## 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_____

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._________

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._____

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._______

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. $$\frac{5}{6}$$ – $$\frac{3}{6}$$

$$\frac{5}{6}$$ – $$\frac{3}{6}$$ = $$\frac{2}{6}$$

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. $$\frac{6}{8}$$ – $$\frac{4}{8}$$

$$\frac{6}{8}$$ – $$\frac{4}{8}$$ = $$\frac{2}{8}$$

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. $$\frac{3}{10}$$ – $$\frac{3}{10}$$

$$\frac{3}{10}$$ – $$\frac{3}{10}$$ = $$\frac{0}{0}$$

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. $$\frac{5}{5}$$ – $$\frac{4}{5}$$

$$\frac{5}{5}$$ – $$\frac{4}{5}$$ = $$\frac{1}{5}$$

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. $$\frac{5}{4}$$ – $$\frac{4}{4}$$

$$\frac{5}{4}$$ – $$\frac{4}{4}$$ = $$\frac{1}{4}$$

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. $$\frac{5}{4}$$ – $$\frac{3}{4}$$

$$\frac{5}{4}$$ – $$\frac{3}{4}$$ = $$\frac{2}{4}$$

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.

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. $$\frac{12}{6}$$ – $$\frac{5}{6}$$

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. $$\frac{9}{5}$$ – $$\frac{3}{5}$$

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. $$\frac{14}{8}$$ – $$\frac{3}{8}$$

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. $$\frac{8}{4}$$ – $$\frac{2}{4}$$

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. $$\frac{15}{10}$$ – $$\frac{3}{10}$$

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._

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.___

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. $$\frac{2}{8}$$ + $$\frac{5}{8}$$

$$\frac{2}{8}$$ + $$\frac{5}{8}$$ = $$\frac{7}{8}$$

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. $$\frac{4}{12}$$ + $$\frac{5}{12}$$

$$\frac{4}{12}$$ + $$\frac{5}{12}$$ = $$\frac{9}{12}$$

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.

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. $$\frac{4}{4}$$ + $$\frac{3}{4}$$

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. $$\frac{6}{9}$$ + $$\frac{6}{9}$$

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. $$\frac{7}{10}$$ + $$\frac{6}{10}$$

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. $$\frac{5}{6}$$ + $$\frac{7}{6}$$

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. $$\frac{9}{8}$$ + $$\frac{5}{8}$$

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.
a. $$\frac{7}{4}$$ – $$\frac{5}{4}$$

$$\frac{7}{4}$$ – $$\frac{5}{4}$$ = $$\frac{2}{4}$$

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. $$\frac{5}{4}$$ + $$\frac{2}{4}$$

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.
$$\frac{16}{9}$$ – $$\frac{5}{9}$$

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.
$$\frac{5}{12}$$ + $$\frac{10}{12}$$

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___________

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._____

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._________

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._____

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. $$\frac{3}{5}$$ – $$\frac{2}{5}$$

$$\frac{3}{5}$$ – $$\frac{2}{5}$$ = $$\frac{1}{5}$$

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. $$\frac{7}{9}$$ – $$\frac{3}{9}$$

$$\frac{7}{9}$$ – $$\frac{3}{9}$$ = $$\frac{4}{9}$$

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. $$\frac{7}{12}$$ – $$\frac{3}{12}$$

$$\frac{7}{12}$$ – $$\frac{3}{12}$$ = $$\frac{4}{12}$$

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. $$\frac{6}{6}$$ – $$\frac{4}{6}$$

$$\frac{6}{6}$$ – $$\frac{4}{6}$$ = $$\frac{2}{6}$$

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. $$\frac{5}{3}$$ – $$\frac{2}{3}$$

$$\frac{5}{3}$$ – $$\frac{2}{3}$$ = $$\frac{3}{3}$$

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. $$\frac{7}{4}$$ – $$\frac{5}{4}$$

$$\frac{7}{4}$$ – $$\frac{5}{4}$$ = $$\frac{3}{4}$$

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.

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. $$\frac{17}{8}$$ – $$\frac{6}{8}$$

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. $$\frac{9}{5}$$ – $$\frac{3}{5}$$

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. $$\frac{11}{4}$$ – $$\frac{6}{4}$$

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. $$\frac{10}{7}$$ – $$\frac{2}{7}$$

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. $$\frac{21}{10}$$ – $$\frac{9}{10}$$

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.____

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.______

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. $$\frac{3}{11}$$ + $$\frac{6}{11}$$

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. $$\frac{3}{10}$$ + $$\frac{6}{10}$$

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. $$\frac{3}{4}$$ + $$\frac{3}{4}$$

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. $$\frac{8}{12}$$ + $$\frac{6}{12}$$

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. $$\frac{5}{8}$$ + $$\frac{7}{8}$$

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. $$\frac{8}{10}$$ + $$\frac{5}{10}$$

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. $$\frac{3}{5}$$ + $$\frac{6}{5}$$

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.

a. $$\frac{11}{9}$$ – $$\frac{5}{9}$$

$$\frac{11}{9}$$ – $$\frac{5}{9}$$ = $$\frac{6}{9}$$

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. $$\frac{13}{12}$$ + $$\frac{4}{12}$$