## Engage NY Eureka Math 4th Grade Module 5 Lesson 15 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 15 Problem Set Answer Key

Question 1.
Draw an area model for each pair of fractions, and use it to compare the two fractions by writing >, <, or = on the line. The first two have been partially done for you. Each rectangle represents 1.
a. $$\frac{1}{2}$$ _____< ______ $$\frac{2}{3}$$ 1/2  = 3/6.

Explanation:
In the above-given question,
given that,
Each rectangle represents 1.
1 x 3/2 x 3.
1 x 3 = 3.
2 x 3 = 6.
3/6.

2/3  = 4/6.

Explanation:
In the above-given question,
given that,
Each rectangle represents 1.
2 x 2/3 x 2.
2 x 2 = 4.
2 x 3 = 6.
4/6.

b. $$\frac{4}{5}$$ __________ $$\frac{3}{4}$$ $$\frac{4}{5}$$ __>___ $$\frac{3}{4}$$.

Explanation:
In the above-given question,
given that,
$$\frac{4}{5}$$.
4/5 = 4 fifths.
4/5 = 0.8.
$$\frac{3}{4}$$.
3/4 = 3 fourths.
3/4 = 0.75.
0.8 > 0.75.
4 fifths are greater than 3 fourths.
4/5 > 3/4.

c. $$\frac{3}{5}$$ __________ $$\frac{4}{7}$$

$$\frac{3}{5}$$ __=__ $$\frac{4}{7}$$.

Explanation:
In the above-given question,
given that,
$$\frac{3}{5}$$.
3/5 = 3 fifths.
3/5 = 0.6.
$$\frac{4}{7}$$.
4/7 = 4 sevenths.
4/7 = 0.6.
0.6 = 0.6.
3 fifths are equal to 4 sevenths.
3/5 = 4/7.

d. $$\frac{3}{7}$$ __________ $$\frac{2}{6}$$

$$\frac{3}{7}$$ __>___ $$\frac{2}{6}$$.

Explanation:
In the above-given question,
given that,
$$\frac{3}{7}$$.
3/7 = 3 sevenths.
3/7 = 0.42.
$$\frac{2}{6}$$.
2/6 = 2 sixths.
2/6 = 0.33.
0.42 > 0.33.
3 sevenths are greater than 2 sixths.
3/7 > 2/6.

e. $$\frac{5}{8}$$ __________ $$\frac{6}{9}$$

$$\frac{5}{8}$$ __<___ $$\frac{6}{9}$$.

Explanation:
In the above-given question,
given that,
$$\frac{5}{8}$$.
5/8 = 5 eights.
5/8 = 0.625.
$$\frac{6}{9}$$.
6/9 = 6 ninths.
6/9 = 0.66.
0.625 < 0.66.
5 eights are less than 6 ninths.
5/8 < 6/9.

f. $$\frac{2}{3}$$ __________ $$\frac{3}{4}$$

$$\frac{2}{3}$$ __<___ $$\frac{3}{4}$$.

Explanation:
In the above-given question,
given that,
$$\frac{2}{3}$$.
2/3 = 2 thirds.
2/3 = 0.6
$$\frac{3}{4}$$.
3/4 = 3 fourths.
3/4 = 0.75.
0.6 < 0.75.
2 thirds are less than 3 fourths.
2/3 < 3/4.

Rename the fractions, as needed, using multiplication in order to compare each pair of fractions by writing >, <, or =.
a. $$\frac{3}{5}$$ __________ $$\frac{5}{6}$$

$$\frac{3}{5}$$ __<___ $$\frac{5}{6}$$.

Explanation:
In the above-given question,
given that,
$$\frac{3}{5}$$.
3/5 = 3 fifths.
3/5 = 0.6.
$$\frac{5}{6}$$.
5/6 = 5 sixths.
5/6 = 0.83.
0.6 < 0.83.
3 fifths are less than 5 sixths.
3/5 < 5/6.

b. $$\frac{2}{6}$$ __________ $$\frac{3}{8}$$

$$\frac{2}{6}$$ __<___ $$\frac{3}{8}$$.

Explanation:
In the above-given question,
given that,
$$\frac{2}{6}$$.
2/6 = 2 sixths.
2/6 = 0.33.
$$\frac{3}{8}$$.
3/8 = 3 eights.
3/8 = 0.375.
0.3 = 0.3.
2 sixths are equal to 3 eights.
2/6 = 3/8.

c. $$\frac{7}{5}$$ __________ $$\frac{10}{8}$$

$$\frac{7}{5}$$ __<___ $$\frac{10}{8}$$.

Explanation:
In the above-given question,
given that,
$$\frac{7}{5}$$.
7/5 = 7 fifths.
7/5 = 1.4.
$$\frac{10}{8}$$.
10/8 = 10 eights.
10/8 = 1.25.
1.4 > 1.25.
7 fifths are greater than 10 eights.
7/5 > 10/8.

d. $$\frac{4}{3}$$ __________ $$\frac{6}{5}$$

$$\frac{4}{3}$$ __<___ $$\frac{6}{5}$$.

Explanation:
In the above-given question,
given that,
$$\frac{4}{3}$$.
4/3 = 4 thirds.
4/3 = 1.33.
$$\frac{6}{5}$$.
6/5 = 6 fifths.
6/5 = 1.2.
1.33 > 1.2.
4 thirds are greater than 6 fifths.
4/3 > 6/5.

Question 3.
Use any method to compare the fractions. Record your answer using >, <, or =.
a. $$\frac{3}{4}$$ __________ $$\frac{7}{8}$$

$$\frac{3}{4}$$ __<___ $$\frac{7}{8}$$.

Explanation:
In the above-given question,
given that,
$$\frac{3}{4}$$.
3/4 = 3 fourths.
3/4 = 0.75.
$$\frac{7}{8}$$.
7/8 = 7 eights.
7/8 = 0.875.
0.75 < 0.87.
3 fourths are less than 7 eights.
3/4 < 7/8.

b. $$\frac{6}{8}$$ __________ $$\frac{3}{5}$$

$$\frac{6}{8}$$ __<___ $$\frac{3}{5}$$.

Explanation:
In the above-given question,
given that,
$$\frac{6}{8}$$.
6/8 = 6 eights.
6/8 = 0.75.
$$\frac{3}{5}$$.
3/5 = 3 fifths.
3/5 = 0.6.
0.75 > 0.6.
6 eights are greater than 3 fifths.
6/8 > 3/5.

c. $$\frac{6}{4}$$ __________ $$\frac{8}{6}$$

$$\frac{6}{4}$$ __>___ $$\frac{8}{6}$$.

Explanation:
In the above-given question,
given that,
$$\frac{6}{4}$$.
6/4 = 6 fourths.
6/4 = 1.5
$$\frac{8}{6}$$.
8/6 = 8 sixths.
8/6 = 1.33.
1.5 > 1.33.
6 fourths are greater than 8 sixths.
6/4 > 8/6.

d. $$\frac{8}{5}$$ __________ $$\frac{9}{6}$$

$$\frac{8}{5}$$ __<___ $$\frac{9}{6}$$.

Explanation:
In the above-given question,
given that,
$$\frac{8}{5}$$.
8/5 = 8 fifths.
8/5 = 1.6.
$$\frac{9}{6}$$.
9/6 = 9 sixths.
9/6 = 1.5.
1.6 > 1.5.
8 fifths are greater than 9 sixths.
8/5 > 9/6.

Question 4.
Explain two ways you have learned to compare fractions. Provide evidence using words, pictures, or numbers.

### Eureka Math Grade 4 Module 5 Lesson 15 Exit Ticket Answer Key

Draw an area model for each pair of fractions, and use it to compare the two fractions by writing >, <, or = on the line.

Question 1.
$$\frac{3}{4}$$ ________ $$\frac{4}{5}$$

$$\frac{3}{4}$$ __<___ $$\frac{4}{5}$$.

Explanation:
In the above-given question,
given that,
$$\frac{3}{4}$$.
3/4 = 3 fourths.
3/4 = 0.75.
$$\frac{4}{5}$$.
4/5 = 4 fifths.
4/5 = 0.8.
0.75 < 0.8.
3 fourths are less than 4 fifths.
3/4 < 4/5.

Question 2.
$$\frac{2}{6}$$ ________ $$\frac{3}{5}$$

$$\frac{2}{6}$$ __>___ $$\frac{3}{5}$$.

Explanation:
In the above-given question,
given that,
$$\frac{3}{5}$$.
3/5 = 3 fifths.
3/5 = 0.6.
$$\frac{2}{6}$$.
2/6 = 2 sixths.
2/6 = 0.33.
0.6 > 0.33.
3 fifths are greater than 2 sixths.
3/5 > 2/6.

### Eureka Math Grade 4 Module 5 Lesson 15 Homework Answer Key

Draw an area model for each pair of fractions, and use it to compare the two fractions by writing >, <, or = on the line. The first two have been partially done for you. Each rectangle represents 1.

a. $$\frac{1}{2}$$ ____<______ $$\frac{3}{5}$$ $$\frac{1}{2}$$ __<___ $$\frac{3}{5}$$.

Explanation:
In the above-given question,
given that,
$$\frac{1}{2}$$.
1/2 = 1 twos.
1/2 = 0.5.
$$\frac{3}{5}$$.
3/5 = 3 fifths.
3/5 = 0.6.
0.5 < 0.6.
1 two are less than 3 fifths.
1/2 < 3/5.

b. $$\frac{2}{3}$$ _____ $$\frac{3}{4}$$ $$\frac{2}{3}$$ __<___ $$\frac{3}{4}$$.

Explanation:
In the above-given question,
given that,
$$\frac{2}{3}$$.
2/3 = 2 threes.
2/3 = 0.6.
$$\frac{3}{4}$$.
3/4 = 3 fourths.
3/4 = 0.75.
0.6 < 0.75.
2 threes are less than 3 fourths.
2/3 < 3/4.

c. $$\frac{4}{6}$$ _______ $$\frac{5}{8}$$

$$\frac{4}{6}$$ __=__ $$\frac{5}{8}$$.

Explanation:
In the above-given question,
given that,
$$\frac{4}{6}$$.
4/6 = 4 sixths.
4/6 = 0.6.
$$\frac{5}{8}$$.
5/8 = 5 eights.
5/8 = 0.625.
0.6 = 0.75.
4 sixths are equal to 5 eights.
4/6 = 5/8.

d. $$\frac{2}{7}$$ _____ $$\frac{3}{5}$$

$$\frac{2}{7}$$ __<___ $$\frac{3}{5}$$.

Explanation:
In the above-given question,
given that,
$$\frac{2}{7}$$.
2/7 = 2 sevenths.
2/7 = 0.28.
$$\frac{3}{5}$$.
3/5 = 3 fifths.
3/5 = 0.6.
0.28 < 0.6.
2 sevenths are less than 3 fifths.
2/7 < 3/5.

e. $$\frac{4}{6}$$ __________ $$\frac{6}{9}$$

$$\frac{4}{6}$$ __=___ $$\frac{6}{9}$$.

Explanation:
In the above-given question,
given that,
$$\frac{4}{6}$$.
4/6 = 4 sixths.
4/6 = 0.6.
$$\frac{6}{9}$$.
6/9 = 6 ninths.
6/9 = 0.6.
0.6 = 0.6.
4 sixths are equal t0 6 ninths.
4/6 = 6/9.

f. $$\frac{4}{5}$$ _______ $$\frac{5}{6}$$

$$\frac{4}{5}$$ __<___ $$\frac{5}{6}$$.

Explanation:
In the above-given question,
given that,
$$\frac{4}{5}$$.
4/5 = 4 fifths.
4/5 = 0.8.
$$\frac{5}{6}$$.
5/6 = 5 sixths.
5/6 = 0.83.
0.8 = 0.8.
4 fifths are equal to 5 sixths.
4/5 = 5/6.

Question 2.
Rename the fractions, as needed, using multiplication in order to compare each pair of fractions by writing >, <, or =.

a. $$\frac{2}{3}$$ __________ $$\frac{2}{4}$$

$$\frac{2}{3}$$ __>___ $$\frac{2}{4}$$.

Explanation:
In the above-given question,
given that,
$$\frac{2}{3}$$.
2/3 = 2 thirds.
2/3 = 0.6.
$$\frac{2}{4}$$.
2/4 = 2 fourths.
2/4 = 0.5.
0.6 > 0.5.
2 thirds are greater than 2 fourths.
2/3 > 2/4.

b. $$\frac{4}{7}$$ __________ $$\frac{1}{2}$$

$$\frac{4}{5}$$ __<___ $$\frac{1}{2}$$.

Explanation:
In the above-given question,
given that,
$$\frac{4}{5}$$.
4/5 = 4 fifths.
4/5 = 0.8.
$$\frac{1}{2}$$.
1/2 = 1 twos.
1/2 = 0.5.
0.8 > 0.5.
4 fifths are greater than 1 two.
4/5 > 1/2.

c. $$\frac{5}{4}$$ _________ $$\frac{9}{8}$$

$$\frac{5}{4}$$ __<___ $$\frac{9}{8}$$.

Explanation:
In the above-given question,
given that,
$$\frac{5}{4}$$.
5/4 = 5 fourths.
5/4 = 1.25.
$$\frac{9}{8}$$.
9/8 = 9 eights.
9/8 = 1.125.
1.25 > 1.125.
5 fourths are greater than 9 eights.
5/4 > 9/8.

d. $$\frac{8}{12}$$ _____ $$\frac{5}{8}$$

$$\frac{8}{12}$$ __=___ $$\frac{5}{8}$$.

Explanation:
In the above-given question,
given that,
$$\frac{8}{12}$$.
8/12 = 8 twelfths.
8/12 = 0.6.
$$\frac{5}{8}$$.
5/8 = 5 eights.
5/8 = 0.625.
0.6 = 0.6.
8 twelfths are less than 5 eighths.
8/12 = 5/18.

Question 3.
Use any method to compare the fractions. Record your answer using >, <, or =.
a. $$\frac{8}{9}$$ __________ $$\frac{2}{3}$$

$$\frac{8}{9}$$ __>___ $$\frac{2}{3}$$.

Explanation:
In the above-given question,
given that,
$$\frac{8}{9}$$.
8/9 = 8 nines.
8/9 = 0.88.
$$\frac{2}{3}$$.
2/3 = 2 thirds.
2/3 = 0.6.
0.88 > 0.6.
8 nines are greater than 2 thirds.
8/9 > 2/3.

b. $$\frac{4}{7}$$ __________ $$\frac{4}{5}$$

$$\frac{4}{7}$$ __<___ $$\frac{4}{5}$$.

Explanation:
In the above-given question,
given that,
$$\frac{4}{7}$$.
4/7 = 4 sevens.
4/7 = 0.5.
$$\frac{4}{5}$$.
4/5 = 4 fives.
4/5 = 0.8.
0.5 < 0.8.
4 sevens are less than 4 fives.
4/7 < 4/5.

c. $$\frac{3}{2}$$ __________ $$\frac{9}{6}$$

$$\frac{3}{2}$$ __<___ $$\frac{9}{6}$$.

Explanation:
In the above-given question,
given that,
$$\frac{3}{2}$$.
3/2 = 3 twos.
3/2 = 1.5.
$$\frac{9}{6}$$.
9/6 = 9 sixths.
9/6 = 1.5.
1.5 = 1.5.
3 twos are equal to 9 sixths.
3/2 = 9/6.

d. $$\frac{11}{7}$$ __________ $$\frac{5}{3}$$

$$\frac{11}{7}$$ __>___ $$\frac{5}{3}$$.

Explanation:
In the above-given question,
given that,
$$\frac{11}{7}$$.
11/7 = 11 sevens.
11/7 = 1.57.
$$\frac{5}{3}$$.
5/3 = 5 thirds.
5/3 = 0.75.
1.57 > 0.75.
11 sevens are less than 5 thirds.
11/7 > 5/3.

Question 4.
Explain which method you prefer using to compare fractions. Provide an example using words, pictures, or numbers.