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

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

Question 1.

Fill in the blank using one of the following scaling factors to make each number sentence true.

a. 3.4 × _______ = 3.4

Answer:

3.4 × 1.00 = 3.4

b. _______ × 0.21 > 0.21

Answer:

1.021 × 0.21 > 0.21.

c. 8.04 × _______ < 8.04

Answer:

8.04 × 0.989 < 8.04.

Question 2.

a. Sort the following expressions by rewriting them in the table.

The product is less than the boxed number: |
The product is greater than the boxed number: |

0.3 × 0.069 602 × 0.489 0.2 × 0.1 |
13.89 × 1.004 0.72 × 1.24 102.03 × 4.015 |

b. Explain your sorting by writing a sentence that tells what the expressions in each column of the table have in common.

Answer:

Here, in the first column, the boxed number is multiplied by a scaling factor less than 1. So the product will be less than the boxed number. In the second column, the boxed number is multiplied by a scaling factor greater than 1.

Question 3.

Write a statement using one of the following phrases to compare the value of the expressions.

Then, explain how you know.

a. 4 × 0.988 _________________________________ 4

b. 1.05 × 0.8 _________________________________ 0.8

c. 1,725 × 0.013 _________________________________ 1,725

d. 989.001 × 1.003 _________________________________ 1.003

e. 0.002 × 0.911 _________________________________ 0.002

Answer:

a. 4 × 0.988 is less than slightly 4 because 0.988 is slightly less than 1.

b. 1.05 × 0.8 is slightly more than 0.8 because 0.1 is a little more than 1.

c. 1,725 × 0.013 is a lot less than 1,725 because 0.013 is a lot less than 1.

d. 989.001 × 1.003 is a lot more than 1.003 because 989.001 is a lot more than 1.

e. 0.002 × 0.911 is slightly less than 0.002 because 0.911 is a little less than 1.

Question 4.

During science class, Teo, Carson, and Dhakir measure the length of their bean sprouts. Carson’s sprout is 0.9 times the length of Teo’s, and Dhakir’s is 1.08 times the length of Teo’s. Whose bean sprout is the longest? The shortest? Explain your reasoning.

Answer:

Dhakir’s bean sprouts are the longest and Teo’s bean sprouts are the shortest.

Explanation:

Here, Dhakir’s bean sprouts are the longest, because it is slightly more than 1 time. The length of the Teo’s bean sprouts. Carson bean sprout is the shortest because it is a little less than 1 time the length of the Teo’s.

Question 5.

Complete the following statements; then use decimals to give an example of each.

• a × b > a will always be true when b is…

Answer:

It’s true when b is greater than one.

Explanation:

Let’s take an example of a × b > a

3.15 × 1.3 = 4.095 and here 4.095 > 3.15 and it is true when b is greater than one.

• a × b < a will always be true when b is…

Answer:

It’s true when b is less than one.

Explanation:

Let’s take an example of a × b < a

3.15 × 0.7 = 2.205 and here 2.205 < 3.15 and it is true when b is less than one.

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

Question 1.

Fill in the blank using one of the following scaling factors to make each number sentence true.

a. 3.06 × _______ < 3.06

b. 5.2 × _______ = 5.2

c. _______ × 0.89 > 0.89

Answer:

a. 3.06 × 0.898 < 3.06.

b. 5.2 × 1.00 = 5.2.

c. 1.009× 0.89 > 0.89.

Question 2.

Will the product of 22.65 × 0.999 be greater than or less than 22.65? Without calculating, explain how you know.

Answer:

It will be less.

Explanation:

It’s a decimal so it’ll be a bit less than 22.65.

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

Question 1.

Sort the following expressions by rewriting them in the table.

The product is less than the boxed number: |
The product is greater than the boxed number: |

828 × 0.921 0.05 × 0.1 |
12.5 × 1.989 0.007 × 1.02 2.16 × 1.11 321.46 × 1.26 |

b. What do the expressions in each column have in common?

Answer:

Here, in the first column, the boxed number is multiplied by a scaling factor less than 1. So the product will be less than the boxed number. In the second column, the boxed number is multiplied by a scaling factor greater than 1.

Question 2.

Write a statement using one of the following phrases to compare the value of the expressions.

Then, explain how you know.

a. 14 × 0.999 _______________________________ 14

b. 1.01 × 2.06 _______________________________ 2.06

c. 1,955 × 0.019 _______________________________ 1,955

d. Two thousand × 1.0001 _______________________________ two thousand

e. Two-thousandths × 0.911 _______________________________ two-thousandths

Answer:

a. 14 × 0.999 is slightly less than 14.

b. 1.01 × 2.06 is slightly more than 2.06.

c. 1,955 × 0.019 a lot less than 1,955.

d. Two thousand × 1.0001 is slightly more than two thousand.

e. Two-thousandths × 0.911 is slightly less than two-thousandths.

Question 3.

Rachel is 1.5 times as heavy as her cousin, Kayla. Another cousin, Jonathan, weighs 1.25 times as much as Kayla. List the cousins, from lightest to heaviest, and explain your thinking.

Answer:

Kayal, Jonathan, Rachel.

Explanation:

Here, Kayal is the lightest after Kayal Jonathan and then Rachel is the heaviest

Question 4.

Circle your choice.

a. a × b > a

Write two expressions that support your answer. Be sure to include one decimal example.

Answer:

Greater than 1

Explanation:

4.15 × 1.3 = 4.095 and here 5.395 > 4.15 and it is true when b is greater than one.

2.5 × 0.5 = 1.25 and here 1.25 < 2.5 and it is true when b is less than one.

b. a × b < a

Write two expressions that support your answer. Be sure to include one decimal example.

Answer:

It’s true when b is less than one.

Explanation:

Let’s take an example of a × b < a

3.15 × 0.7 = 2.205 and here 2.205 < 3.15 and it is true when b is less than one.

5.2 × 1.6 = 8.32 and here 8.32 > 5.2 and it is true when b is greater than one.