## Engage NY Eureka Math 4th Grade Module 5 Lesson 32 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 32 Problem Set Answer Key

Question 1.

Subtract. Model with a number line or the arrow way.

a. 3\(\frac{3}{4}\) – \(\frac{1}{4}\)

Answer:

3(3/4) – 1/4 = 2(7/4).

Explanation:

In the above-given question,

given that,

subtract the fractions.

3(3/4) – 1/4.

2(1/4) + 6/4.

2(7/4).

b. 4\(\frac{7}{10}\) – \(\frac{3}{10}\)

Answer:

4(7/10) – 3/10 = 4(7/10).

Explanation:

In the above-given question,

given that,

subtract the fractions.

4(7/10) – 3/10.

4(1/10) + 6/10.

4(7/10).

c. 5\(\frac{1}{3}\) – \(\frac{2}{3}\)

Answer:

5(1/3) – 2/3 = 4(4/3).

Explanation:

In the above-given question,

given that,

subtract the fractions.

5(1/3) – 2/3.

4(1/3) + 3/3.

4(4/3).

d. 9\(\frac{3}{5}\) – \(\frac{4}{5}\)

Answer:

9(3/5) – 4/5 = 5(23/5).

Explanation:

In the above-given question,

given that,

subtract the fractions.

9(3/5) – 4/5.

5(3/5) + 20/5.

5(23/5).

Question 2.

Use decomposition to subtract the fractions. Model with a number line or the arrow way.

Answer:

5(3/5) – 4/5 = 24/5.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

5(3/5) – 4/5.

5 x 5 = 25.

25 + 3/5 = 28/5.

4/5 = 3/5 + 1/5.

28/5 – 4/5 = 24/5.

b. 4\(\frac{1}{4}\) – \(\frac{2}{4}\)

Answer:

4(1/4) – 2/4 = 15/4.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

4(1/4) – 2/4.

4 x 4 = 16.

16 + 1/4 = 17/4.

2/4 = 1/4 + 1/4.

17/4 – 2/4 = 15/4.

c. 5\(\frac{1}{3}\) – \(\frac{2}{3}\)

Answer:

5(1/3) – 2/3 = 14/3.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

5(1/3) – 2/3.

5 x 3 = 15.

15 + 1/3 = 16/3.

2/3 = 1/3 + 1/3.

16/3 – 2/3 = 14/3.

d. 2\(\frac{3}{8}\) – \(\frac{5}{8}\)

Answer:

2(3/8) – 5/8 = 14/8.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

2(3/8) – 5/8.

8 x 2 = 16.

16 + 3/8 = 19/8.

5/8 = 3/8 + 2/8.

19/8 – 5/8 = 14/8.

Question 3.

Decompose the total to subtract the fractions.

Answer:

3(1/8) – 3/8 = 2(6/8).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

3(1/8) – 3/8.

2(1/8) + 5/8.

2(6/8).

b. 5\(\frac{1}{8}\) – \(\frac{7}{8}\)

Answer:

5(1/8) – 7/8 = 4(9/8).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

5(1/8) – 7/8.

4(1/8) + 8/8.

4(9/8).

c. 5\(\frac{3}{5}\) – \(\frac{4}{5}\)

Answer:

5(3/5) – 4/5 = 4(8/5).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

5(3/5) – 4/5.

4(2/5) + 6/5.

4(8/5).

d. 5\(\frac{4}{6}\) – \(\frac{5}{6}\)

Answer:

5(4/6) – 5/6 = 4(9/6).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

5(4/6) – 5/6.

4(2/6) + 7/6.

4(9/6).

e. 6\(\frac{4}{12}\) – \(\frac{7}{12}\)

Answer:

6(4/12) – 7/12 = 5(16/12).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

6(4/12) – 7/12.

5(4/12) + 12/12.

5(16/12).

f. 9\(\frac{1}{8}\) – \(\frac{5}{8}\)

Answer:

9(1/8) – 5/8 = 8(8/8).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

9(1/8) – 5/8.

8(1/8) + 7/8.

8(8/8).

g. 7\(\frac{1}{6}\) – \(\frac{5}{6}\)

Answer:

7(1/6) – 5/6 = 6(7/6).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

7(1/6) – 5/6.

6(1/6) + 6/6.

6(7/6).

h. 8\(\frac{3}{10}\) – \(\frac{4}{10}\)

Answer:

8(3/10) – 4/10 = 7(13/10).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

8(3/10) – 4/10.

7(2/10) + 11/10.

7(13/10).

i. 12\(\frac{3}{5}\) – \(\frac{4}{5}\)

Answer:

12(3/5) – 4/5 = 11(8/5).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

12(3/5) – 4/5.

11(3/5) + 5/5.

11(8/5).

j. 11\(\frac{2}{6}\) – \(\frac{5}{6}\)

Answer:

11(2/6) – 5/6 = 2(6/8).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

11(2/6) – 5/6.

10(1/6) + 7/6.

10(8/6).

## Eureka Math Grade 4 Module 5 Lesson 32 Exit Ticket Answer Key

Solve.

Question 1.

10\(\frac{5}{6}\) – \(\frac{4}{6}\)

Answer:

10(5/6) – 4/6 = 9(11/6).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

10(5/6) – 4/6.

9(4/6) + 7/6.

9(11/6).

Question 2.

8\(\frac{3}{8}\) – \(\frac{6}{8}\)

Answer:

8(3/8) – 6/8 = 2(6/8).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

8(3/8) – 6/8.

8(2/8) + 1/8.

8(3/8).

### Eureka Math Grade 4 Module 5 Lesson 32 Homework Answer Key

Question 1.

Subtract. Model with a number line or the arrow way.

a. 6\(\frac{3}{5}\) – \(\frac{1}{5}\)

Answer:

6(3/5) – 1/5 = 5(8/5).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

6(3/5) – 1/5.

5(2/5) + 6/5.

5(8/5).

b. 4\(\frac{9}{12}\) – \(\frac{7}{12}\)

Answer:

4(9/12) – 7/12 = 2(6/8).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

4(9/12) – 7/12.

5(8/12) + 9/12.

5(17/12).

c. 7\(\frac{1}{4}\) – \(\frac{3}{4}\)

Answer:

7(1/4) – 3/4 = 2(6/8).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

7(1/4) – 3/4.

6(1/6) + 4/6.

6(5/6).

d. 8\(\frac{3}{8}\) – \(\frac{5}{8}\)

Answer:

8(3/8) – 5/8 = 7(11/8).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

8(3/8) – 5/8.

7(2/8) + 9/8.

7(11/8).

Question 2.

Use decomposition to subtract the fractions. Model with a number line or the arrow way.

Answer:

2(2/5) – 4/5 = 8/5.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

2(2/5) – 4/5.

5 x 2 = 10.

10 + 2/5 = 12/5.

4/5 = 3/5 + 1/5.

12/5 – 4/5 = 8/5.

b. 2\(\frac{1}{3}\) – \(\frac{2}{3}\)

Answer:

2(1/3) – 2/3 = 5/3.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

2(1/3) – 2/3.

2 x 3 = 6.

6 + 1/3 = 7/3.

2/3 = 1/3 + 1/3.

7/3 – 2/3 = 5/3.

c. 4\(\frac{1}{6}\) – \(\frac{4}{6}\)

Answer:

5(1/3) – 2/3 = 14/3.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

5(1/3) – 2/3.

5 x 3 = 15.

15 + 1/3 = 16/3.

2/3 = 1/3 + 1/3.

16/3 – 2/3 = 14/3.

d. 3\(\frac{3}{6}\) – \(\frac{5}{6}\)

Answer:

3(3/6) – 5/6 = 16/6.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

3(3/6) – 5/6.

6 x 3 = 18.

18 + 3/6 = 21/6.

5/6 = 3/6 + 2/6.

21/6 – 5/6 = 16/6.

e. 9\(\frac{3}{8}\) – \(\frac{7}{8}\)

Answer:

9(3/8) – 7/8 = 68/8.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

9(3/8) – 7/8.

9 x 8 = 72.

72 + 3/8 = 75/8.

7/8 = 5/8 + 3/8.

75/8 – 7/8 = 68/8.

f. 7\(\frac{1}{10}\) – \(\frac{6}{10}\)

Answer:

7(1/10) – 6/10 = 65/10.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

7(1/10) – 6/10.

7 x 10 = 70.

70 + 1/10 = 71/10.

6/10 = 5/10 + 1/10.

71/10 – 6/10 = 65/10

.

g. 10\(\frac{1}{8}\) – \(\frac{5}{8}\)

Answer:

10(1/8) – 5/8 = 14/3.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

10(1/8) – 5/8.

10 x 8 = 80.

80 + 1/8 = 81/8.

5/8 = 3/8 + 2/8.

81/8 – 5/8 = 76/8.

h. 9\(\frac{4}{12}\) – \(\frac{7}{12}\)

Answer:

9(4/12) – 7/12 = 14/3.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

9(4/12) – 7/12.

12 x 9 = 108.

108 + 4/12 = 112/12.

7/12 = 5/12 + 2/12.

112/12 – 7/12 = 105/12.

i. 11\(\frac{3}{5}\) – \(\frac{4}{5}\)

Answer:

11(3/5) – 4/5 = 54/5.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

11(3/5) – 4/5.

11 x 5 = 55.

55 + 3/5 = 58/5.

4/5 = 3/5 + 1/5.

58/5 – 4/5 = 54/5.

j. 17\(\frac{1}{9}\) – \(\frac{5}{9}\)

Answer:

17(1/9) – 5/9 = 149/9.

Explanation:

In the above-given question,

given that,

use decomposition to subtract the fractions.

17(1/9) – 5/9.

17 x 9 = 153.

153 + 1/9 = 154/9.

5/9 = 4/9 + 1/9.

154/9 – 5/9 = 149/9.

Question 3.

Decompose the total to subtract the fractions.

b. 5\(\frac{2}{5}\) – \(\frac{3}{5}\)

Answer:

5(2/5) – 3/5 = 4(7/5).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

5(2/5) – 3/5.

4(1/5) + 6/5.

4(7/5).

c. 7\(\frac{1}{8}\) – \(\frac{3}{8}\)

Answer:

7(1/8) – 3/8 = 6(9/8).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

7(1/8) – 3/8.

6(1/8) + 8/8.

6(9/8).

d. 3\(\frac{3}{9}\) – \(\frac{4}{9}\)

Answer:

3(3/9) – 4/9 = 2(12/9).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

3(3/9) – 4/9.

2(3/9) + 9/9.

2(12/9).

e. 6\(\frac{3}{10}\) – \(\frac{7}{10}\)

Answer:

6(3/10) – 7/10 = 5(13/10).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

6(3/10) – 7/10.

5(2/10) + 11/10.

5(13/10).

f. 2\(\frac{5}{9}\) – \(\frac{8}{9}\)

Answer:

2(5/9) – 8/9 = 1(5/9).

Explanation:

In the above-given question,

given that,

decompose the total to subtract the fractions.

2(5/9) – 8/9.

2(4/9) + 1/9.

1(5/9).