## Engage NY Eureka Math 4th Grade Module 5 Lesson 13 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 13 Problem Set Answer Key

Question 1.

Place the following fractions on the number line given.

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

Answer:

\(\frac{4}{3}\) = 1.33.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{4}{3}\) = 1.33.

4/3 = 1.33.

b. \(\frac{11}{6}\)

Answer:

\(\frac{11}{6}\) = 1.83.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{11}{6}\) = 1.83.

11/6 = 1.83.

c. \(\frac{17}{12}\)

Answer:

\(\frac{17}{12}\) = 1.41.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{17}{12}\) = 1.41.

17/12 = 1.41.

Question 2.

Use the number line in Problem 1 to compare the fractions by writing >, ˂, or = on the lines.

a. 1\(\frac{5}{6}\) ________ 1\(\frac{5}{12}\)

Answer:

1\(\frac{5}{6}\) > 1\(\frac{5}{12}\)

Explanation:

In the above-given question,

given that,

1\(\frac{5}{6}\) = 1(5/6).

6 +5/6 = 11/6.

11/6 = 1.83

1\(\frac{5}{12}\) = 1(5/12).

12 + 5/12 = 17/12.

17/12 = 1.41.

1\(\frac{7}{12}\) > 1\(\frac{1}{2}\)

b. 1\(\frac{1}{3}\) ________ 1\(\frac{5}{12}\)

Answer:

1\(\frac{1}{3}\) <1\(\frac{5}{12}\)

Explanation:

In the above-given question,

given that,

1\(\frac{1}{3}\) = 1(1/3).

3 +1/3 = 4/3.

4/3 = 1.33

1\(\frac{5}{12}\) = 1(5/12).

12 + 5/12 = 17/12.

17/12 = 1.41.

1\(\frac{1}{3}\) < 1\(\frac{1}{2}\)

Question 3.

Place the following fractions on the number line given.

a. \(\frac{11}{8}\)

Answer:

\(\frac{11}{8}\) = 1.375.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{11}{8}\) = 1.375.

11/8 = 1.375.

b. \(\frac{7}{4}\)

Answer:

\(\frac{7}{4}\) = 1.75.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{7}{4}\) = 1.75.

7/4 = 1.75.

c. \(\frac{15}{12}\)

Answer:

\(\frac{15}{12}\) = 1.25.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{15}{12}\) = 1.25.

15/12 = 1.25.

Question 4.

Use the number line in Problem 3 to explain the reasoning you used when determining whether \(\frac{11}{8}\) or \(\frac{15}{12}\) is greater.

Question 5.

Compare the fractions given below by writing > or ˂ on the lines. Give a brief explanation for each answer referring to benchmarks.

a. \(\frac{3}{8}\) _________ \(\frac{7}{12}\)

Answer:

\(\frac{3}{8}\) < \(\frac{7}{12}\)

Explanation:

In the above-given question,

given that,

\(\frac{3}{8}\) = (3/8).

3/8 = 0.375.

\(\frac{7}{12}\) = (7/12).

7/12 = 0.583.

\(\frac{3}{8}\) < \(\frac{7}{12}\)

b. \(\frac{3}{8}\) _________ \(\frac{7}{8}\)

Answer:

\(\frac{3}{8}\) < \(\frac{7}{8}\)

Explanation:

In the above-given question,

given that,

\(\frac{3}{8}\) = (3/8).

3/8 = 0.375.

\(\frac{7}{8}\) = (7/8).

7/8 = 0.875.

\(\frac{3}{8}\) < \(\frac{7}{8}\)

c. \(\frac{8}{6}\) _________ \(\frac{11}{12}\)

Answer:

\(\frac{8}{6}\) > \(\frac{11}{12}\)

Explanation:

In the above-given question,

given that,

\(\frac{8}{6}\) = (8/6).

8/6 = 1.33.

\(\frac{11}{12}\) = (11/12).

11/12 = 0.916.

\(\frac{8}{6}\) > \(\frac{11}{12}\)

d. \(\frac{5}{12}\) _________ \(\frac{1}{3}\)

Answer:

\(\frac{5}{12}\) > \(\frac{1}{3}\)

Explanation:

In the above-given question,

given that,

\(\frac{5}{12}\) = (5/12).

5/12 = 0.416.

\(\frac{1}{3}\) = (1/3).

1/3 = 0.33.

\(\frac{5}{12}\) > \(\frac{1}{3}\)

e. \(\frac{7}{5}\) _________ \(\frac{11}{10}\)

Answer:

\(\frac{7}{5}\) > \(\frac{11}{10}\)

Explanation:

In the above-given question,

given that,

\(\frac{7}{5}\) = (7/5).

7/5 = 1.4.

\(\frac{11}{10}\) = (11/10).

11/10 = 1.1.

\(\frac{7}{5}\) > \(\frac{11}{10}\)

f. \(\frac{5}{4}\) _________ \(\frac{7}{8}\)

Answer:

\(\frac{5}{4}\) > \(\frac{7}{8}\)

Explanation:

In the above-given question,

given that,

\(\frac{5}{4}\) = (5/4).

5/4 = 1.25.

\(\frac{7}{8}\) = (7/8).

7/8 = 0.875.

\(\frac{5}{4}\) > \(\frac{7}{8}\)

g. \(\frac{13}{3}\) _________ \(\frac{9}{10}\)

Answer:

\(\frac{13}{3}\) < \(\frac{9}{10}\)

Explanation:

In the above-given question,

given that,

\(\frac{13}{3}\) = (13/3).

13/3 = 4.3.

\(\frac{9}{10}\) = (9/10).

9/10 = 0.9.

\(\frac{13}{3}\) < \(\frac{9}{10}\)

h. \(\frac{6}{8}\) _________ \(\frac{5}{4}\)

Answer:

\(\frac{6}{8}\) < \(\frac{5}{4}\)

Explanation:

In the above-given question,

given that,

\(\frac{6}{8}\) = (6/8).

6/8 = 0.75.

\(\frac{5}{4}\) = (5/4).

5/4 = 1.25.

\(\frac{6}{8}\) < \(\frac{5}{4}\)

i. \(\frac{8}{12}\) __________ \(\frac{8}{4}\)

Answer:

\(\frac{8}{12}\) < \(\frac{8}{4}\)

Explanation:

In the above-given question,

given that,

\(\frac{8}{12}\) = (8/12).

8/12 = 0.375.

\(\frac{8}{4}\) = (8/4).

8/4 = 2.

\(\frac{8}{12}\) < \(\frac{8}{4}\)

j. \(\frac{7}{5}\) __________ \(\frac{16}{10}\)

Answer:

\(\frac{7}{5}\) < \(\frac{16}{10}\)

Explanation:

In the above-given question,

given that,

\(\frac{7}{5}\) = (7/5).

7/5 = 1.4.

\(\frac{16}{10}\) = (16/10).

16/10 = 1.6.

\(\frac{7}{5}\) < \(\frac{16}{10}\)

### Eureka Math Grade 4 Module 5 Lesson 13 Exit Ticket Answer Key

Question 1.

Place the following fractions on the number line given.

a. \(\frac{5}{4}\)

Answer:

\(\frac{11}{8}\) = 1.375.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{11}{8}\) = 1.375.

11/8 = 1.375.

b. \(\frac{10}{7}\)

Answer:

\(\frac{10}{7}\) = 1.42.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{10}{7}\) = 1.42.

10/7 = 1.42.

c. \(\frac{16}{9}\)

Answer:

\(\frac{16}{9}\) = 1.77.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{16}{9}\) = 1.77.

16/9 = 1.77.

Question 2.

Compare the fractions using >, ˂, or =.

a. \(\frac{5}{4}\) ________ \(\frac{10}{7}\)

Answer:

\(\frac{5}{4}\) = \(\frac{10}{7}\)

Explanation:

In the above-given question,

given that,

\(\frac{5}{4}\) = (5/4).

5/4 = 1.25.

\(\frac{10}{7}\) = (10/7).

10/7 = 1.25.

\(\frac{8}{12}\) = \(\frac{8}{4}\)

b. \(\frac{5}{4}\) ________ \(\frac{16}{9}\)

Answer:

\(\frac{5}{4}\) < \(\frac{16}{9}\)

Explanation:

In the above-given question,

given that,

\(\frac{5}{4}\) = (5/4).

5/4 = 1.25.

\(\frac{16}{9}\) = (16/9).

16/9 = 1.77.

\(\frac{5}{4}\) < \(\frac{16}{9}\)

c. \(\frac{16}{9}\) ________ \(\frac{10}{7}\)

Answer:

\(\frac{16}{9}\) < \(\frac{10}{7}\)

Explanation:

In the above-given question,

given that,

\(\frac{16}{9}\) = (16/9).

16/9 = 0.375.

\(\frac{10}{7}\) = (10/7).

10/7 = 1.42.

\(\frac{16}{9}\) < \(\frac{10}{7}\)

### Eureka Math Grade 4 Module 5 Lesson 13 Homework Answer Key

Question 1.

Place the following fractions on the number line given.

a. \(\frac{3}{2}\)

Answer:

\(\frac{3}{2}\) = 1.5.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{3}{2}\) = 3/2.

3/2 = 1.5.

b. \(\frac{9}{5}\)

Answer:

\(\frac{9}{5}\) = 1.8.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{9}{5}\) = 1.8.

9/5 = 1.8.

c. \(\frac{14}{10}\)

Answer:

\(\frac{14}{10}\) = 1.4.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{14}{10}\) = 1.4.

14/10 = 1.4.

Question 2.

Use the number line in Problem 1 to compare the fractions by writing >, ˂, or = on the lines.

a. 1\(\frac{1}{6}\) ________ 1\(\frac{4}{12}\)

Answer:

1\(\frac{1}{6}\) < 1\(\frac{4}{12}\)

Explanation:

In the above-given question,

given that,

1\(\frac{1}{6}\) = 1(1/6).

6 + 1/6 = 7/6.

7/6 = 1.16.

1\(\frac{4}{12}\) = 1(4/12).

12 + 4/12 = 16/12.

16/12 = 1.33.

1\(\frac{1}{6}\) < 1\(\frac{4}{12}\)

b. 1\(\frac{1}{2}\) ________ 1\(\frac{4}{5}\)

Answer:

1\(\frac{1}{2}\) < 1\(\frac{4}{5}\)

Explanation:

In the above-given question,

given that,

1\(\frac{1}{2}\) = 1(1/2).

2 + 1/2 = 3/2.

3/2 = 1.5.

1\(\frac{4}{5}\) = 1(4/5).

5 + 4/5 = 9/5.

9/5 = 1.8.

1\(\frac{1}{2}\) < 1\(\frac{4}{5}\)

Question 3.

Place the following fractions on the number line given.

a. \(\frac{12}{9}\)

Answer:

\(\frac{12}{9}\) = 1.33.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{12}{9}\) = 12/9.

12/9 = 1.33.

b. \(\frac{6}{5}\)

Answer:

\(\frac{6}{5}\) = 1.2.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{6}{5}\) = 1.2.

6/5 = 1.2.

c. \(\frac{18}{15}\)

Answer:

\(\frac{18}{15}\) = 1.2.

Explanation:

In the above-given question,

given that,

plot the following points on the number line without measuring.

\(\frac{18}{15}\) = 1.2.

18/15 = 1.2.

Question 4.

Use the number line in Problem 3 to explain the reasoning you used when determining whether \(\frac{12}{9}\) or \(\frac{18}{15}\) was greater.

Question 5.

Compare the fractions given below by writing > or ˂ on the lines. Give a brief explanation for each answer referring to benchmarks.

a. \(\frac{2}{5}\) _________ \(\frac{6}{8}\)

Answer:

\(\frac{2}{5}\) < \(\frac{6}{8}\)

Explanation:

In the above-given question,

given that,

\(\frac{2}{5}\) = (2/5).

2/5 = 0.4.

\(\frac{6}{8}\) = (6/8).

6/8 = 0.75.

\(\frac{2}{5}\) < \(\frac{6}{8}\)

b. \(\frac{6}{10}\) _________ \(\frac{5}{6}\)

Answer:

\(\frac{6}{10}\) < \(\frac{5}{6}\)

Explanation:

In the above-given question,

given that,

\(\frac{6}{10}\) = (6/10).

6/10 = 0.6.

\(\frac{5}{6}\) = (5/6).

5/6 = 0.83.

\(\frac{6}{10}\) < \(\frac{5}{6}\)

c. \(\frac{6}{4}\) _________ \(\frac{7}{8}\)

Answer:

\(\frac{6}{4}\) < \(\frac{7}{8}\)

Explanation:

In the above-given question,

given that,

\(\frac{6}{4}\) = (6/4).

6/4 = 0.375.

\(\frac{7}{8}\) = (7/8).

7/8 = 0.875.

\(\frac{6}{4}\) < \(\frac{7}{8}\)

d. \(\frac{1}{4}\) _________ \(\frac{8}{12}\)

Answer:

\(\frac{1}{4}\) < \(\frac{8}{12}\)

Explanation:

In the above-given question,

given that,

\(\frac{1}{4}\) = (1/4).

1/4 = 0.25.

\(\frac{8}{12}\) = (8/12).

8/12 = 0.66.

\(\frac{1}{4}\) < \(\frac{8}{12}\)

e. \(\frac{14}{12}\) _________ \(\frac{11}{6}\)

Answer:

\(\frac{14}{12}\) > \(\frac{11}{6}\)

Explanation:

In the above-given question,

given that,

\(\frac{14}{12}\) = (14/12).

14/12 = 1.16.

\(\frac{11}{6}\) = (11/6).

11/6 = 1.83.

\(\frac{14}{12}\) > \(\frac{11}{6}\)

f. \(\frac{8}{9}\) _________ \(\frac{3}{2}\)

Answer:

\(\frac{16}{9}\) < \(\frac{10}{7}\)

Explanation:

In the above-given question,

given that,

\(\frac{16}{9}\) = (16/9).

16/9 = 0.375.

\(\frac{10}{7}\) = (10/7).

10/7 = 1.42.

\(\frac{16}{9}\) < \(\frac{10}{7}\)

g. \(\frac{7}{9}\) _________ \(\frac{10}{7}\)

Answer:

\(\frac{7}{9}\) < \(\frac{10}{7}\)

Explanation:

In the above-given question,

given that,

\(\frac{7}{9}\) = (7/9).

7/9 = 0.77.

\(\frac{10}{7}\) = (10/7).

10/7 = 1.42.

\(\frac{7}{9}\) < \(\frac{10}{7}\)

h. \(\frac{3}{4}\) _________ \(\frac{4}{3}\)

Answer:

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

Explanation:

In the above-given question,

given that,

\(\frac{3}{4}\) = (3/4).

3/4 = 0.75.

\(\frac{4}{3}\) = (4/3).

4/3 = 1.33.

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

i. \(\frac{3}{8}\) _________ \(\frac{3}{2}\)

Answer:

\(\frac{3}{8}\) < \(\frac{3}{2}\)

Explanation:

In the above-given question,

given that,

\(\frac{3}{8}\) = (3/8).

3/8 = 0.375.

\(\frac{3}{2}\) = (3/2).

3/2 = 1.5.

\(\frac{3}{8}\) < \(\frac{3}{2}\)

j. \(\frac{9}{6}\) _________ \(\frac{16}{12}\)

Answer:

\(\frac{9}{6}\) > \(\frac{16}{12}\)

Explanation:

In the above-given question,

given that,

\(\frac{9}{6}\) = (9/6).

9/6 = 1.5.

\(\frac{16}{12}\) = (10/7).

16/12 = 1.33.

\(\frac{9}{6}\) > \(\frac{16}{12}\)