## 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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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. \(\frac{2}{5}\) = \(\frac{4}{10}\)

Answer:

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. \(\frac{2}{3}\) = \(\frac{8}{12}\)

Answer:

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. \(\frac{3}{6}\) = \(\frac{6}{12}\)

Answer:

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. \(\frac{4}{6}\) = \(\frac{8}{12}\)

Answer:

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. \(\frac{3}{4}\)

Answer:

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. \(\frac{4}{5}\)

Answer:

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. \(\frac{7}{6}\)

Answer:

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. \(\frac{12}{7}\)

Answer:

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. \(\frac{4}{3}\) = \(\frac{8}{9}\)

Answer:

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. \(\frac{5}{4}\) = \(\frac{10}{8}\)

Answer:

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. \(\frac{4}{5}\) = \(\frac{12}{10}\)

Answer:

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. \(\frac{4}{6}\) = \(\frac{12}{18}\)

Answer:

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.

\(\frac{2}{5}\)

Answer:

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.

\(\frac{3}{4}\) = \(\frac{9}{8}\)

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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. \(\frac{1}{3}\) = \(\frac{2}{6}\)

Answer:

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. \(\frac{2}{5}\) = \(\frac{4}{10}\)

Answer:

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. \(\frac{5}{7}\) = \(\frac{10}{14}\)

Answer:

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. \(\frac{3}{6}\) = \(\frac{9}{18}\)

Answer:

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. \(\frac{2}{3}\)

Answer:

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. \(\frac{5}{6}\)

Answer:

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. \(\frac{6}{5}\)

Answer:

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. \(\frac{10}{8}\)

Answer:

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. \(\frac{2}{3}\) = \(\frac{4}{9}\)

Answer:

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. \(\frac{5}{6}\) = \(\frac{10}{12}\)

Answer:

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. \(\frac{3}{5}\) = \(\frac{6}{15}\)

Answer:

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. \(\frac{7}{4}\) = \(\frac{21}{12}\).

Answer:

7/4 = 21/12.

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.

7/4 = 7 x 3/4 x 3.

7 x 3 = 21.

4 x 3 = 12.

7/4 = 21/12.