## 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. $$\frac{4}{3}$$

$$\frac{4}{3}$$ = 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. $$\frac{11}{6}$$

$$\frac{11}{6}$$ = 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. $$\frac{17}{12}$$

$$\frac{17}{12}$$ = 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$$\frac{5}{12}$$

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$$\frac{5}{12}$$

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. $$\frac{11}{8}$$

$$\frac{11}{8}$$ = 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. $$\frac{7}{4}$$

$$\frac{7}{4}$$ = 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. $$\frac{15}{12}$$

$$\frac{15}{12}$$ = 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. $$\frac{3}{8}$$ _________ $$\frac{7}{12}$$

$$\frac{3}{8}$$ < $$\frac{7}{12}$$

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. $$\frac{3}{8}$$ _________ $$\frac{7}{8}$$

$$\frac{3}{8}$$ < $$\frac{7}{8}$$

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. $$\frac{8}{6}$$ _________ $$\frac{11}{12}$$

$$\frac{8}{6}$$ > $$\frac{11}{12}$$

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. $$\frac{5}{12}$$ _________ $$\frac{1}{3}$$

$$\frac{5}{12}$$ > $$\frac{1}{3}$$

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. $$\frac{7}{5}$$ _________ $$\frac{11}{10}$$

$$\frac{7}{5}$$ > $$\frac{11}{10}$$

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. $$\frac{5}{4}$$ _________ $$\frac{7}{8}$$

$$\frac{5}{4}$$ > $$\frac{7}{8}$$

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. $$\frac{13}{3}$$ _________ $$\frac{9}{10}$$

$$\frac{13}{3}$$ < $$\frac{9}{10}$$

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. $$\frac{6}{8}$$ _________ $$\frac{5}{4}$$

$$\frac{6}{8}$$ < $$\frac{5}{4}$$

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. $$\frac{8}{12}$$ __________ $$\frac{8}{4}$$

$$\frac{8}{12}$$ < $$\frac{8}{4}$$

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. $$\frac{7}{5}$$ __________ $$\frac{16}{10}$$

$$\frac{7}{5}$$ < $$\frac{16}{10}$$

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. $$\frac{5}{4}$$

$$\frac{11}{8}$$ = 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. $$\frac{10}{7}$$

$$\frac{10}{7}$$ = 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. $$\frac{16}{9}$$

$$\frac{16}{9}$$ = 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. $$\frac{5}{4}$$ ________ $$\frac{10}{7}$$

$$\frac{5}{4}$$ = $$\frac{10}{7}$$

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. $$\frac{5}{4}$$ ________ $$\frac{16}{9}$$

$$\frac{5}{4}$$ < $$\frac{16}{9}$$

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. $$\frac{16}{9}$$ ________ $$\frac{10}{7}$$

$$\frac{16}{9}$$ < $$\frac{10}{7}$$

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. $$\frac{3}{2}$$

$$\frac{3}{2}$$ = 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. $$\frac{9}{5}$$

$$\frac{9}{5}$$ = 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. $$\frac{14}{10}$$

$$\frac{14}{10}$$ = 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$$\frac{4}{12}$$

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$$\frac{4}{5}$$

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. $$\frac{12}{9}$$

$$\frac{12}{9}$$ = 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. $$\frac{6}{5}$$

$$\frac{6}{5}$$ = 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. $$\frac{18}{15}$$

$$\frac{18}{15}$$ = 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. $$\frac{2}{5}$$ _________ $$\frac{6}{8}$$

$$\frac{2}{5}$$ < $$\frac{6}{8}$$

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. $$\frac{6}{10}$$ _________ $$\frac{5}{6}$$

$$\frac{6}{10}$$ < $$\frac{5}{6}$$

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. $$\frac{6}{4}$$ _________ $$\frac{7}{8}$$

$$\frac{6}{4}$$ < $$\frac{7}{8}$$

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. $$\frac{1}{4}$$ _________ $$\frac{8}{12}$$

$$\frac{1}{4}$$ < $$\frac{8}{12}$$

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. $$\frac{14}{12}$$ _________ $$\frac{11}{6}$$

$$\frac{14}{12}$$ > $$\frac{11}{6}$$

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. $$\frac{8}{9}$$ _________ $$\frac{3}{2}$$

$$\frac{16}{9}$$ < $$\frac{10}{7}$$

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. $$\frac{7}{9}$$ _________ $$\frac{10}{7}$$

$$\frac{7}{9}$$ < $$\frac{10}{7}$$

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. $$\frac{3}{4}$$ _________ $$\frac{4}{3}$$

$$\frac{3}{4}$$ < $$\frac{4}{3}$$

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. $$\frac{3}{8}$$ _________ $$\frac{3}{2}$$

$$\frac{3}{8}$$ < $$\frac{3}{2}$$

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. $$\frac{9}{6}$$ _________ $$\frac{16}{12}$$

$$\frac{9}{6}$$ > $$\frac{16}{12}$$
$$\frac{9}{6}$$ = (9/6).
$$\frac{16}{12}$$ = (10/7).
$$\frac{9}{6}$$ > $$\frac{16}{12}$$