## Engage NY Eureka Math 4th Grade Module 5 Lesson 26 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 26 Problem Set Answer Key

Question 1.
a. Plot the following points on the number line without measuring.
i. 2$$\frac{7}{8}$$
ii. 3$$\frac{1}{6}$$
iii. $$\frac{29}{12}$$ 2$$\frac{7}{8}$$ = 2.8.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
2(7/8).
2 x 8 = 16.
16 + 7/8.
23/8 = 2.875.
2$$\frac{7}{8}$$ = 2.8.

$$\frac{29}{12}$$ = 2.4.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
29/12 = 2.41.
$$\frac{29}{12}$$ = 2.4

3$$\frac{1}{6}$$ = 3.1.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
3(1/6).
3 x 6 = 18.
18 + 1/6.
19/6 = 3.1.
3$$\frac{1}{6}$$ = 3.1 b. Use the number line in Problem 1(a) to compare the fractions by writing >, ˂, or =.
i. $$\frac{29}{12}$$ ____<___ 2$$\frac{7}{8}$$

29/12  <  2(7/8).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
2(7/8).
2 x 8 = 16.
16 + 7/8.
23/8 = 2.875.
29/12 = 2.4
2.4 < 2.875.

ii. $$\frac{29}{12}$$ ___<______ 3$$\frac{1}{6}$$

29/12  <  3(1/6).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
3(1/6).
3 x 6 = 18.
18 + 1/6.
19/6 = 3.1.
29/12 = 2.4
3.1 > 2.4.

Question 2.
a. Plot the following points on the number line without measuring.
i. $$\frac{70}{9}$$

$$\frac{70}{9}$$ = 7.7

Explanation:
In the above-given question,
given that,
plot the points on the number line.
70/9 = 7.7.
$$\frac{70}{9}$$ = 7.7.

ii. 8$$\frac{2}{4}$$

8$$\frac{2}{4}$$ = 8.5.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
8(2/4).
8 x 4 = 32.
32 + 2/4.
34/4 = 8.5..
8$$\frac{2}{4}$$ = 8.5.

iii. $$\frac{25}{3}$$

$$\frac{25}{3}$$ = 8.3.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
25/3 = 8.3.
$$\frac{25}{3}$$ = 8.3.  b. Compare the following by writing >, ˂, or =.
i. 8$$\frac{2}{4}$$ ___<____ $$\frac{25}{3}$$

25/3  <  8(2/4).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
8(2/4).
8 x 4 = 32.
32 + 2/4.
34/4 = 8.5.
25/3 = 8.3.
8.3 < 8.5.

ii. $$\frac{70}{9}$$ ____<_____ 8$$\frac{2}{4}$$

70/9  <  8(2/4).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
8(2/4).
8 x 4 = 32.
32 + 2/4.
34/4 = 8.5.
70/9 = 7.7
7.7 < 8.5.
c. Explain how you plotted the points in Problem 2(a).

2$$\frac{7}{8}$$ = 2.8.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
2(7/8).
2 x 8 = 16.
16 + 7/8.
23/8 = 2.875.
2$$\frac{7}{8}$$ = 2.8.

Question 3.
Compare the fractions given below by writing >, ˂, or =. Give a brief explanation for each answer, referring to benchmark fractions.
a. 5$$\frac{1}{3}$$ ____>______ 4$$\frac{3}{4}$$

4(3/4)  >  5(1/3).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
4(3/4).
4 x 4 = 16.
16 + 3/4.
19/4 = 4.75.
5(1/3).
5 x 3 = 15.
15 + 1/3.
16/3 = 5.3.
4.7 < 5.3.

b. $$\frac{12}{6}$$ ____=_______ $$\frac{25}{12}$$

12/6  =  25/12.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
12/6 = 2.
25/12 = 2.0.
2.0 = 2.0.

c. $$\frac{18}{7}$$ ____<______ $$\frac{17}{5}$$

18/7  <  17/5.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
18/7 = 2.5.
17/5 = 3.4.
2.5 < 3.4.

d. 5$$\frac{2}{5}$$ _____<_____ 5$$\frac{5}{8}$$

5(2/5)  <  5(5/8).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
5(2/5).
5 x 5 = 25.
25 + 2/5.
27/5 = 5.4.
5(5/8).
5 x 8 = 40.
40 + 5/8.
45/8 = 5.6.
5.4 < 5.6.

e. 6$$\frac{2}{3}$$ ___>_______ 6$$\frac{3}{7}$$

6(2/3)  >  6(3/7).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
6(2/3).
6 x 3 = 18.
18 + 2/3.
20/3 = 6.6.
6(3/7).
6 x 7 = 42.
42 + 3/7.
45/7 = 6.4.
6.6 > 6.4

f. $$\frac{31}{7}$$ ____>______ $$\frac{32}{8}$$

31/7  >  32/8.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
31/7 = 4.4.
32/8 = 4.
4.4 > 4.

g. $$\frac{31}{10}$$ _____=_____ $$\frac{25}{8}$$

31/10  =  25/8.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
31/10 = 3.1.
25/8 = 3.1.
3.1 = 3.1.

h. $$\frac{39}{12}$$ ____>_____ $$\frac{19}{6}$$

39/12  >  19/6.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
39/12 = 3.2.
19/6 = 3.1.
3.2 > 3.1.

i. $$\frac{49}{50}$$ ____<______ 3$$\frac{90}{100}$$

49/50 <  3(90/100).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
3(90/100).
3 x 100 = 300.
300 + 90/100.
390/100 = 3.9.
49/50 = 0.98.
0.98 < 3.9.

j. 5$$\frac{5}{12}$$ ____>_____ 5$$\frac{51}{100}$$

5(5/12)  >  5(51/100).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
5(5/12).
5 x 12 = 60.
60 + 5/12.
65/12 = 5.4.
5(51/100).
5 x 100 = 500.
500 + 51/100.
551/100 = 5.1.
5.4 > 5.1.

Eureka Math Grade 4 Module 5 Lesson 26 Exit Ticket Answer Key

Compare the fractions given below by writing >, ˂, or =.
Give a brief explanation for each answer, referring to benchmark fractions.
Question 1.
3$$\frac{2}{3}$$ ____=______ 3$$\frac{4}{6}$$

3(2/3)  =  3(4/6).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
3(2/3).
3 x 3 = 9.
9 + 2/3.
11/3 = 3.6.
3(4/6).
6 x 3 = 18.
18 + 4/6.
22/6 = 3.6.
3.6 = 3.6.

Question 2.
$$\frac{12}{3}$$ _____>_____ $$\frac{27}{7}$$

12/3  >  27/7.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
12/3 = 4.
27/7 = 3.8.
4 > 3.8.

Question 3.
$$\frac{10}{6}$$ __________ $$\frac{5}{4}$$

10/6  >  5/4.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
10/6 = 1.6.
5/4 = 1.2.
1.6 > 1.2.

Question 4.
3$$\frac{2}{5}$$ __________ 3$$\frac{3}{10}$$

3(2/5)  >  3(3/10).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
3(2/5).
3 x 5 = 15.
15 + 2/5.
17/5 = 3.4.
3(3/10).
10 x 3 = 30.
30 + 3/10.
33/10 = 3.3.
3.4 > 3.3.

## Eureka Math Grade 4 Module 5 Lesson 26 Homework Answer Key

Question 1.
a. Plot the following points on the number line without measuring.
i. 2$$\frac{1}{6}$$
ii. 3$$\frac{3}{4}$$
iii. $$\frac{33}{9}$$ 2$$\frac{1}{6}$$ = 2.1.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
2(1/6).
2 x 6 = 12.
12 + 1/6.
13/6 = 2.1.
2$$\frac{1}{6}$$ = 2.1.

3$$\frac{3}{4}$$ = 3.75.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
3(3/4).
3 x 4 = 12.
12 + 3/4.
15/4 = 3.75.
3$$\frac{3}{4}$$ = 3.7.

$$\frac{33}{9}$$ = 3.6.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
33/9 = 3.6.
$$\frac{33}{9}$$ = 3.6 b. Use the number line in Problem 1(a) to compare the fractions by writing >, ˂, or =.
i. $$\frac{33}{9}$$ ____>______ 2$$\frac{1}{6}$$

33/9 >  2(1/6).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
2(1/6).
2 x 6 = 12.
12 + 1/6.
13/6 = 2.1.
33/9 = 3.6.
3.6 > 2.1.

ii. $$\frac{33}{9}$$ ____<______ 3$$\frac{3}{4}$$

33/9 <  3(3/4).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
3(3/4).
3 x 4 = 12.
12 + 3/4.
15/4 = 3.7.
33/9 = 3.6.
3.7 > 3.6.

Question 2.
a. Plot the following points on the number line without measuring.
i. $$\frac{65}{8}$$
ii. 8$$\frac{5}{6}$$
iii. $$\frac{29}{4}$$ $$\frac{65}{8}$$ = 8.1.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
65/8 = 8.1.
$$\frac{65}{8}$$ = 8.1

$$\frac{29}{4}$$ = 7.2.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
29/4 = 7.2.
$$\frac{29}{4}$$ = 7.2

8$$\frac{5}{6}$$ = 8.8.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
8(5/6).
6 x 8 = 48.
48 + 5/6.
53/6 = 8.8.
8$$\frac{5}{6}$$ = 8.8. b. Compare the following by writing >, ˂, or =.
i. 8$$\frac{5}{6}$$ ____<_______ $$\frac{65}{8}$$

65/8 <  8(5/6).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
8(5/6).
8 x 6 = 48.
48 + 5/6.
53/6 = 8.8.
65/8 = 8.1.
8.1 < 8.8.

ii. $$\frac{29}{4}$$ ____<______ $$\frac{65}{8}$$

29/4  <  65/8.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
29/4 = 7.2.
65/8 = 8.1.
7.2 < 8.1.

c. Explain how you plotted the points in Problem 2(a).

2$$\frac{7}{8}$$ = 2.8.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
2(7/8).
2 x 8 = 16.
16 + 7/8.
23/8 = 2.875.
2$$\frac{7}{8}$$ = 2.8.

Question 3.
Compare the fractions given below by writing >, ˂, or =. Give a brief explanation for each answer, referring to benchmark fractions.
a. 5$$\frac{1}{3}$$ ___<______ 5$$\frac{3}{4}$$

5(1/3)  <  5(3/4).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
5(1/3).
3 x 5 = 15.
15 + 1/3.
16/3 = 5.3.
5(3/4).
5 x 4 = 20.
20 + 3/4.
23/4 = 5.7.
5.3 < 5.7.

b. $$\frac{12}{4}$$ ____>______ $$\frac{25}{8}$$

12/4  >  25/8.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
12/4 = 3.
25/8 = 3.1.
3 > 3.1.

c. $$\frac{18}{6}$$ ___<______ $$\frac{17}{4}$$

18/6  <  17/4.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
18/6 = 3.
17/4 = 4.2.
3 < 4.2.

d. 5$$\frac{3}{5}$$ ___>______ 5$$\frac{5}{10}$$

5(3/5)  >  5(5/10).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
5(3/5).
5 x 5 = 25.
25 + 3/5.
28/5 = 5.6.
5(5/10).
10 x 5 = 50.
50 + 5/10.
55/10 = 5.5.
5.6 > 5.5.

e. 6$$\frac{3}{4}$$ ______>_____ 6$$\frac{3}{5}$$

6(3/4)  >  6(3/5).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
6(3/4).
6 x 4 = 24.
24 + 3/4.
27/4 = 6.7.
6(3/5).
6 x 5 = 30.
30 + 3/5.
33/5 = 6.6.
6.7 > 6.6.

f. $$\frac{33}{6}$$ _____>______ $$\frac{34}{7}$$

33/6  >  34/7.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
33/6 = 5.5.
34/7 = 4.8.
5.5 > 4.8.

g. $$\frac{23}{10}$$ __________ $$\frac{20}{8}$$

23/10  <  20/8.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
23/10 = 2.3.
20/8 = 2.5.
2.3 < 2.5.

h. $$\frac{27}{12}$$ _________ $$\frac{15}{6}$$

27/12  <  15/6.

Explanation:
In the above-given question,
given that,
plot the points on the number line.
27/12 = 2.2.
15/6 = 2.5.
2.2 < 2.5.

i. 2$$\frac{49}{50}$$ __________ 2$$\frac{99}{100}$$

2(49/50)  =  2(99/100).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
2(49/50).
2 x 50 = 100.
100 + 49/50.
149/50 = 2.98.
2(99/100).
100 x 2 = 200.
200 + 99/100.
299/100 = 2.99.
2.9 = 2.9.

j. 6$$\frac{5}{9}$$ __________ 6$$\frac{49}{100}$$

6(5/9)  >  6(49/100).

Explanation:
In the above-given question,
given that,
plot the points on the number line.
6(5/9).
6 x 9 = 54.
54 + 5/9.
59/9 = 6.5.
6(49/100).
100 x 6 = 600.
600 + 49/100.
649/100 = 6.4.
6.5 > 6.4.