## 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. \(\frac{29}{12}\)

Answer:

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.

Answer:

\(\frac{29}{12}\) = 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

Answer:

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\(\frac{7}{8}\)

Answer:

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\(\frac{1}{6}\)

Answer:

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. \(\frac{70}{9}\)

Answer:

\(\frac{70}{9}\) = 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\(\frac{2}{4}\)

Answer:

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. \(\frac{25}{3}\)

Answer:

\(\frac{25}{3}\) = 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\(\frac{2}{4}\) ___<____ \(\frac{25}{3}\)

Answer:

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\(\frac{2}{4}\)

Answer:

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).

Answer:

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\(\frac{3}{4}\)

Answer:

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. \(\frac{12}{6}\) ____=_______ \(\frac{25}{12}\)

Answer:

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. \(\frac{18}{7}\) ____<______ \(\frac{17}{5}\)

Answer:

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\(\frac{5}{8}\)

Answer:

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\(\frac{3}{7}\)

Answer:

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. \(\frac{31}{7}\) ____>______ \(\frac{32}{8}\)

Answer:

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. \(\frac{31}{10}\) _____=_____ \(\frac{25}{8}\)

Answer:

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. \(\frac{39}{12}\) ____>_____ \(\frac{19}{6}\)

Answer:

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\(\frac{90}{100}\)

Answer:

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\(\frac{51}{100}\)

Answer:

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\(\frac{4}{6}\)

Answer:

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.

\(\frac{12}{3}\) _____>_____ \(\frac{27}{7}\)

Answer:

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.

\(\frac{10}{6}\) __________ \(\frac{5}{4}\)

Answer:

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\(\frac{3}{10}\)

Answer:

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. \(\frac{33}{9}\)

Answer:

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.

Answer:

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.

Answer:

\(\frac{33}{9}\) = 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\(\frac{1}{6}\)

Answer:

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\(\frac{3}{4}\)

Answer:

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. \(\frac{29}{4}\)

Answer:

\(\frac{65}{8}\) = 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

Answer:

\(\frac{29}{4}\) = 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

Answer:

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\(\frac{5}{6}\) ____<_______ \(\frac{65}{8}\)

Answer:

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. \(\frac{29}{4}\) ____<______ \(\frac{65}{8}\)

Answer:

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).

Answer:

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\(\frac{3}{4}\)

Answer:

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. \(\frac{12}{4}\) ____>______ \(\frac{25}{8}\)

Answer:

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. \(\frac{18}{6}\) ___<______ \(\frac{17}{4}\)

Answer:

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\(\frac{5}{10}\)

Answer:

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\(\frac{3}{5}\)

Answer:

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. \(\frac{33}{6}\) _____>______ \(\frac{34}{7}\)

Answer:

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. \(\frac{23}{10}\) __________ \(\frac{20}{8}\)

Answer:

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. \(\frac{27}{12}\) _________ \(\frac{15}{6}\)

Answer:

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\(\frac{99}{100}\)

Answer:

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\(\frac{49}{100}\)

Answer:

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.