## Engage NY Eureka Math 4th Grade Module 5 Lesson 16 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 16 Problem Set Answer Key

Question 1.

Solve.

a. 3 fifths – 1 fifth = _____2 __fifths_____

Answer:

3 fifths – 1 fifth = 2 fifths.

Explanation:

In the above-given question,

given that,

3 fifths = 3/5.

3/5 = 0.6.

1 fifth = 1/5.

1/5 = 0.2.

0.6 – 0.2 = 0.4.

2/5 = 0.4.

3 fifths – 1 fifth = 2 fifths.

b. 5 fifths – 3 fifths = _____2_fifths._________

Answer:

5 fifths – 3 fifth = 2 fifths.

Explanation:

In the above-given question,

given that,

5 fifths = 5/5.

5/5 = 1.

3 fifth = 3/5.

3/5 = 0.6.

1 – 0.6 = 0.4.

2/5 = 0.4.

3 fifths – 1 fifth = 2 fifths.

c. 3 halves – 2 halves = _____1_ halves._____

Answer:

3 halves – 2 halves = 1 halves

Explanation:

In the above-given question,

given that,

3 halves = 3/2.

3/2 = 1.5.

2 halves = 2/2.

2/2 = 1.

1.5 – 1 = 0.5.

1/2 = 0.5.

3 halves – 2 halves = 1 half.

d. 6 fourths – 3 fourths = ____3__fourths._______

Answer:

6 fourths – 3 fourths = 3 fourths.

Explanation:

In the above-given question,

given that,

6 fourths = 6/4.

6/4 = 1.5.

3 fourths = 3/4.

3/4 = 0.75.

1.5 – 0.75 = 0.75.

3/4 = 0.75.

6 fourths – 3 fourths = 3 fourths.

Question 2.

Solve.

a. \(\frac{5}{6}\) – \(\frac{3}{6}\)

Answer:

\(\frac{5}{6}\) – \(\frac{3}{6}\) = \(\frac{2}{6}\)

Explanation:

In the above-given question,

given that,

5 sixths = 5/6.

5/6 = 0.83.

3 sixths = 3/6.

3/6 = 0.5.

0.83 – 0.5 = 0.33.

2/6 = 0.33.

\(\frac{5}{6}\) – \(\frac{3}{6}\) = \(\frac{2}{6}\)

b. \(\frac{6}{8}\) – \(\frac{4}{8}\)

Answer:

\(\frac{6}{8}\) – \(\frac{4}{8}\) = \(\frac{2}{8}\)

Explanation:

In the above-given question,

given that,

6 eights = 6/8.

6/8 = 0.75.

4 eights = 4/8.

4/8 = 0.5.

0.75 – 0.5 = 0.25.

2/8 = 0.25.

\(\frac{6}{8}\) – \(\frac{4}{8}\) = \(\frac{2}{8}\)

c. \(\frac{3}{10}\) – \(\frac{3}{10}\)

Answer:

\(\frac{3}{10}\) – \(\frac{3}{10}\) = \(\frac{0}{0}\)

Explanation:

In the above-given question,

given that,

3 tens = 3/10.

3/10 = 0.3.

3 tens = 3/10.

3/10 = 0.3.

0.3 – 0.3 = 0.

0/6 = 0.

\(\frac{3}{10}\) – \(\frac{3}{10}\) = \(\frac{0}{0}\)

d. \(\frac{5}{5}\) – \(\frac{4}{5}\)

Answer:

\(\frac{5}{5}\) – \(\frac{4}{5}\) = \(\frac{1}{5}\)

Explanation:

In the above-given question,

given that,

5 fifths = 5/5.

5/5 = 1.

4 fifths = 4/5.

4/5 = 0.8.

1 – 0.8 = 0.2.

1/5 = 0.2.

\(\frac{5}{5}\) – \(\frac{4}{5}\) = \(\frac{1}{5}\)

e. \(\frac{5}{4}\) – \(\frac{4}{4}\)

Answer:

\(\frac{5}{4}\) – \(\frac{4}{4}\) = \(\frac{1}{4}\)

Explanation:

In the above-given question,

given that,

5 fours = 5/4.

5/4 = 1.25.

4 fours = 4/4.

4/4 = 1.

1.25 – 1 = 0.25.

1/4 = 0.25.

\(\frac{5}{4}\) – \(\frac{4}{4}\) = \(\frac{1}{4}\)

f. \(\frac{5}{4}\) – \(\frac{3}{4}\)

Answer:

\(\frac{5}{4}\) – \(\frac{3}{4}\) = \(\frac{2}{4}\)

Explanation:

In the above-given question,

given that,

5 fours = 5/4.

5/4 = 1.25.

3 fours = 3/4.

3/4 = 0.75.

1.25 – 0.75 = 0.5.

2/4 = 0.5.

\(\frac{5}{4}\) – \(\frac{3}{4}\) = \(\frac{2}{4}\)

Question 3.

Solve. Use a number bond to show how to convert the difference to a mixed number. Problem (a) has been completed for you.

a.

Answer:

12/8 – 3/8 = 9/8.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

12/8 – 3/8.

9/8.

9/8 = 8/8 + 1/8.

b. \(\frac{12}{6}\) – \(\frac{5}{6}\)

Answer:

12/6 – 5/6 = 7/6.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

12/6 – 5/6.

7/6.

7/6 = 6/6 + 1/6.

c. \(\frac{9}{5}\) – \(\frac{3}{5}\)

Answer:

9/5 – 3/5 = 6/5.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

9/5 – 3/5.

6/5.

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

d. \(\frac{14}{8}\) – \(\frac{3}{8}\)

Answer:

14/8 – 3/8 = 11/8.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

14/8 – 3/8.

11/8.

11/8 = 8/8 + 3/8.

e. \(\frac{8}{4}\) – \(\frac{2}{4}\)

Answer:

8/4 – 2/4 = 6/4.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

8/4 – 2/4.

6/4.

6/4 = 4/4 + 2/4.

f. \(\frac{15}{10}\) – \(\frac{3}{10}\)

Answer:

15/10 – 3/10 = 7/10.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

15/10 – 3/10.

7/10.

7/10 = 10/10 + 1/6.

Question 4.

Solve. Write the sum in unit form.

a. 2 fourths + 1 fourth = _3 fourths._

Answer:

2 fourths + 1 fourth = 3 fourths.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

2 fourths = 1/4 + 1/4.

2 fourths + 1 fourth = 3 fourths.

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

b. 4 fifths + 3 fifths = ____7__fifths.___

Answer:

4 fifths + 3 fifths = 7 fifths.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

4 fifths = 1/5 + 1/5 + 1/5 + 1/5.

3 fifths = 1/5 + 1/5 + 1/5.

4 fifths + 3 fifths = 7 fifths.

1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 7/5.

Question 5.

Solve.

a. \(\frac{2}{8}\) + \(\frac{5}{8}\)

Answer:

\(\frac{2}{8}\) + \(\frac{5}{8}\) = \(\frac{7}{8}\)

Explanation:

In the above-given question,

given that,

2 eights = 2/8.

2/8 = 0.25.

5 eights = 5/8.

5/8 = 0.625.

0.25 + 0.625 = 0.875.

7/8 = 0.875.

\(\frac{2}{8}\) + \(\frac{5}{8}\) = \(\frac{7}{8}\)

b. \(\frac{4}{12}\) + \(\frac{5}{12}\)

Answer:

\(\frac{4}{12}\) + \(\frac{5}{12}\) = \(\frac{9}{12}\)

Explanation:

In the above-given question,

given that,

4 twelfths = 4/12.

4/12 = 0.33.

5 twelfths = 5/12.

5/12 = 0.41.

0.33 + 0.41 = 0.74.

9/12 = 0.74.

\(\frac{4}{12}\) + \(\frac{5}{12}\) = \(\frac{9}{12}\)

Question 6.

Solve. Use a number bond to decompose the sum. Record your final answer as a mixed number.

Problem (a) has been completed for you.

a.

Answer:

3/5 + 4/5 = 7/5.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

3/5 + 4/5.

7/5.

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

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

Answer:

4/4 + 3/4 = 7/4.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

4/4 + 3/4.

7/4.

7/4 = 4/4 + 3/4.

c. \(\frac{6}{9}\) + \(\frac{6}{9}\)

Answer:

6/9 + 6/9 = 12/9.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

6/9 + 6/9.

12/9.

12/9 = 9/9 + 3/9.

d. \(\frac{7}{10}\) + \(\frac{6}{10}\)

Answer:

7/10 + 6/10 = 13/10.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

7/10 + 6/10.

13/10.

13/10 = 10/10 + 3/10.

e. \(\frac{5}{6}\) + \(\frac{7}{6}\)

Answer:

5/6 + 7/6 = 12/6.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

5/6 + 7/6.

12/6.

12/6 = 6/6 + 7/6.

f. \(\frac{9}{8}\) + \(\frac{5}{8}\)

Answer:

9/8 + 5/8 = 14/8.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

9/8 + 5/8.

14/8.

14/8 = 8/8 + 6/8.

Question 7.

Solve. Use a number line to model your answer.

a. \(\frac{7}{4}\) – \(\frac{5}{4}\)

Answer:

\(\frac{7}{4}\) – \(\frac{5}{4}\) = \(\frac{2}{4}\)

Explanation:

In the above-given question,

given that,

7 fours = 7/4.

7/4 = 1.75.

5 fours = 5/4.

5/4 = 1.25.

1.75 – 1.25 = 0.5.

2/4 = 0.5.

\(\frac{7}{4}\) – \(\frac{5}{4}\) = \(\frac{2}{4}\)

b. \(\frac{5}{4}\) + \(\frac{2}{4}\)

Answer:

5/4 + 2/4 = 7/4.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

5/4 + 2/4.

7/4.

7/4 = 4/4 + 3/4.

### Eureka Math Grade 4 Module 5 Lesson 16 Exit Ticket Answer Key

Question 1.

Solve. Use a number bond to decompose the difference. Record your final answer as a mixed number.

\(\frac{16}{9}\) – \(\frac{5}{9}\)

Answer:

16/9 – 5/9 = 11/9.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

16/9 – 5/9.

11/9.

11/9 = 9/9 + 2/9.

Question 2.

Solve. Use a number bond to decompose the sum. Record your final answer as a mixed number.

\(\frac{5}{12}\) + \(\frac{10}{12}\)

Answer:

5/12 + 10/12 = 15/12.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

5/12 + 10/12.

15/12.

15/12 = 12/12 + 3/12.

### Eureka Math Grade 4 Module 5 Lesson 16 Homework Answer Key

Question 1.

Solve.

a. 3 sixths – 2 sixths = __1__sixths___________

Answer:

3 sixths – 2 sixths = 1 sixths.

Explanation:

In the above-given question,

given that,

3 sixths = 3/6.

3/6 = 0.5.

2 sixths = 2/6.

2/6 = 0.33.

0.5 – 0.3 = 0.1.

1/6 = 0.1.

b. 5 tenths – 3 tenths = ___2 tenths._____

Answer:

5 tenths – 3 tenths = 2 tenths.

Explanation:

In the above-given question,

given that,

5 tenths = 5/10.

5/10 = 0.5.

3 tenths = 3/10.

3/10 = 0.3.

0.5 – 0.3 = 0.2.

2/10 = 0.2.

c. 3 fourths – 2 fourths = ____1__fourth._________

Answer:

3 fourths – 2 fourths = 1 fourth.

Explanation:

In the above-given question,

given that,

3 fourths = 3/4.

3/4 = 0.75.

2 fourths = 2/4.

2/4 = 0.5.

0.75 – 0.5 = 0.25.

1/4 = 0.25.

d. 5 thirds – 2 thirds = ___3__thirds._____

Answer:

5 thirds – 2 thirds = 3 thirds.

Explanation:

In the above-given question,

given that,

5 thirds = 5/3.

3/5 = 1.6.

2 thirds = 2/3.

2/3 = 0.6.

1.6 – 0.6 = 1.

3/3 = 1.

Question 2.

Solve.

a. \(\frac{3}{5}\) – \(\frac{2}{5}\)

Answer:

\(\frac{3}{5}\) – \(\frac{2}{5}\) = \(\frac{1}{5}\)

Explanation:

In the above-given question,

given that,

3 fives = 3/5.

3/5 = 0.6.

2 fives = 2/5.

2/5 = 0.4.

0.6 – 0.4 = 0.2.

1/5 = 0.2.

\(\frac{3}{5}\) – \(\frac{2}{5}\) = \(\frac{1}{5}\)

b. \(\frac{7}{9}\) – \(\frac{3}{9}\)

Answer:

\(\frac{7}{9}\) – \(\frac{3}{9}\) = \(\frac{4}{9}\)

Explanation:

In the above-given question,

given that,

7 nines = 7/9.

7/9 = 0.7.

3 nines = 3/9.

3/9 = 0.3.

0.7 – 0.3 = 0.4.

4/9 = 0.4.

\(\frac{7}{9}\) – \(\frac{3}{9}\) = \(\frac{4}{9}\)

c. \(\frac{7}{12}\) – \(\frac{3}{12}\)

Answer:

\(\frac{7}{12}\) – \(\frac{3}{12}\) = \(\frac{4}{12}\)

Explanation:

In the above-given question,

given that,

7 twelfths = 7/12.

7/12 = 0.58.

3 twelfths = 3/12.

3/12 = 0.25.

0.58 – 0.25 = 0.33.

4/12 = 0.33.

\(\frac{7}{12}\) – \(\frac{3}{12}\) = \(\frac{4}{12}\)

d. \(\frac{6}{6}\) – \(\frac{4}{6}\)

Answer:

\(\frac{6}{6}\) – \(\frac{4}{6}\) = \(\frac{2}{6}\)

Explanation:

In the above-given question,

given that,

6 sixs = 6/6.

6/6 = 1.

4 sixs = 4/6.

4/6 = 0.6.

1 – 0.6 = 0.4.

2/6 = 0.4.

\(\frac{6}{6}\) – \(\frac{4}{6}\) = \(\frac{2}{6}\)

e. \(\frac{5}{3}\) – \(\frac{2}{3}\)

Answer:

\(\frac{5}{3}\) – \(\frac{2}{3}\) = \(\frac{3}{3}\)

Explanation:

In the above-given question,

given that,

5 threes = 5/3.

5/3 = 1.6.

2 threes = 2/3.

2/3 = 0.6.

1.25 – 1 = 0.25.

3/3 = 1.

\(\frac{5}{3}\) – \(\frac{2}{3}\) = \(\frac{3}{3}\)

f. \(\frac{7}{4}\) – \(\frac{5}{4}\)

Answer:

\(\frac{7}{4}\) – \(\frac{5}{4}\) = \(\frac{3}{4}\)

Explanation:

In the above-given question,

given that,

7 fours = 7/4.

7/4 = 1.75.

5 fours = 4/4.

5/4 = 1.25.

1.75 – 1.25 = 0.75.

3/4 = 0.75.

\(\frac{7}{4}\) – \(\frac{5}{4}\) = \(\frac{3}{4}\)

Question 3.

Solve. Use a number bond to decompose the difference. Record your final answer as a mixed number. Problem (a) has been completed for you.

Answer:

12/6 – 3/6 = 9/6.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

12/6 – 3/4.

9/6.

9/6 = 6/6 + 3/6.

b. \(\frac{17}{8}\) – \(\frac{6}{8}\)

Answer:

17/8 – 6/8 = 11/8.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

17/8 – 6/8.

11/8.

11/8 = 8/8 + 2/8.

c. \(\frac{9}{5}\) – \(\frac{3}{5}\)

Answer:

9/5 – 3/5 = 6/5.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

9/5 – 3/5.

6/5.

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

d. \(\frac{11}{4}\) – \(\frac{6}{4}\)

Answer:

11/4 – 6/4 = 5/4.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

11/4 – 6/4.

5/4.

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

e. \(\frac{10}{7}\) – \(\frac{2}{7}\)

Answer:

10/7 – 2/7 = 8/7.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

10/7 – 2/7.

8/7.

8/7 = 7/7 + 1/7.

f. \(\frac{21}{10}\) – \(\frac{9}{10}\)

Answer:

21/10 – 9/10 = 11/10.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

21/10 – 9/10.

11/10.

11/10 = 10/10 + 1/10.

Question 4.

Solve. Write the sum in unit form.

a. 4 fifths + 2 fifths = ____6__fifths.____

Answer:

4 fifths + 2 fifths = 6 fifths.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

4 fifths = 1/5 + 1/5 + 1/5 + 1/5.

2 fifths = 1/5 + 1/5.

4 fifths + 2 fifth = 6 fifths.

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

b. 5 eighths + 2 eighths = __7___eights.______

Answer:

5 eights + 2 eighths = 7 eights.

Explanation:

In the above-given question,

given that,

Use a number bond to show how to convert the difference to a mixed number.

5 eights = 1/8 + 1/8 + 1/8 + 1/8 + 1/8.

2 eights = 1/8 + 1/8.

5 eights + 2 eights = 7 eights.

1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 7/8.

Question 5.

Solve.

a. \(\frac{3}{11}\) + \(\frac{6}{11}\)

Answer:

3/11 + 6/11 = 9/11.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

3/11 + 6/11.

9/11.

9/11 = 3/11 + 9/11.

b. \(\frac{3}{10}\) + \(\frac{6}{10}\)

Answer:

3/10 + 6/10 = 9/10.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

3/10 + 6/10.

9/10.

9/10 = 3/10 + 6/10.

Question 6.

Solve. Use a number bond to decompose the sum. Record your final answer as a mixed number.

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

Answer:

3/4 + 3/4 = 6/4.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

3/4 + 3/4.

6/4.

6/4 = 4/4 + 5/4.

b. \(\frac{8}{12}\) + \(\frac{6}{12}\)

Answer:

8/12 + 6/12 = 14/12.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

8/12 + 6/12.

14/12.

14/12 = 12/12 + 2/12.

c. \(\frac{5}{8}\) + \(\frac{7}{8}\)

Answer:

5/8 + 7/8 = 12/8.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

5/8 + 7/8.

12/8.

12/8 = 8/8 + 4/8.

d. \(\frac{8}{10}\) + \(\frac{5}{10}\)

Answer:

8/10 + 5/10 = 13/10.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

8/10 + 5/10.

13/10.

13/10 = 10/10 + 3/10.

e. \(\frac{3}{5}\) + \(\frac{6}{5}\)

Answer:

3/5 + 6/5 = 9/5.

Explanation:

In the above-given question,

given that,

Use a number bond to decompose the sum.

3/5 + 6/5.

9/5.

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

Question 7.

Solve. Use a number line to model your answer.

a. \(\frac{11}{9}\) – \(\frac{5}{9}\)

Answer:

\(\frac{11}{9}\) – \(\frac{5}{9}\) = \(\frac{6}{9}\)

Explanation:

In the above-given question,

given that,

11 nines = 11/9.

11/9 = 0.58.

5 nines = 5/9.

5/9 = 0.25.

0.58 – 0.25 = 0.33.

6/9 = 0.33.

\(\frac{11}{9}\) – \(\frac{5}{9}\) = \(\frac{6}{1}\)

b. \(\frac{13}{12}\) + \(\frac{4}{12}\)