions equivalent to ⫺
3 . He wrote ⫺
3 ⫽⫺
30 . Do you agree with
Frank? Explain.
2
, so
=
.
2
10
2. Jessie showed the strategy she used to decide ⫺
6 ⫽⫺
30 .
2 x 5 = 10
2 = ————
2
–
30
6 6 x 5 ——
2 2strategy.
2
I used a multiplication
I multiplied both the
10 , so 2 = 10 .
numerator and denominator by 5 and got ——
—
30
30
6 ——
=. . .
Use Jessie’s multiplication strategy to find other fractions that are
2
2
equivalent to ⫺
6 .
6
2
2
2
2
2, then
2—
6 == —.—
2 2=2–2——
–—— = —
6–
and B.
= —
=—
A. — = ———— = ——
C. —
=—
—
6 62
6 66
6 6
18
D. Explain why multiplying both the numerator and denominator by the same
number will result in an equivalent fraction.
2
and
=
22 2
and
64
, then
=
=
Copyright © Kendall Hunt Publishing Company
Find Equivalent Fractions (SG pp. 64–67)
Questions 1–9
1.*Yes; Possible response: If you multiply both the
numerator and denominator for –13 by 10, the
– . So –13 is equivalent to
new fraction will be 10
30
10
–.
30
–4
B. 12
–
C. –33
2. A. 12
36
D.*When you multiply both the numerator and
denominator by the same number it is like
multiplying it by one. That means the
fraction has the same value, but it is divided
into a different number of pieces.
B.* false
C.* true
3. A.* true
D.* Possible response: I used the Equivalent
–3 is equal to –14 .
Fraction Chart to see that 12
I then multiplied both the numerator and
denominator for –14 by 5 and the fraction is
–5 . That means that –14 12
–3 20
–5 .
20
B. –45
C. –99
4. A. –35
D. When you divide both the numerator and
dominator by the same number it is like
dividing by one. That means the fraction has
the same value, but it is just divided into a
different number of pieces.
.
= , then
, then
, then
= = == = =. . .
SG • Grade 5 • Unit 2 • Lesson 3
Student Guide - Page 64
Find Equivalent Fractions
2
2
2
2
, so
=
, so
=
, so
=
2
2
5
3. John showed the multiplication strategy he used to decide that ⫺
6 ⫽⫺
15 .
2
2
2
1
5
1
I know that ⫺
multiply both the
6 ⫽⫺
3 . Does ⫺
3 ? Is there a number I can
15 ⫽ ⫺
5
numerator and the denominator by to make the fraction ⫺
15 ?
, so
=
2
5
1 = 1 x 5 = ——
–
3 x 5 15
3 ————
5
1 2 ——
1 2
1 5
If —
6 = 15 .
3=—
3=—
3 = ——
15 , then —
6 and —
2
2
2
and
, then= and
= , then
= = . =, then
=
.=
=
.
Use John’s multiplication strategy to decide if the following number sentences
are true.
4 =—
9
B. —
—
6 15
2 =—
7
A. —
—
6 21
5
C. —3— = —
—
12
20
Copyright © Kendall Hunt Publishing Company
D. Show or tell how you decided your answer for Question 3C.
18
4. Maya used a division strategy to find a fraction that is equivalent to ⫺
24.
I know that 6 is a factor of 18. It is
also a factor of 24.
Copyright © Kendall Hunt Publishing Company
3
18 6 = —
——
6 4
24 —
Use Maya’s division strategy to solve each number sentence and find an
equivalent fraction.
9
3 = ——
A. —
— —
15
3
32
8 = ——
B. —
— —
40
8
45
5
C. —
— —— = —
54
6
D. Explain why dividing both the numerator and denominator by the same
number will result in an equivalent fraction.
Find Equivalent Fractions
SG • Grade 5 • Unit 2 • Lesson 3
65
Student Guide - Page 65
*Answers and/or discussion are included in the lesson.
TG • Grade 5 • Unit 2 • Lesson 3 • Answer Key 1
Answer Key • Lesson 3: Find Equivalent Fractions
5. A. 30
B. 10
C. 4
D. 8
E. 10
F. 20
G. Possible response: I know that if you
multiply the numerator 8 by 2 you will get a
numerator of 16. So if you also multiply the
denominator 10 by 2, you will get a
denominator of 20. So the equivalent
–.
fraction is 16
20
6. Answers will vary but could include:
10 15 20 25 30
– , 18
– , 24
– , 30
– , 36
–.
12
7. Yes; Possible response: If you divide both the
–9 by 3 the
numerator and denominator of 12
3
equivalent fraction is –4. If you divide both the
– by 4 the
numerator and denominator of 12
16
3
equivalent fraction is also –4 . That means that
9
12
–
–.
12 16
2
–
8. A. –3 24
36
B. 24 inches long
C. 12 inches
–6
9. A. 6 pieces; –14 24
B. 4 pieces; –16 24
–4
C. Possible response: –13 –39 24
–8
D. Yes, Ana will get the last 6 pieces. She gave
away 6 4 8 18 pieces.
–6 ÷ –22 12
–3 .
24 18 6 pieces left. 24
Use the fraction circle pieces and multiplication or division strategies to
solve the problems.
5. Ming wrote number sentences to show equivalent fractions. He forgot to write
in some of the numerators and denominators. Complete Ming’s number
sentences by filling in the missing numbers to make each sentence true.
1 =—
15
A. —
—
2
?
B.
2 =—
?
—
—
5
25
24
?
C. —
—=—
30
5
14
7
D. —
—=—
16
?
E.
5
?
—
—=—
—
12
24
F.
8
16
—
—=—
—
10
?
G. Explain how you solved Question 5F.
5
9
12
7. Luis said ⫺
12 is equivalent to ⫺
16 . Do you agree with Luis? Explain why or why
not.
2
8. Jacob has a board that is 1 yard, or 36 inches, long. He needs ⫺
3 of the board
for a project.
A. Complete the number sentence to help Jacob decide how many inches
2
?
long his board needs to be. ⫺
3 ⫽⫺
36
Copyright © Kendall Hunt Publishing Company
6. Write 5 fractions that are equivalent to ⫺
6 .
B. How many inches long should his board be?
C. How many inches will be left?
66
SG • Grade 5 • Unit 2 • Lesson 3
Find Equivalent Fractions
Student Guide - Page 66

Check-In: Question 9
Copyright © Kendall Hunt Publishing Company
9. Ana bought a box of candy with
24 pieces in it. She will share
the candy but first each person
must figure out how many
pieces of candy they will receive
from the box.
1
A. Roberto will get ⫺
4 of the
candy. How many pieces of
candy will Ana give Roberto?
1
?
Solve ⫺
4 ⫽⫺
24 .
1
B. Cindy will get ⫺
6 of the candy. How many pieces of candy will Ana give
Cindy? Write a number sentence.
3
C. Ana’s brother will get ⫺
9 of the candy. Ana gave him 8 pieces of candy
3
8
because ⫺
9 ⫽⫺
24 .
What other fractions make this sentence true?
Copyright © Kendall Hunt Publishing Company
3 =—
8
—
—— = —
9
24
D. Ana decided to keep the candy that was left.
3 of the candy.
I get to keep —
12
Do you agree with Ana? Explain why or why not.
Find Equivalent Fractions
SG • Grade 5 • Unit 2 • Lesson 3
67
Student Guide - Page 67
2
TG • Grade 5 • Unit 2 • Lesson 3 • Answer Key
Answer Key • Lesson 3: Find Equivalent Fractions
Student Guide
Copyright © Kendall Hunt Publishing Company
2. A.
B.
3. A.
B.
C.
D.
E.
F.
G.
4. A.
B.
C.
D.
E.
F.
G.
Use the Fraction Circle Pieces from the Student Activity Book Reference
section or number sentences to solve the problems.
1. Write two other equivalent fractions for each fraction below.
2
A. —
3
D.
—3—
15
3
2. Luis is looking for three fractions equivalent to 4 .
A. Complete Luis’ number sentence: 34 8? ?9
B. Find 2 more fractions that are equivalent to 34 .
3. Use a multiplication or division strategy to find an equivalent fraction.
Answers will vary but can include: 12
– , 15
–
16
20
–
–
–
–
–
–
4 C. —
4
5
E. Show or tell how you found the answer for Question 1D.
–34 –68 12
–9
4
16
25
40
7
7
2
3
4
4
8
8
B. —4—
10
1—
4 = ——
A. —
——
44
5—
5 = ——
B. —
——
85
3—
21
C. —
—
——— = —
49
7
6—
3 = ——
D. —
——
93
12
——— = —
3
E. —
——
4
16 1
8—
F. –—
——— = —
3
24 G. Explain how you solved Question 3E.
4. Shannon wrote number sentences to show equivalent fractions but she forgot
some of the numerators and denominators. Fill in the missing numbers to
make each number sentence true.
7
?
A. —
—=—
—
12 24
1 =—
8
B. —
—
?
16
3 =—
?
C. —
—
5 30
2 =—
6
D. —
—
? 18
1 =—
8
E. —
3
?
F.
Copyright © Kendall Hunt Publishing Company
Homework (SG p. 68)
Questions 1–4
1. A. Answers will vary but can include: –46 , –69
B. Answers will vary but can include: –25 , 15
–6
C. Answers will vary but can include: 10
–8 , 12
–
15
1 2
D. Answers will vary but can include: –5 , 10
–
E. Possible response: If you divide both the
numerator and denominator by 3, you will
get –15 as an equivalent fraction.
27
?
—
—=—
36
4
G. Explain how you solved Question 4F.
Find Equivalent Fractions
Possible response: I thought about
multiplication. I know 3 4 12 and
4 4 16.
14
2
18
6
24
3
Possible response: First I thought about
what times 4 is equal to 36. The answer is
9. I know that 3 9 27 so the numerator
is 3.
68
SG • Grade 5 • Unit 2 • Lesson 3
Student Guide - Page 68
TG • Grade 5 • Unit 2 • Lesson 3 • Answer Key 3