## Engage NY Eureka Math 4th Grade Module 5 Lesson 29 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 29 Problem Set Answer Key

Question 1.

Estimate each sum or difference to the nearest half or whole number by rounding. Explain your estimate using words or a number line.

a. 2\(\frac{1}{12}\) + 1\(\frac{7}{8}\) ≈ ____40/12________

Answer:

2(1/12) + 1(7/8) = 40/12.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

2(1/12) + 1(7/8).

12 x 2 = 24.

1 x 8 = 8.

24 + 1/12 = 25/12.

8 + 7/8 = 15/8.

25/12 + 15/8 = 40/12.

b. 1\(\frac{11}{12}\) + 5\(\frac{3}{4}\) ≈ ____46/4_________

Answer:

1(11/12) + 5(3/4) = 46/4.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

1(11/12) + 5(3/4).

12 x 1 = 12.

5 x 4 = 20.

12 + 11/12 = 23/12.

20 + 3/4 = 23/4.

23/12 + 23/4 = 46/4.

c. 8\(\frac{7}{8}\) – 2\(\frac{1}{9}\) ≈ ____52/9________

Answer:

8(7/8) – 2(1/9) = 52/9.

Explanation:

In the above-given question,

given that,

Estimate each difference to the nearest half.

8(7/8) – 2(1/9).

8 x 8 = 64.

2 x 9 = 18.

64 + 7/8 = 71/8.

18 + 1/9 = 19/9.

71/8 – 19/9 = 52/9.

d. 6\(\frac{1}{8}\) – 2\(\frac{1}{12}\) ≈ __________

Answer:

6(1/8) – 2(1/12) = 24/12.

Explanation:

In the above-given question,

given that,

Estimate each difference to the nearest half.

6(1/8) – 2(1/12).

6 x 8 = 48.

2 x 12 = 24.

48 + 1/8 = 49/8.

24 + 1/12 = 25/12.

49/8 – 25/12 = 24/12.

e. 3\(\frac{3}{8}\) + 5\(\frac{1}{9}\) ≈ _____73/9______

Answer:

3(3/8) + 5(1/9) = 73/9.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

3(3/8) + 5(1/9).

8 x 3 = 24.

5 x 9 = 45.

24 + 3/8 = 27/8.

45 + 1/9 = 46/9.

27/8 + 46/9 = 73/9.

Question 2.

Estimate each sum or difference to the nearest half or whole number by rounding. Explain your estimate using words or a number line.

a. \(\frac{16}{5}\) + \(\frac{11}{4}\) ≈ ______

Answer:

16/5 + 11/4 = 6.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

16/5 + 11/4.

16/5 = 3.2.

11/4 = 2.75.

3.2 + 2.75 = 5.95.

16/5 + 11/4 = 5.95.

b. \(\frac{17}{3}\) – \(\frac{15}{7}\) ≈ _______

Answer:

17/3 + 15/7 = 8.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

17/3 + 15/7.

17/3 = 5.6.

15/7 = 2.14.

5.6 + 2.14 = 7.74.

17/3 + 15/7 = 7.74.

c. \(\frac{59}{10}\) + \(\frac{26}{10}\) ≈ _______

Answer:

59/10 + 26/10 = 8.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

59/10 + 26/10.

59/10 = 5.9.

26/10 = 2.6.

5.9 + 2.6 = 8.5.

59/10 + 26/10 = 8.

Question 3.

Montoya’s estimate for 8\(\frac{5}{8}\) – 2\(\frac{1}{3}\) was 7. Julio’s estimate was 6\(\frac{1}{2}\). Whose estimate do you think is closer to the actual difference? Explain.

Answer:

8(5/8) -2(1/3) = 62/5.

Explanation:

In the above-given question,

given that,

Estimate each difference to the nearest half.

8(5/8) – 2(1/3).

8 x 8 = 64.

2 x 3 = 6.

64 + 5/8 = 69/8.

6 + 1/3 = 7/3.

69/8 – 7/3 = 62/5.

Question 4.

Use benchmark numbers or mental math to estimate the sum or difference.

a. 14\(\frac{3}{4}\) + 29\(\frac{11}{12}\)

Answer:

14(3/4) + 29(11/12) = 418/12.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

14(3/4) + 29(11/12).

14 x 4 = 56.

29 x 12 = 348.

56 + 3/4 = 59/4.

348 + 11/12 = 359/12.

59/4 + 359/12 = 418/12.

b. 3\(\frac{5}{12}\) + 54\(\frac{5}{8}\)

Answer:

3(5/12) + 54(5/8) = 478/12.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

3(5/12) + 54(5/8).

12 x 3 = 36.

54 x 8 = 432.

36 + 5/12 = 41/12.

432 + 5/8 = 437/8.

41/12 + 437/8 = 478/12.

c. 17\(\frac{4}{5}\) – 8\(\frac{7}{12}\)

Answer:

17(4/5) – 8(7/12) = 192/60.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

17(4/5) – 8(7/12).

17 x 5 = 85.

12 x 8 = 96.

85 + 4/5 = 89/5.

96 + 7/12 = 103/12.

89/5 + 103/12 = 192/60.

d. \(\frac{65}{8}\) – \(\frac{37}{6}\)

Answer:

65/8 – 37/6 = 4.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

65/8 – 37/6.

65/8 = 8.1.

37/6 = 6.1.

8.1 – 6.1 = 4.1.

65/8 – 37/6 = 4.1.

## Eureka Math Grade 4 Module 5 Lesson 29 Exit Ticket Answer Key

Estimate each sum or difference to the nearest half or whole number by rounding. Explain your estimate using words or a number line.

Question 1.

2\(\frac{9}{10}\) + 2\(\frac{1}{4}\) ≈ _________

Answer:

2(9/10) + 2(1/4) = 38/40.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

2(9/10) + 2(1/4).

2 x 10 = 20.

2 x 4 = 8.

20 + 9/10 = 29/10.

8 + 1/4 = 9/4.

29/10 + 9/4 = 38/40.

Question 2.

11\(\frac{8}{9}\) – 3\(\frac{3}{8}\) ≈ _________

Answer:

11(8/9) – 3(3/8) = 80/72.

Explanation:

In the above-given question,

given that,

Estimate each difference to the nearest half.

11(8/9) – 3(3/8).

11 x 9 = 99.

3 x 8 = 24.

99 + 8/9 = 107/9.

24 + 3/8 = 27/8.

107/9 – 27/8 = 80/72.

## Eureka Math Grade 4 Module 5 Lesson 29 Homework Answer Key

Question 1.

Estimate each sum or difference to the nearest half or whole number by rounding. Explain your estimate using words or a number line.

a. 3\(\frac{1}{10}\) + 1\(\frac{3}{4}\) ≈ ___________

Answer:

3(1/10) + 1(3/4) = 38/40.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

3(1/10) + 1(3/4).

10 x 3 = 30.

1 x 4 = 4.

30 + 1/10 = 31/10.

4 + 3/4 = 7/4.

31/10 + 7/4 = 38/40.

b. 2\(\frac{9}{10}\) + 4\(\frac{4}{5}\) ≈ __________

Answer:

2(9/10) + 4(4/5) = 53/50.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

2(9/10) + 4(4/5).

2 x 10 = 20.

5 x 4 = 20.

20 + 9/10 = 29/10.

20 + 4/5 = 24/5.

29/10 + 24/5 = 53/50.

c. 9\(\frac{9}{10}\) – 5\(\frac{1}{5}\) ≈ __________

Answer:

9(9/10) – 5(1/5) = 73/5.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

9(9/10) – 5(1/5).

9 x 10 = 90.

5 x 5 = 25.

90 + 9/10 = 99/10.

25 + 1/5 = 26/5.

99/10 – 26/5 = 73/5.

d. 4\(\frac{1}{9}\) – 1\(\frac{1}{10}\) ≈ __________

Answer:

4(1/9) – 1(1/10) = 48/10.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

4(1/9) – 1(1/10).

9 x 4 = 36.

1 x 10 = 10.

36 + 1/9 = 37/9.

10 + 1/10 = 11/10.

37/9 + 11/10 = 48/10.

e. 6\(\frac{3}{12}\) + 5\(\frac{1}{9}\) ≈ _______

Answer:

6(3/12) + 5(1/9) = 121/9.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

6(3/12) + 5(1/9).

6 x 12 = 72.

5 x 9 = 45.

72 + 3/12 = 75/12.

45 + 1/9 = 46/9.

75/12 + 46/9 = 121/9.

Question 2.

Estimate each sum or difference to the nearest half or whole number by rounding. Explain your estimate using words or a number line.

a. \(\frac{16}{3}\) + \(\frac{17}{8}\) ≈ __________

Answer:

16/3 + 17/8 = 7.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

16/3 + 17/8.

16/3 = 5.3.

17/8 = 2.1.

5.3 + 2.1 = 7.4.

16/3 + 17/8 = 7.

b. \(\frac{17}{3}\) – \(\frac{15}{4}\) ≈ __________

Answer:

17/3 – 15/4 = 9.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

17/3 – 15/4.

17/3 = 5.6.

15/4 = 3.7.

5.6 + 3.7 = 9.3.

15/4 + 17/3 = 9.

c. \(\frac{57}{8}\) + \(\frac{26}{8}\) ≈ __________

Answer:

57/8 + 26/8 = 10.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

57/8 + 26/8.

57/8 = 7.1.

26/8 = 3.2.

7.1 + 3.2 = 10.3.

57/8 + 26/8 = 10.

Question 3.

Gina’s estimate for 7\(\frac{5}{8}\) – 2\(\frac{1}{2}\) was 5. Dominick’s estimate was 5\(\frac{1}{2}\). Whose estimate do you think is closer to the actual difference? Explain.

Answer:

7(5/8) – 2(1/2) = 56/4.

Explanation:

In the above-given question,

given that,

Estimate each difference to the nearest half.

7(5/8) – 2(1/2).

8 x 7 = 56.

2 x 2 = 4.

56 + 5/8 = 61/8.

4 + 1/2 = 5/2.

61/8 – 5/2 = 56/4.

Question 4.

Use benchmark numbers or mental math to estimate the sum or difference.

a. 10\(\frac{3}{4}\) + 12\(\frac{11}{12}\)

Answer:

10(3/4) + 12(11/12) = 199/3.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

10(3/4) + 12(11/12).

10 x 4 = 40.

12 x 12 = 144.

40 + 3/4 = 43/4.

144 + 11/12 = 156/12.

43/4 + 156/12 = 199/3.

b. 2\(\frac{7}{10}\) + 23\(\frac{3}{8}\)

Answer:

2(7/10) + 23(3/8) = 214/80.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

2(7/10) + 23(3/8).

2 x 10 = 20.

23 x 8 = 184.

20 + 7/10 = 27/10.

184 + 3/8 = 187/8.

27/10 + 187/8 = 214/80.

c. 15\(\frac{9}{12}\) – 8\(\frac{11}{12}\)

Answer:

15(9/12) – 8(11/12) = 82/12.

Explanation:

In the above-given question,

given that,

Estimate each difference to the nearest half.

15(9/12) – 8(11/12).

15 x 12 = 180.

8 x 12 = 96.

180 + 9/12 = 189/12.

96 + 11/12 = 107/12.

189/12 – 107/12 = 82/12.

d. \(\frac{56}{7}\) – \(\frac{31}{8}\)

Answer:

56/7 – 31/8 = 4.2.

Explanation:

In the above-given question,

given that,

Estimate each sum to the nearest half.

56/7 – 31/8.

56/7 = 8.

31/8 = 3.8.

8 – 3.8 = 4.2.

56/7 – 31/8 = 4.2.