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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.

\(\frac{8}{14}\) > \(\frac{1}{2}\)