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## Engage NY Eureka Math 4th Grade Module 5 Lesson 12 Answer Key

People of highly subject expertise prepared the solutions in a concise manner for easy grasping. The ace up your preparation using the Eureka Math Book 4th Grade Answer Key. By using the Eureka Math Answers Grade 4 Lesson 12, you can understand the concepts in depth and score the highest marks in the exam.

### Eureka Math Grade 4 Module 5 Lesson 12 Problem Set Answer Key

a. Plot the following points on the number line without measuring.
i. $$\frac{1}{3}$$

$$\frac{1}{3}$$ = 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. $$\frac{5}{6}$$

$$\frac{5}{6}$$ = 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. $$\frac{7}{12}$$

$$\frac{7}{12}$$ = 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. $$\frac{7}{12}$$ __ $$\frac{1}{2}$$

$$\frac{7}{12}$$ < $$\frac{1}{2}$$

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. $$\frac{7}{12}$$ __ $$\frac{5}{6}$$

$$\frac{7}{12}$$ < $$\frac{5}{6}$$

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. $$\frac{11}{12}$$

$$\frac{11}{12}$$ = 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. $$\frac{1}{4}$$

$$\frac{1}{4}$$ = 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. $$\frac{3}{8}$$

$$\frac{3}{8}$$ = 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 =.

$$\frac{5}{6}$$ >$$\frac{3}{8}$$

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).

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. $$\frac{1}{2}$$ _________ $$\frac{3}{4}$$

$$\frac{1}{2}$$ < $$\frac{3}{4}$$

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. $$\frac{1}{2}$$ _________ $$\frac{7}{8}$$

$$\frac{1}{2}$$ < $$\frac{7}{8}$$

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. $$\frac{2}{3}$$ _________ $$\frac{2}{5}$$

$$\frac{2}{3}$$ < $$\frac{2}{5}$$

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. $$\frac{9}{10}$$ _________ $$\frac{3}{5}$$

$$\frac{9}{10}$$ > $$\frac{3}{5}$$

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. $$\frac{2}{3}$$ _________ $$\frac{7}{8}$$

$$\frac{2}{3}$$ > $$\frac{7}{8}$$

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. $$\frac{1}{3}$$ _________ $$\frac{2}{4}$$

$$\frac{1}{3}$$ >$$\frac{2}{4}$$

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. $$\frac{2}{3}$$ _________ $$\frac{5}{10}$$

$$\frac{2}{3}$$ <$$\frac{5}{10}$$

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. $$\frac{11}{12}$$ _________ $$\frac{2}{5}$$

$$\frac{11}{12}$$ >$$\frac{12}{5}$$

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. $$\frac{49}{100}$$ _________ $$\frac{51}{100}$$

$$\frac{49}{100}$$ >$$\frac{51}{100}$$

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. $$\frac{7}{16}$$ _________ $$\frac{51}{100}$$

$$\frac{7}{16}$$ <$$\frac{51}{100}$$

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. $$\frac{8}{10}$$

$$\frac{8}{10}$$ = 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. $$\frac{3}{5}$$

$$\frac{3}{5}$$ = 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. $$\frac{1}{4}$$

$$\frac{1}{4}$$ = 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. $$\frac{1}{4}$$ _________ $$\frac{1}{2}$$

$$\frac{1}{4}$$ >$$\frac{1}{2}$$

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. $$\frac{8}{10}$$ _________ $$\frac{3}{5}$$

$$\frac{8}{10}$$ >$$\frac{3}{5}$$

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. $$\frac{1}{2}$$ _________ $$\frac{3}{5}$$

$$\frac{1}{2}$$ <$$\frac{3}{5}$$

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. $$\frac{1}{4}$$ _________ $$\frac{8}{10}$$

$$\frac{1}{4}$$ >$$\frac{8}{10}$$

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

$$\frac{2}{3}$$ = 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. $$\frac{1}{6}$$

$$\frac{1}{6}$$ = 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. $$\frac{4}{10}$$

$$\frac{4}{10}$$ = 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. $$\frac{2}{3}$$ _________ $$\frac{1}{2}$$

$$\frac{2}{3}$$ >$$\frac{1}{2}$$

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. $$\frac{4}{10}$$ _________ $$\frac{1}{6}$$

$$\frac{1}{4}$$ >$$\frac{1}{2}$$

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

$$\frac{5}{12}$$ = 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. $$\frac{3}{4}$$

$$\frac{3}{4}$$ = 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. $$\frac{2}{6}$$

$$\frac{2}{6}$$ = 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).

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. $$\frac{1}{2}$$ _________ $$\frac{1}{4}$$

$$\frac{1}{2}$$ <$$\frac{1}{4}$$

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. $$\frac{6}{8}$$ _________ $$\frac{1}{2}$$

$$\frac{6}{8}$$ >$$\frac{1}{2}$$

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. $$\frac{3}{4}$$ _________ $$\frac{3}{5}$$

$$\frac{3}{4}$$ >$$\frac{3}{5}$$

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. $$\frac{4}{6}$$ _________ $$\frac{9}{12}$$

$$\frac{4}{6}$$ <$$\frac{9}{12}$$

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. $$\frac{2}{3}$$ _________ $$\frac{1}{4}$$

$$\frac{2}{3}$$ >$$\frac{1}{4}$$

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. $$\frac{4}{5}$$ _________ $$\frac{8}{12}$$

$$\frac{4}{5}$$ >$$\frac{8}{12}$$

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. $$\frac{1}{3}$$ _________ $$\frac{3}{6}$$

$$\frac{1}{3}$$ <$$\frac{3}{6}$$

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. $$\frac{7}{8}$$ _________ $$\frac{3}{5}$$

$$\frac{7}{8}$$ >$$\frac{3}{5}$$

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. $$\frac{51}{100}$$ _________ $$\frac{5}{10}$$

$$\frac{51}{100}$$ =$$\frac{5}{10}$$

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. $$\frac{8}{14}$$ _________ $$\frac{49}{100}$$

$$\frac{8}{14}$$ > $$\frac{49}{100}$$
$$\frac{49}{100}$$.
$$\frac{8}{14}$$.
$$\frac{8}{14}$$ > $$\frac{1}{2}$$