## Engage NY Eureka Math 4th Grade Module 5 Lesson 8 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 8 Problem Set Answer Key

Each rectangle represents 1.

Question 1.
The shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. The first one has been done for you.
a.

2/3 = 4/6.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
2/3 = 2 x 2/3 x 2.
2 x 2 = 4.
3 x 2 = 6.
2/3 = 4/6.

b.

3/4 = 9/16.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
3/4 = 3 x 3/4 x 4.
3 x 3 = 9.
4 x 4 = 16.
3/4 = 9/16.

c.

4/5 = 8/10.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
4/5 = 4 x 2/5 x 2.
4 x 2 = 8.
5 x 2 = 10.
4/5 = 8/10.

d.

5/6 = 10/12.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
5/6 = 5 x 2/6 x 2.
5 x 2 = 10.
6 x 2 = 12.
5/6 = 10/12.

Question 2.
Decompose the shaded fractions into smaller units, as given below. Express the equivalent fractions in a number sentence using multiplication.
a. Decompose into tenths.

3/5 = 6/10.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
3/5 = 3 x 2/5 x 2.
3 x 2 = 6.
5 x 2 = 10.
3/5 = 6/10.

b. Decompose into fifteenths.

3/5 = 9/15.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
3/5 = 3 x 3/5 x 3.
3 x 3 = 9.
5 x 3 = 15.
3/5 = 9/15.

Question 3.
Draw area models to prove that the following number sentences are true.
a. $$\frac{2}{5}$$ = $$\frac{4}{10}$$

2/5 = 4/10.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
2/5 = 2 x 2/5 x 2.
2 x 2 = 4.
5 x 2 = 10.
2/5 = 4/10.

b. $$\frac{2}{3}$$ = $$\frac{8}{12}$$

2/3 = 8/12.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
2/3 = 2 x 4/4 x 3.
2 x 4 = 8.
4 x 3 = 12.
2/3 = 8/12.

c. $$\frac{3}{6}$$ = $$\frac{6}{12}$$

3/6 = 6/12.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
3/6 = 3 x 2/6 x 2.
3 x 2 = 6.
6 x 2 = 12.
3/6 = 6/12.

d. $$\frac{4}{6}$$ = $$\frac{8}{12}$$

4/6 = 8/12.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
4/6 = 4 x 2/6 x 2.
4 x 2 = 8.
6 x 2 = 12.
4/6 = 8/12.

Question 4.
Use multiplication to find an equivalent fraction for each fraction below.
a. $$\frac{3}{4}$$

3/4 = 9/16.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
3/4 = 3 x 3/4 x 4.
3 x 3 = 9.
4 x 4 = 16.
3/4 = 9/16.

b. $$\frac{4}{5}$$

4/5 = 8/15.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
4/5 = 4 x 2/5 x 3.
4 x 2 = 8.
5 x 3 = 15.
4/5 = 8/15.

c. $$\frac{7}{6}$$

7/6 = 14/12.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
7/6 = 7 x 2/6 x 2.
7 x 2 = 14.
6 x 2 = 12.
7/6 = 14/12.

d. $$\frac{12}{7}$$

12/7 = 24/14.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
12/7 = 12 x 2/7 x 2.
12 x 2 = 24.
7 x 2 = 14.
12/7 = 24/14.

Question 5.
Determine which of the following are true number sentences. Correct those that are false by changing the right-hand side of the number sentence.
a. $$\frac{4}{3}$$ = $$\frac{8}{9}$$

4/3 = 8/9.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
4/3 = 4 x 2/3 x 3.
4 x 2 = 8.
3 x 3 = 9.
4/3 = 8/9.

b. $$\frac{5}{4}$$ = $$\frac{10}{8}$$

5/4 = 10/8.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
5/4 = 5 x 2/4 x 2.
5 x 2 = 10.
4 x 2 = 8.
5/4 = 10/8.

c. $$\frac{4}{5}$$ = $$\frac{12}{10}$$

4/5 = 12/10 is wrong.
4/5 = 8/10 is correct.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
4/5 = 4 x 2/5 x 2.
4 x 2 = 8.
5 x 2 = 10.
4/5 = 8/10.

d. $$\frac{4}{6}$$ = $$\frac{12}{18}$$

4/6 = 12/18.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
4/6 = 4 x 3/6 x 3.
4 x 3 = 12.
6 x 3 = 18.
4/6 = 12/18.

### Eureka Math Grade 4 Module 5 Lesson 8 Exit Ticket Answer Key

Question 1.
Use multiplication to create an equivalent fraction for the fraction below.
$$\frac{2}{5}$$

2/5 = 4/10.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
2/5 = 2 x 2/5 x 2.
2 x 4 = 8.
5 x 2 = 10.
2/5 = 4/10.

Question 2.
Determine if the following is a true number sentence. If needed, correct the statement by changing the right-hand side of the number sentence.
$$\frac{3}{4}$$ = $$\frac{9}{8}$$

3/4 = 9/8.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
3/4 = 3 x 3/4 x 2.
3 x 3 = 9.
4 x 2 = 8.
3/4 = 9/8.

### Eureka Math Grade 4 Module 5 Lesson 8 Homework Answer Key

Each rectangle represents 1.

Question 1.
The shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. The first one has been done for you.
a.

2/3 = 4/6.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
2/3 = 2 x 2/3 x 2.
2 x 2 = 4.
3 x 2 = 6.
2/3 = 4/6.

b.

3/4 = 6/8.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
3/4 = 3 x 2/4 x 2.
3 x 2 = 6.
4 x 2 = 8.
3/4 = 6/8.

c.

4/5 = 12/15.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
4/5 = 4 x 3/5 x 3.
4 x 3 = 12.
5 x 3 = 15.
4/5 = 12/15.

d.

7/8 = 14/16.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
7/8 = 7 x 2/8 x 2.
7 x 2 = 14.
8 x 2 = 16.
7/8 = 14/16.

Question 2.
Decompose both shaded fractions into twelfths. Express the equivalent fractions in a number sentence using multiplication.
a.

3/6 = 9/12.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
3/6 = 3 x 3/6 x 2.
3 x 3 = 9.
6 x 2 = 12.
3/6 = 9/12.

b.

2/4 = 6/12.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
2/4 = 2 x 3/4 x 3.
3 x 2 = 6.
4 x 3 = 12.
2/4 = 6/12.

Question 3.
Draw area models to prove that the following number sentences are true.
a. $$\frac{1}{3}$$ = $$\frac{2}{6}$$

1/3 = 2/6.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
1/3 = 1 x 2/3 x 2.
1 x 2 = 2.
3 x 2 = 6.
1/3 = 2/6.

b. $$\frac{2}{5}$$ = $$\frac{4}{10}$$

2/5 = 4/10.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
2/5 = 2 x 2/5 x 2.
2 x 2 = 4.
5 x 2 = 10.
2/5 = 4/10.

c. $$\frac{5}{7}$$ = $$\frac{10}{14}$$

5/7 = 10/14.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
5/7 = 5 x 2/7 x 2.
5 x 2 = 10.
7 x 2 = 14.
5/7 = 10/14.

d. $$\frac{3}{6}$$ = $$\frac{9}{18}$$

3/6 = 9/18.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
3/6 = 3 x 3/6 x 3.
3 x 3 = 9.
6 x 3 = 18.
3/6 = 9/18.

Question 4.
Use multiplication to create an equivalent fraction for each fraction below.
a. $$\frac{2}{3}$$

2/3 = 4/6.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
2/3 = 2 x 2/3 x 2.
2 x 2 = 4.
3 x 2 = 6.
2/3 = 4/6.

b. $$\frac{5}{6}$$

5/6 = 10/12.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
5/6 = 5 x 2/6 x 2.
5 x 2 = 10.
6 x 2 = 12.
5/6 = 10/12.

c. $$\frac{6}{5}$$

6/5 = 12/10.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
6/5 = 6 x 2/5 x 2.
6 x 2 = 12.
5 x 2 = 10.
6/5 = 12/10.

d. $$\frac{10}{8}$$

10/8 = 5/4.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
10/8 = 5 x 2/2 x 2.
5 x 2 = 10.
2 x 2 = 4.
10/8 = 5/4.

Question 5.
Determine which of the following are true number sentences. Correct those that are false by changing the right-hand side of the number sentence.
a. $$\frac{2}{3}$$ = $$\frac{4}{9}$$

2/3 = 4/9.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
2/3 = 2 x 2/3 x 3.
2 x 2 = 4.
3 x 3 = 9.
2/3 = 4/9.

b. $$\frac{5}{6}$$ = $$\frac{10}{12}$$

5/6 = 10/12.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
5/6 = 5 x 2/6 x 2.
5 x 2 = 10.
6 x 2 = 12.
5/6 = 10/12.

c. $$\frac{3}{5}$$ = $$\frac{6}{15}$$

3/5 = 6/15 is wrong.
3/5 = 9/15 is correct.

Explanation:
In the above-given question,
given that,
the shaded fractions have been decomposed into smaller units.
Express the equivalent fractions in a number sentence using multiplication.
3/5 = 3 x 3/ 5 x 3.
3 x 3 = 9.
5 x 3 = 15.
3/5 = 9/15.

d. $$\frac{7}{4}$$ = $$\frac{21}{12}$$.