## Engage NY Eureka Math 4th Grade Module 5 Lesson 23 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 23 Problem Set Answer Key

Question 1.

Circle any fractions that are equivalent to a whole number. Record the whole number below the fraction.

a. Count by 1 thirds. Start at 0 thirds. End at 6 thirds.

Answer:

0/3, 1/3, 2/3, 3/3, 4/3, 5/3, 6/3.

Explanation:

In the above-given question,

given that,

circle any fractions that are equivalent to a whole number.

count by 1 third.

start at 0 thirds.

end at 6 thirds.

0/3 + 1 = 1/3.

1/3 + 1 = 2/3.

2/3 + 1 = 3/3.

3/3 + 1 = 4/3.

4/3 + 1 = 5/3.

5/3 + 1 = 6/3.

0/3 = 0, 3/3 = 1, 6/3 = 2.

b. Count by 1 halves. Start at 0 halves. End at 8 halves.

Answer:

0/2, 1/2, 2/2, 3/2, 4/2, 5/2, 6/2, 7/2, 8/2.

Explanation:

In the above-given question,

given that,

circle any fractions that are equivalent to a whole number.

count by 1 half.

start at 0 halves.

end at 8 halves.

0/2 + 1 = 1/2.

1/2 + 1 = 2/2.

2/2 + 1 = 3/2.

3/2 + 1 = 4/2.

4/2 + 1 = 5/2.

5/2 + 1 = 6/2.

6/2 + 1 = 7/2.

7/2 + 1 = 8/2.

0/2 = 0, 2/2 = 1, 4/2 = 2, 6/2 = 3, 8/2 = 4.

Question 2.

Use parentheses to show how to make ones in the following number sentence.

\(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) = 3

Answer:

1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4.

Explanation:

In the above-given question,

given that,

use parantheses to make ones .

(1/4) + (1/4) + (1/4) + (1/4).

1/4 = 0.25.

0.25 + 0.25 + 0.25 + 0.25.

0.50 + 0.50 = 1.

1 + 1 + 1 = 3.

Question 3.

Multiply, as shown below. Draw a number line to support your answer.

a. 6 Ã— \(\frac{1}{3}\)

Answer:

6 x 1/3 = 2.

Explanation:

In the above-given question,

given that,

6 x 1/3.

3 x 1/3 + 3 x 1/3.

2 x 3/3 = 2.

2 x 1 = 2.

b. 6 Ã— \(\frac{1}{2}\)

Answer:

6 x 1/2 = 3.

Explanation:

In the above-given question,

given that,

6 x 1/2.

3 x 1/2 + 3 x 1/2.

3 x 2/2 = 3.

3 x 1 = 3.

c. 12 Ã— \(\frac{1}{4}\)

Answer:

12 x 1/4 = 3.

Explanation:

In the above-given question,

given that,

12 x 1/4.

6 x 1/4 + 6 x 1/4.

6 x 2/2 = 3.

3 x 1 = 3.

Question 4.

Multiply, as shown below. Write the product as a mixed number. Draw a number line to support your answer.

a. 7 copies of 1 third

Answer:

7 x 1/3Â = 7/3 = 2(1/3).

Explanation:

In the above-given question,

given that,

write the product as a mixed number.

7 x 1/3.

(2 x 3/3) + 1/3.

2 + 1/3.

2(1/3).

b. 7 copies of 1 half

Answer:

7 x 1/2Â = 7/2 = 3(1/2).

Explanation:

In the above-given question,

given that,

write the product as a mixed number.

7 x 1/2.

(3 x 2/2) + 1/2.

3 + 1/2.

3(1/2).

c. 10 Ã— \(\frac{1}{4}\)

Answer:

10 x 1/4Â = 10/4 = 2(2/4).

Explanation:

In the above-given question,

given that,

write the product as a mixed number.

10 x 1/4.

(2 x 4/4) + 2/4.

2 + 2/4.

2(2/4).

d. 14 Ã— \(\frac{1}{3}\)

Answer:

14 x 1/3Â = 14/3 = 4(2/3).

Explanation:

In the above-given question,

given that,

write the product as a mixed number.

14 x 1/3.

(4 x 3/3) + 2/3.

4 + 2/3.

4(2/3).

### Eureka Math Grade 4 Module 5 Lesson 23 Exit Ticket Answer Key

Multiply and write the product as a mixed number. Draw a number line to support your answer.

Question 1.

8 Ã— \(\frac{1}{2}\)

Answer:

8 x 1/2 = 4.

Explanation:

In the above-given question,

given that,

8 x 1/2.

4 x 1/2 + 4 x 1/2.

4 x 2/2 = 4.

4 x 1 = 4.

Question 2.

7 copies of 1 fourth

Answer:

7 x 1/4Â = 7/4 = 4(3/4).

Explanation:

In the above-given question,

given that,

write the product as a mixed number.

7 x 1/4.

(4 x 2/2) + 3/4.

4 + 3/4.

4(3/4).

Question 3.

13 Ã— \(\frac{1}{3}\)

Answer:

13 x 1/3 = 13/3.

Explanation:

In the above-given question,

given that,

13 x 1/3.

6 x 1/3 + 7 x 1/3.

13 x 1/3.

13/3.

### Eureka Math Grade 4 Module 5 Lesson 23 Homework Answer Key

Question 1.

Circle any fractions that are equivalent to a whole number. Record the whole number below the fraction.

a. Count by 1 fourths. Start at 0 fourths. Stop at 6 fourths.

Answer:

0/4, 1/4, 2/4, 3/4, 4/4, 5/4, 6/4.

Explanation:

In the above-given question,

given that,

circle any fractions that are equivalent to a whole number.

count by 1 fourth.

start at 0 fourths.

end at 6 fourths.

0/4 + 1 = 1/4.

1/4 + 1 = 2/4.

2/4 + 1 = 3/4.

3/4 + 1 = 4/4.

4/4 + 1 = 5/4.

5/4 + 1 = 6/4.

0/4 = 0, 2/4 = 2, 4/4 = 1.

b. Count by 1 sixths. Start at 0 sixths. Stop at 14 sixths.

Answer:

0/6, 1/6, 2/6, 3/6, 4/6, 5/6, 6/6, 7/6, 8/6, 9/6, 10/6, 11/6, 12/6, 13/6, 14/6.

Explanation:

In the above-given question,

given that,

circle any fractions that are equivalent to a whole number.

count by 1 sixth.

start at 0 sixths.

end at 14 sixths.

0/6 + 1 = 1/6.

1/6 + 1 = 2/6.

2/6 + 1 = 3/6.

3/6 + 1 = 4/6.

4/6 + 1 = 5/6.

5/6 + 1 = 6/6.

6/6 + 1 = 7/6.

7/6 + 1 = 8/6.

8/6 + 1 = 9/6.

9/6 + 1 = 10/6.

10/6 + 1 = 11/6.

11/6 + 1 = 12/6.

12/6 + 1 = 13/6.

13/6 + 1 = 14/6.

0/6 = 0, 12/6 = 2, 6/6 = 1.

Question 2.

Use parentheses to show how to make ones in the following number sentence.

\(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) = 4

Answer:

1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3.

Explanation:

In the above-given question,

given that,

use parantheses to make ones .

(1/3) + (1/3) + (1/3) + (1/3).

1/3 = 0.75.

0.75 + 0.75 + 0.75 + 0.75.

1.5 + 1.5 = 3.

3 + 1 = 4.

Question 3.

Multiply, as shown below. Draw a number line to support your answer.

a. 6 Ã— \(\frac{1}{3}\)

Answer:

6 x 1/3 = 2.

Explanation:

In the above-given question,

given that,

6 x 1/3.

3 x 1/3 + 3 x 1/3.

2 x 3/3 = 2.

2 x 1 = 2.

b. 10 Ã— \(\frac{1}{2}\)

Answer:

10 x 1/2 = 5.

Explanation:

In the above-given question,

given that,

10 x 1/2.

5 x 1/2 + 5 x 1/2.

5 x 2/2 = 5.

5 x 1 = 5.

c. 8 Ã— \(\frac{1}{4}\)

Answer:

8 x 1/4 = 2.

Explanation:

In the above-given question,

given that,

8 x 1/4.

4 x 1/4 + 4 x 1/4.

2 x 4/4 = 2.

2 x 1 = 2.

Question 4.

Multiply, as shown below. Write the product as a mixed number. Draw a number line to support your answer.

a. 7 copies of 1 third

Answer:

7 x 1/3Â = 7/3 = 2(1/3).

Explanation:

In the above-given question,

given that,

write the product as a mixed number.

7 x 1/3.

(2 x 3/3) + 1/3.

2 + 1/3.

2(1/3).

b. 7 copies of 1 fourth

Answer:

7 x 1/4Â = 7/4 = 1(3/4).

Explanation:

In the above-given question,

given that,

write the product as a mixed number.

7 x 1/4.

(1 x 4/4) + 3/4.

1 + 3/4.

1(3/4).

c. 11 groups of 1 fifth

Answer:

11 x 1/5Â = 11/5 = 2(1/5).

Explanation:

In the above-given question,

given that,

write the product as a mixed number.

11 x 1/5.

( 2 x 5/5) + 1/5.

2 + 1/5.

2(1/5).

d. 7 Ã— \(\frac{1}{2}\)

Answer:

7 x 1/2Â = 7/2 = 3(1/2).

Explanation:

In the above-given question,

given that,

write the product as a mixed number.

7 x 1/2.

(3 x 2/2) + 1/2.

3 + 1/2.

3(1/2).

e. 9 Ã— \(\frac{1}{5}\)

Answer:

9 x 1/5Â = 9/5 = 1(4/5).

Explanation:

In the above-given question,

given that,

write the product as a mixed number.

9 x 1/5.

(1 x 5/5) + 4/5.

1 + 4/5.

1(4/5).