## Engage NY Eureka Math 4th Grade Module 5 Lesson 17 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 17 Problem Set Answer Key

Question 1.

Use the following three fractions to write two subtraction and two addition number sentences.

a. \(\frac{8}{5}\), \(\frac{2}{5}\), \(\frac{10}{5}\)

Answer:

Subtraction sentences = 7/5, 6/5, 1/5, -1/5, 9/5, 8/5.

Addition sentences = 9/5,10/5, 3/5, 4/5, 11/5, 12/5.

Explanation:

In the above-given question,

given that,

8/5, 2/5, 10/5.

8/5 + 1 = 9/5.

9/5 + 1 = 10/5.

2/5 + 1 = 3/5.

3/5 + 1 = 4/5.

10/5 + 1 = 11/5.

11/5 + 1 = 12/5.

8/5 – 1 = 7/5.

7/5 – 1 = 6/5.

2/5 – 1 = 1/5.

1/5 – 1 = -1/5.

10/5 – 1 = 9/5.

9/5 – 1 = 8/5.

b. \(\frac{15}{8}\), \(\frac{7}{8}\), \(\frac{8}{8}\)

Answer:

Subtraction sentences = 14/8, 13/8, 6/8, 5/8, 7/8, 6/8.

Addition sentences = 16/8,17/8, 8/8, 9/8, 9/8, 10/8.

Explanation:

In the above-given question,

given that,

15/8, 7/8, 8/8.

15/8 + 1 = 16/8.

16/8 + 1 = 17/8.

7/8 + 1 = 8/8.

8/8 + 1 = 9/8.

9/8 + 1 = 10/8.

10/8 + 1 = 11/8.

15/8 – 1 = 14/8.

14/8 – 1 = 13/8.

7/8 – 1 = 6/8.

6/8 – 1 = 5/8.

8/8 – 1 = -7/8.

7/8 – 1 = 6/8.

Question 2.

Solve. Model each subtraction problem with a number line, and solve by both counting up and subtracting. Part (a) has been completed for you.

a. 1 – \(\frac{3}{4}\)

Answer:

1 – 3/4 = 1/4.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 3/4.

4 – 3/4.

1/4.

b. 1 – \(\frac{8}{10}\)

Answer:

1 – 8/10 = 2/10.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 8/10.

10 – 8/10.

2/10.

c. 1 – \(\frac{3}{5}\)

Answer:

1 – 3/5 = 2/5.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 3/5.

5 – 3/5.

2/5.

d. 1 – \(\frac{5}{8}\)

Answer:

1 – 5/8 = 3/8.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 5/8.

8 – 5/8.

3/8.

e. 1\(\frac{2}{10}\) – \(\frac{7}{10}\)

Answer:

1 – 2/10 – 7/10 = 1/10.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 2/10.

10 – 2/10.

8/10 – 7/10.

1/10.

f. 1\(\frac{1}{5}\) – \(\frac{3}{5}\)

Answer:

1 – 1/5 – 3/5 = 1/5.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 1/5.

5 – 1/5.

4/5 – 3/5.

1/5.

Question 3.

Find the difference in two ways. Use number bonds to decompose the total. Part (a) has been completed for you.

a.

Answer:

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

Explanation:

In the above-given question,

given that,

1(2/5) – 4/5.

7/5 – 4/5 = 3/5.

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

7/5 – 4/5 = 3/5.

5/5 – 4/5 = 1/5.

1/5 + 2/5 = 3/5.

b. 1\(\frac{3}{6}\) – \(\frac{4}{6}\)

Answer:

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

Explanation:

In the above-given question,

given that,

1(3/6) – 4/6.

9/6 – 4/6 = 5/6.

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

9/6 – 4/6 = 5/6.

6/6 – 4/6 = 2/6.

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

c. 1\(\frac{6}{8}\) – \(\frac{7}{8}\)

Answer:

10/8 + 4/8 = 14/8.

Explanation:

In the above-given question,

given that,

1(6/8) – 7/8.

14/8 – 7/8 = 7/8.

10/8 + 4/8 = 14/8.

14/8 – 7/8 = 7/8.

10/8 – 7/8 = 3/8.

3/8 + 4/8 = 7/8.

d. 1\(\frac{1}{10}\) – \(\frac{7}{10}\)

Answer:

8/10 + 3/10 = 11/10.

Explanation:

In the above-given question,

given that,

1(1/10) – 7/10.

11/10 – 7/10 = 4/10.

8/10 + 3/10 = 11/10.

11/10 – 7/10 = 4/10.

8/10 – 7/10 = 2/10.

2/10 + 3/10 = 5/10.

e. 1\(\frac{3}{12}\) – \(\frac{6}{12}\)

Answer:

6/12 + 3/12 = 9/12.

Explanation:

In the above-given question,

given that,

1(3/12) – 9/12.

15/12 – 9/12 = 3/12.

7/12 + 8/12 = 15/12.

9/12 – 6/12 = 3/12.

6/12 – 6/12 = 0.

6/12 + 3/12 = 9/12.

### Eureka Math Grade 4 Module 5 Lesson 17 Exit Ticket Answer Key

Question 1.

Solve. Model the problem with a number line, and solve by both counting up and subtracting.

1 – \(\frac{2}{5}\)

Answer:

1 – 2/5 = 3/5.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 2/5.

5 – 2/5.

3/5.

Question 2.

Find the difference in two ways. Use a number bond to show the decomposition.

1\(\frac{2}{7}\) – \(\frac{5}{7}\)

Answer:

5/7 + 4/7 = 9/7.

Explanation:

In the above-given question,

given that,

1(2/7) – 5/7.

9/7 – 5/7 = 4/7.

5/7 + 4/7 = 9/7.

9/7 – 5/7 = 4/7.

5/7 – 4/5 = 1/7.

1/7 + 2/7 = 3/7.

### Eureka Math Grade 4 Module 5 Lesson 17 Homework Answer Key

Question 1.

Use the following three fractions to write two subtraction and two addition number sentences.

a. \(\frac{5}{6}\), \(\frac{4}{6}\), \(\frac{9}{6}\)

Answer:

Subtraction sentences = 4/6, 3/6, 3/6, 2/6, 8/6, 7/6.

Addition sentences = 6/6,7/6, 5/6, 6/6, 10/6, 11/6.

Explanation:

In the above-given question,

given that,

5/6, 4/6, 9/6.

5/6 + 1 = 6/6.

6/6 + 1 = 7/6.

4/6 + 1 = 5/6.

5/6 + 1 = 6/6.

9/6 + 1 = 10/6.

10/6 + 1 = 11/6.

5/6 – 1 = 4/6.

4/6 – 1 = 3/6.

4/6 – 1 = 3/6.

3/6 – 1 = 2/6.

9/6 – 1 = -8/6.

8/6 – 1 = 7/6.

b. \(\frac{5}{9}\), \(\frac{13}{9}\), \(\frac{8}{9}\)

Answer:

Subtraction sentences = 4/9, 3/9, 12/9, 11/9, 7/9, 6/9.

Addition sentences = 6/9,7/9, 14/9, 15/9, 9/9, 10/9.

Explanation:

In the above-given question,

given that,

5/9, 13/9, 8/9.

5/9 + 1 = 6/9.

6/9 + 1 = 7/9.

13/9 + 1 = 14/9.

14/9 + 1 = 15/9.

8/9 + 1 = 9/9.

9/9 + 1 = 10/9.

5/9 – 1 = 4/9.

4/9 – 1 = 3/9.

13/9 – 1 = 12/9.

12/9 – 1 = 11/9.

8/9 – 1 = 7/9.

7/9 – 1 = 6/9.

Question 2.

Solve. Model each subtraction problem with a number line, and solve by both counting up and subtracting.

a. 1 – \(\frac{5}{8}\)

Answer:

1 – 5/8 = 3/8.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 5/8.

8 – 5/8.

3/8.

b. 1 – \(\frac{2}{5}\)

Answer:

1 – 2/5 = 3/5.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 2/5.

5 – 2/5.

3/5.

c. 1\(\frac{3}{6}\) – \(\frac{5}{6}\)

Answer:

1 – 3/6 – 5/6 = -2/6.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 3/6.

6 – 3/6.

3/6 – 5/6.

-2/6.

d. 1 – \(\frac{1}{4}\)

Answer:

1 – 1/4 = 3/4.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 1/4.

4 – 1/4.

3/4.

e. 1\(\frac{1}{3}\) – \(\frac{2}{3}\)

Answer:

1 – 1/3 – 2/3 = 0.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 1/3.

3 – 1/3.

2/3 – 2/3.

0

f. 1\(\frac{1}{5}\) – \(\frac{2}{5}\)

Answer:

1 – 1/5 – 2/5 = 2/5.

Explanation:

In the above-given question,

given that,

Model each subtraction problem with a number line.

1 – 1/5.

5 – 1/5.

4/5 – 2/5.

2/5.

Question 3.

Find the difference in two ways. Use number bonds to decompose the total. Part (a) has been completed for you.

a.

b. 1\(\frac{3}{8}\) – \(\frac{7}{8}\)

Answer:

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

Explanation:

In the above-given question,

given that,

1(3/8) – 7/8.

11/8 – 7/8 = 4/8.

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

11/8 – 7/8 = 4/8.

8/8 – 7/8 = 1/8.

1/8 + 3/8 = 4/8.

c. 1\(\frac{1}{4}\) – \(\frac{3}{4}\)

Answer:

8/10 + 3/10 = 11/10.

Explanation:

In the above-given question,

given that,

1(1/4) – 3/4.

5/4 – 3/4 = 2/4.

3/4 + 2/4 = 5/4.

5/4 – 3/4 = 2/4.

3/4 – 3/4 = 0.

0 + 2/4 = 2/4.

d. 1\(\frac{2}{7}\) – \(\frac{5}{7}\)

Answer:

6/7 + 3/7 = 9/7.

Explanation:

In the above-given question,

given that,

1(2/7) – 5/7.

9/7 – 2/7 = 7/7.

6/7 + 3/7 = 9/7.

9/7 – 2/7 = 7/7.

6/7 – 2/7 = 4/7.

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

e. 1\(\frac{3}{10}\) – \(\frac{7}{10}\)

Answer:

8/10 + 3/10 = 11/10.

Explanation:

In the above-given question,

given that,

1(3/10) – 7/10.

13/10 – 7/10 = 6/10.

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

13/10 – 7/10 = 6/10.

7/10 – 7/10 = 0.

0 + 6/10 = 6/10.