## 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. \(\frac{1}{2}\) _____< ______ \(\frac{2}{3}\)

Answer:

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.

Answer:

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. \(\frac{4}{5}\) __________ \(\frac{3}{4}\)

Answer:

\(\frac{4}{5}\) __>___ \(\frac{3}{4}\).

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. \(\frac{3}{5}\) __________ \(\frac{4}{7}\)

Answer:

\(\frac{3}{5}\) __=__ \(\frac{4}{7}\).

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. \(\frac{3}{7}\) __________ \(\frac{2}{6}\)

Answer:

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

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. \(\frac{5}{8}\) __________ \(\frac{6}{9}\)

Answer:

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

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. \(\frac{2}{3}\) __________ \(\frac{3}{4}\)

Answer:

\(\frac{2}{3}\) __<___ \(\frac{3}{4}\).

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. \(\frac{3}{5}\) __________ \(\frac{5}{6}\)

Answer:

\(\frac{3}{5}\) __<___ \(\frac{5}{6}\).

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. \(\frac{2}{6}\) __________ \(\frac{3}{8}\)

Answer:

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

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. \(\frac{7}{5}\) __________ \(\frac{10}{8}\)

Answer:

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

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. \(\frac{4}{3}\) __________ \(\frac{6}{5}\)

Answer:

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

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. \(\frac{3}{4}\) __________ \(\frac{7}{8}\)

Answer:

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

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. \(\frac{6}{8}\) __________ \(\frac{3}{5}\)

Answer:

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

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. \(\frac{6}{4}\) __________ \(\frac{8}{6}\)

Answer:

\(\frac{6}{4}\) __>___ \(\frac{8}{6}\).

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. \(\frac{8}{5}\) __________ \(\frac{9}{6}\)

Answer:

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

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.

\(\frac{3}{4}\) ________ \(\frac{4}{5}\)

Answer:

\(\frac{3}{4}\) __<___ \(\frac{4}{5}\).

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.

\(\frac{2}{6}\) ________ \(\frac{3}{5}\)

Answer:

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

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. \(\frac{1}{2}\) ____<______ \(\frac{3}{5}\)

Answer:

\(\frac{1}{2}\) __<___ \(\frac{3}{5}\).

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. \(\frac{2}{3}\) _____ \(\frac{3}{4}\)

Answer:

\(\frac{2}{3}\) __<___ \(\frac{3}{4}\).

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. \(\frac{4}{6}\) _______ \(\frac{5}{8}\)

Answer:

\(\frac{4}{6}\) __=__ \(\frac{5}{8}\).

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. \(\frac{2}{7}\) _____ \(\frac{3}{5}\)

Answer:

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

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. \(\frac{4}{6}\) __________ \(\frac{6}{9}\)

Answer:

\(\frac{4}{6}\) __=___ \(\frac{6}{9}\).

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. \(\frac{4}{5}\) _______ \(\frac{5}{6}\)

Answer:

\(\frac{4}{5}\) __<___ \(\frac{5}{6}\).

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. \(\frac{2}{3}\) __________ \(\frac{2}{4}\)

Answer:

\(\frac{2}{3}\) __>___ \(\frac{2}{4}\).

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. \(\frac{4}{7}\) __________ \(\frac{1}{2}\)

Answer:

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

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. \(\frac{5}{4}\) _________ \(\frac{9}{8}\)

Answer:

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

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. \(\frac{8}{12}\) _____ \(\frac{5}{8}\)

Answer:

\(\frac{8}{12}\) __=___ \(\frac{5}{8}\).

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. \(\frac{8}{9}\) __________ \(\frac{2}{3}\)

Answer:

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

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. \(\frac{4}{7}\) __________ \(\frac{4}{5}\)

Answer:

\(\frac{4}{7}\) __<___ \(\frac{4}{5}\).

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. \(\frac{3}{2}\) __________ \(\frac{9}{6}\)

Answer:

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

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. \(\frac{11}{7}\) __________ \(\frac{5}{3}\)

Answer:

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

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.