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