## 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________

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_________

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________

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$$\frac{1}{12}$$ ≈ __________

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______

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. $$\frac{16}{5}$$ + $$\frac{11}{4}$$ ≈ ______

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. $$\frac{17}{3}$$ – $$\frac{15}{7}$$ ≈ _______

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. $$\frac{59}{10}$$ + $$\frac{26}{10}$$ ≈ _______

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.

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$$\frac{11}{12}$$

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$$\frac{5}{8}$$

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$$\frac{7}{12}$$

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. $$\frac{65}{8}$$ – $$\frac{37}{6}$$

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$$\frac{1}{4}$$ ≈ _________

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$$\frac{3}{8}$$ ≈ _________

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$$\frac{3}{4}$$ ≈ ___________

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$$\frac{4}{5}$$ ≈ __________

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$$\frac{1}{5}$$ ≈ __________

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$$\frac{1}{10}$$ ≈ __________

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$$\frac{1}{9}$$ ≈ _______

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. $$\frac{16}{3}$$ + $$\frac{17}{8}$$ ≈ __________

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. $$\frac{17}{3}$$ – $$\frac{15}{4}$$ ≈ __________

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. $$\frac{57}{8}$$ + $$\frac{26}{8}$$ ≈ __________

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.

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$$\frac{11}{12}$$

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$$\frac{3}{8}$$

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$$\frac{11}{12}$$

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. $$\frac{56}{7}$$ – $$\frac{31}{8}$$