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Engage NY Eureka Math 4th Grade Module 5 Lesson 12 Answer Key
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Eureka Math Grade 4 Module 5 Lesson 12 Problem Set Answer Key
a. Plot the following points on the number line without measuring.
i. \(\frac{1}{3}\)
Answer:
\(\frac{1}{3}\) = 0.33.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{1}{3}\) = 0.33.
1/3 = 0.33.
ii. \(\frac{5}{6}\)
Answer:
\(\frac{5}{6}\) = 0.83.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{5}{6}\) = 0.83.
5/6 = 0.83.
iii. \(\frac{7}{12}\)
Answer:
\(\frac{7}{12}\) = 0.58.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{7}{12}\) = 0.58.
7/12 = 0.58.
b. Use the number line in Part (a) to compare the fractions by writing >, ˂, or = on the lines.
i. \(\frac{7}{12}\) __ \(\frac{1}{2}\)
Answer:
\(\frac{7}{12}\) < \(\frac{1}{2}\)
Explanation:
In the above-given question,
given that,
\(\frac{7}{12}\) = 7/12.
7/12 = 0.58.
\(\frac{1}{2}\) = 1/2.
0.5.
\(\frac{7}{12}\) < \(\frac{1}{2}\)
ii. \(\frac{7}{12}\) __ \(\frac{5}{6}\)
Answer:
\(\frac{7}{12}\) < \(\frac{5}{6}\)
Explanation:
In the above-given question,
given that,
\(\frac{7}{12}\) = 7/12.
7/12 = 0.58.
\(\frac{5}{6}\) = 5/6.
0.83.
\(\frac{7}{12}\) > \(\frac{1}{2}\)
Question 2.
a. Plot the following points on the number line without measuring.
i. \(\frac{11}{12}\)
Answer:
\(\frac{11}{12}\) = 0.916.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{11}{12}\) = 11/12.
11/12 = 0.916.
ii. \(\frac{1}{4}\)
Answer:
\(\frac{1}{4}\) = 0.25.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{1}{4}\) = 0.25.
1/4 = 0.25.
iii. \(\frac{3}{8}\)
Answer:
\(\frac{3}{8}\) = 0.375.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{3}{8}\) = 3/8.
3/8 = 0.375.
b. Select two fractions from Part (a), and use the given number line to compare them by writing >, ˂, or =.
Answer:
\(\frac{5}{6}\) >\(\frac{3}{8}\)
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{5}{6}\) = 5/6.
5/6 = 0.83.
\(\frac{3}{8}\) = 3/8.
3/8 = 0.375.
c. Explain how you plotted the points in Part (a).
Answer:
The points are 0.33, 0.83, 0.58.
Explanation:
In the above-given question,
given that,
The points plotted in part a is,
0.33, 0.83, 0.58.
Question 3.
Compare the fractions given below by writing > or ˂ on the lines.
Give a brief explanation for each answer referring to the benchmarks 0, \(\frac{1}{2}\), and 1.
a. \(\frac{1}{2}\) _________ \(\frac{3}{4}\)
Answer:
\(\frac{1}{2}\) < \(\frac{3}{4}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{2}\).
1/2 = 0.5.
\(\frac{3}{4}\).
3/4 = 0.75.
\(\frac{1}{2}\) < \(\frac{3}{4}\)
b. \(\frac{1}{2}\) _________ \(\frac{7}{8}\)
Answer:
\(\frac{1}{2}\) < \(\frac{7}{8}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{2}\).
1/2 = 0.5.
\(\frac{7}{8}\).
7/8 = 0.875.
\(\frac{1}{2}\) < \(\frac{7}{8}\)
c. \(\frac{2}{3}\) _________ \(\frac{2}{5}\)
Answer:
\(\frac{2}{3}\) < \(\frac{2}{5}\)
Explanation:
In the above-given question,
given that,
\(\frac{2}{3}\).
2/3 = 0.66.
\(\frac{2}{5}\).
2/5 = 0.4.
\(\frac{2}{3}\) > \(\frac{2}{5}\).
d. \(\frac{9}{10}\) _________ \(\frac{3}{5}\)
Answer:
\(\frac{9}{10}\) > \(\frac{3}{5}\)
Explanation:
In the above-given question,
given that,
\(\frac{9}{10}\).
9/10 = 0.9.
\(\frac{3}{5}\).
3/5 = 0.6.
\(\frac{1}{2}\) > \(\frac{3}{4}\)
e. \(\frac{2}{3}\) _________ \(\frac{7}{8}\)
Answer:
\(\frac{2}{3}\) > \(\frac{7}{8}\)
Explanation:
In the above-given question,
given that,
\(\frac{2}{3}\).
2/3 = 0.66.
\(\frac{7}{8}\).
7/8 = 0.875.
\(\frac{2}{3}\) >\(\frac{7}{8}\)
f. \(\frac{1}{3}\) _________ \(\frac{2}{4}\)
Answer:
\(\frac{1}{3}\) >\(\frac{2}{4}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{3}\).
1/3 = 0.33.
\(\frac{2}{4}\).
2/4 = 0.5.
\(\frac{1}{3}\) >\(\frac{2}{4}\)
g. \(\frac{2}{3}\) _________ \(\frac{5}{10}\)
Answer:
\(\frac{2}{3}\) <\(\frac{5}{10}\)
Explanation:
In the above-given question,
given that,
\(\frac{2}{3}\).
2/3 = 0.66.
\(\frac{5}{10}\).
5/10 = 0.5.
\(\frac{2}{3}\) <\(\frac{5}{10}\)
h. \(\frac{11}{12}\) _________ \(\frac{2}{5}\)
Answer:
\(\frac{11}{12}\) >\(\frac{12}{5}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{2}\).
11/12 = 0.916.
\(\frac{3}{4}\).
12/5 = 2.4.
\(\frac{11}{12}\) >\(\frac{12}{5}\)
i. \(\frac{49}{100}\) _________ \(\frac{51}{100}\)
Answer:
\(\frac{49}{100}\) >\(\frac{51}{100}\)
Explanation:
In the above-given question,
given that,
\(\frac{49}{100}\).
49/100 = 0.49.
\(\frac{51}{100}\).
51/100 = 0.51.
\(\frac{49}{100}\) >\(\frac{51}{100}\)
j. \(\frac{7}{16}\) _________ \(\frac{51}{100}\)
Answer:
\(\frac{7}{16}\) <\(\frac{51}{100}\)
Explanation:
In the above-given question,
given that,
\(\frac{7}{16}\).
7/16 = 0.43.
\(\frac{51}{100}\).
51/100 = 0.51.
\(\frac{11}{12}\) <\(\frac{12}{5}\)
Eureka Math Grade 4 Module 5 Lesson 12 Exit Ticket Answer Key
Question 1.
Plot the following points on the number line without measuring.
a. \(\frac{8}{10}\)
Answer:
\(\frac{8}{10}\) = 0.8.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{8}{10}\) = 8/10.
8/10 = 0.8.
b. \(\frac{3}{5}\)
Answer:
\(\frac{3}{5}\) = 0.6.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{3}{5}\) = 3/5.
3/5 = 0.6.
c. \(\frac{1}{4}\)
Answer:
\(\frac{1}{4}\) = 0.25.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{1}{4}\) = 0.25.
1/4 = 0.25.
Question 2.
Use the number line in Problem 1 to compare the fractions by writing >, ˂, or = on the lines.
a. \(\frac{1}{4}\) _________ \(\frac{1}{2}\)
Answer:
\(\frac{1}{4}\) >\(\frac{1}{2}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{2}\).
1/2 = 0.5.
\(\frac{1}{4}\).
1/4 = 0.25.
\(\frac{1}{4}\) >\(\frac{1}{2}\)
b. \(\frac{8}{10}\) _________ \(\frac{3}{5}\)
Answer:
\(\frac{8}{10}\) >\(\frac{3}{5}\)
Explanation:
In the above-given question,
given that,
\(\frac{8}{10}\).
8/10 = 0.8.
\(\frac{3}{5}\).
3/5 = 0.6.
\(\frac{8}{10}\) >\(\frac{3}{5}\)
c. \(\frac{1}{2}\) _________ \(\frac{3}{5}\)
Answer:
\(\frac{1}{2}\) <\(\frac{3}{5}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{2}\).
1/2 = 0.5.
\(\frac{3}{5}\).
3/5 = 0.6.
\(\frac{1}{2}\) <\(\frac{3}{5}\)
d. \(\frac{1}{4}\) _________ \(\frac{8}{10}\)
Answer:
\(\frac{1}{4}\) >\(\frac{8}{10}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{4}\).
1/4 = 0.25.
\(\frac{8}{10}\).
8/10 = 0.8.
\(\frac{1}{4}\) <\(\frac{8}{10}\)
Eureka Math Grade 4 Module 5 Lesson 12 Homework Answer Key
Question 1.
a. Plot the following points on the number line without measuring.
i. \(\frac{2}{3}\)
Answer:
\(\frac{2}{3}\) = 0.66.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{2}{3}\) = 2/3.
2/3 = 0.66.
ii. \(\frac{1}{6}\)
Answer:
\(\frac{1}{6}\) = 0.16.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{1}{6}\) = 0.16.
1/6 = 0.16.
iii. \(\frac{4}{10}\)
Answer:
\(\frac{4}{10}\) = 0.4.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{4}{10}\) = 0.4.
4/10 = 0.4.
b. Use the number line in Part (a) to compare the fractions by writing >, ˂, or = on the lines.
i. \(\frac{2}{3}\) _________ \(\frac{1}{2}\)
Answer:
\(\frac{2}{3}\) >\(\frac{1}{2}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{2}\).
1/2 = 0.5.
\(\frac{2}{3}\).
2/3 = 0.66.
\(\frac{1}{4}\) >\(\frac{1}{2}\)
ii. \(\frac{4}{10}\) _________ \(\frac{1}{6}\)
Answer:
\(\frac{1}{4}\) >\(\frac{1}{2}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{4}\).
1/4 = 0.25.
\(\frac{1}{2}\).
1/2 = 0.5.
\(\frac{1}{4}\) >\(\frac{1}{2}\)
Question 2.
a. Plot the following points on the number line without measuring.
i. \(\frac{5}{12}\)
Answer:
\(\frac{5}{12}\) = 0.41.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{5}{12}\) = 0.41.
5/12 = 0.41.
ii. \(\frac{3}{4}\)
Answer:
\(\frac{3}{4}\) = 0.75.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{3}{4}\) = 0.75.
3/4 = 0.75.
iii. \(\frac{2}{6}\)
Answer:
\(\frac{2}{6}\) = 0.33.
Explanation:
In the above-given question,
given that,
plot the following points on the number line without measuring.
\(\frac{2}{6}\) = 0.33.
2/6 = 0.33.
b. Select two fractions from Part (a), and use the given number line to compare them by writing
>, ˂, or =.
c. Explain how you plotted the points in Part (a).
Answer:
The points are 0.33, 0.83, 0.58.
Explanation:
In the above-given question,
given that,
The points plotted in part a is,
0.33, 0.83, 0.58.
Question 3.
Compare the fractions given below by writing > or ˂ on the lines.
Give a brief explanation for each answer referring to the benchmark of 0, \(\frac{1}{2}\), and 1.
a. \(\frac{1}{2}\) _________ \(\frac{1}{4}\)
Answer:
\(\frac{1}{2}\) <\(\frac{1}{4}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{2}\).
1/2 = 0.5.
\(\frac{1}{4}\).
1/4 = 0.25.
\(\frac{1}{4}\) <\(\frac{1}{2}\)
b. \(\frac{6}{8}\) _________ \(\frac{1}{2}\)
Answer:
\(\frac{6}{8}\) >\(\frac{1}{2}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{2}\).
1/2 = 0.5.
\(\frac{6}{8}\).
6/8 = 0.75.
\(\frac{6}{8}\) >\(\frac{1}{2}\)
c. \(\frac{3}{4}\) _________ \(\frac{3}{5}\)
Answer:
\(\frac{3}{4}\) >\(\frac{3}{5}\)
Explanation:
In the above-given question,
given that,
\(\frac{3}{4}\).
3/4 = 0.75.
\(\frac{3}{5}\).
3/5 = 0.6.
\(\frac{3}{4}\) >\(\frac{3}{5}\)
d. \(\frac{4}{6}\) _________ \(\frac{9}{12}\)
Answer:
\(\frac{4}{6}\) <\(\frac{9}{12}\)
Explanation:
In the above-given question,
given that,
\(\frac{4}{6}\).
4/6 = 0.66.
\(\frac{9}{12}\).
9/12 = 0.75.
\(\frac{4}{6}\) <\(\frac{9}{12}\)
e. \(\frac{2}{3}\) _________ \(\frac{1}{4}\)
Answer:
\(\frac{2}{3}\) >\(\frac{1}{4}\)
Explanation:
In the above-given question,
given that,
\(\frac{2}{3}\).
2/3 = 0.66.
\(\frac{1}{4}\).
1/4 = 0.25.
\(\frac{2}{3}\) >\(\frac{1}{4}\)
f. \(\frac{4}{5}\) _________ \(\frac{8}{12}\)
Answer:
\(\frac{4}{5}\) >\(\frac{8}{12}\)
Explanation:
In the above-given question,
given that,
\(\frac{4}{5}\).
4/5 = 0.8.
\(\frac{8}{12}\).
8/12 = 0.66.
\(\frac{4}{5}\) >\(\frac{8}{12}\)
g. \(\frac{1}{3}\) _________ \(\frac{3}{6}\)
Answer:
\(\frac{1}{3}\) <\(\frac{3}{6}\)
Explanation:
In the above-given question,
given that,
\(\frac{1}{3}\).
1/3 = 0.33.
\(\frac{3}{6}\).
3/6 = 0.5.
\(\frac{1}{3}\) <\(\frac{3}{6}\)
h. \(\frac{7}{8}\) _________ \(\frac{3}{5}\)
Answer:
\(\frac{7}{8}\) >\(\frac{3}{5}\)
Explanation:
In the above-given question,
given that,
\(\frac{7}{8}\).
7/8 = 0.875.
\(\frac{3}{5}\).
3/5 = 0.6.
\(\frac{7}{8}\) >\(\frac{3}{5}\)
i. \(\frac{51}{100}\) _________ \(\frac{5}{10}\)
Answer:
\(\frac{51}{100}\) =\(\frac{5}{10}\)
Explanation:
In the above-given question,
given that,
\(\frac{51}{100}\).
51/100 = 0.51.
\(\frac{5}{10}\).
5/10 = 0.5.
\(\frac{1}{4}\) = \(\frac{1}{2}\)
j. \(\frac{8}{14}\) _________ \(\frac{49}{100}\)
Answer:
\(\frac{8}{14}\) > \(\frac{49}{100}\)
Explanation:
In the above-given question,
given that,
\(\frac{49}{100}\).
49/100 = 0.49.
\(\frac{8}{14}\).
8/14 = 0.57.
\(\frac{8}{14}\) > \(\frac{1}{2}\)