# Into Math Grade 5 Module 15 Lesson 3 Answer Key Assess Reasonableness of Products

We included HMH Into Math Grade 5 Answer Key PDF Module 15 Lesson 3 Assess Reasonableness of Products to make students experts in learning maths.

## HMH Into Math Grade 5 Module 15 Lesson 3 Answer Key Assess Reasonableness of Products

I Can assess the reasonableness of the product of a decimal less than one and a whole number.

Rosalind’s school is holding a Math Fun Fair. One of the games is a sorting game with the numerical expressions shown. 8 × 0.45
8 × 0.6
6 × 0.81
8 × 0.52
8 × 0.8
4 × 0.99
8 × 0.49
4 × 0.9
Sort the numerical expression.  Explanation:
8 × 0.45 = 3.6.
8 × 0.6 = 4.8.
6 × 0.81 = 4.86.
8 × 0.52 = 4.16.
8 × 0.8 = 6.4.
4 × 0.99 = 3.96.
8 × 0.49 = 3.92.
4 × 0.9 = 3.6.

Turn and Talk How does the value of the expression 8 × 0.45 compare to the value of the expression 4 × 0.99? Explain how you know.
The value of the expression 8 × 0.45 is comparably less to the value of the expression 4 × 0.99.

Explanation:
8 × 0.45 = 3.6.
4 × 0.99 = 3.96.
=> 8 × 0.45 < 4 × 0.99.

Build Understanding
Question 1.
One of the prizes at the Math Fun Fair is erasers. The value of each eraser is $0.77. There are 8 erasers on the prize table. Joni says the value of the 8 erasers is greater than$6.00. How is she able to make this claim? Is her claim reasonable?
A. Did Joni give an exact value or an estimate for the 8 erasers?
Yes, Joni claim is reasonable.

Explanation:
Cost of each eraser = $0.77. Number of erasers on the prize table = 8. Total cost of 8 erasers = Cost of each eraser × Number of erasers on the prize table =$0.77 × 8
= $6.16. Joni says the value of the 8 erasers is greater than$6.00.

B. Decimals and fractions both name fractional parts of a whole. It is often easier to calculate using fractions rather than decimals. Complete the number line to show the decimal equivalents of some common fractions.  Explanation:
$$\frac { 1 }{ 4 }$$ = 0.25.
$$\frac { 1 }{ 2 }$$ = 0.50.
$$\frac { 3 }{ 4 }$$ = 0.75.

C. To which decimal number is $0.77 closest? Answer: Decimal number is$0.77 closest to $$\frac { 3 }{ 4 }$$ = 0.75

Explanation:
$$\frac { 1 }{ 4 }$$ = 0.25.
$$\frac { 1 }{ 2 }$$ = 0.50.
$$\frac { 3 }{ 4 }$$ = 0.75.

D. What fraction is equivalent to 0.75?
$$\frac { 3 }{ 4 }$$ fraction is equivalent to 0.75.

Explanation:
$$\frac { 1 }{ 4 }$$ = 0.25.
$$\frac { 1 }{ 2 }$$ = 0.50.
$$\frac { 3 }{ 4 }$$ = 0.75.

E. Use the fraction to find the value of the 8 erasers. Show your work.
Total cost of 8 erasers = $6.16. Explanation: Cost of each eraser =$0.77.
Number of erasers on the prize table = 8.
Total cost of 8 erasers = Cost of each eraser × Number of erasers on the prize table
= $0.77 × 8 =$6.16.

F. How does 0.77 compare to 0.75?
0.77 > 0.75.

Explanation:
0.77 compare to 0.75.
=> 0.77 > 0.75

G. Is Joni’s claim reasonable? Explain.
Yes, Joni claim is reasonable.

Explanation:
Cost of each eraser = $0.77. Number of erasers on the prize table = 8. Total cost of 8 erasers = Cost of each eraser × Number of erasers on the prize table =$0.77 × 8
= $6.16. Joni says the value of the 8 erasers is greater than$6.00.

Turn and Talk What would the value of one eraser need to be so that the value of 8 erasers would be greater than or equal to $2.00 and less than or equal to$4.00?
The value of one eraser need to be $0.25 so that the value of 8 erasers would be greater than or equal to$2.00 and  $0.50 less than or equal to$4.00

Explanation:
The value of 8 erasers would be greater than or equal to $2.00. =>$2.00 ÷ 8
= $0.25. The value of 8 erasers would be less than or equal to$4.00
=> $4.00 ÷ 8 =>$0.50.

Step It Out
Question 2.
At another Math Fun Fair booth, a player chooses a digit from 1 to 9, spins the wheel, and multiplies the two numbers. If the product is greater than or equal to the digit, the player wins a prize. A. Taylor chooses the digit 4 and spins the number 0.7. Does she win a prize? How do you know?
No, Taylor wont win the prize because product (4 × 0.7 = 2.8.) is less than 4.

Explanation:
Taylor chooses the digit 4 and spins the number 0.7.
=> Product = 4 × 0.7 = 2.8.
If the product is greater than or equal to the digit, the player wins a prize.

B. Is there any digit Taylor could have chosen for which a spin of 0.7 results in her winning a prize? Why?
Yes, Taylor could chosen for a spin of 0.7 results in her winning a prize are 0.7 × 1 = 0.7 as number is equal to the product.

Explanation: Digit Taylor could have chosen for which a spin of 0.7 results in her winning a prize:
0.7 × 0.5 = 0.35.
0.7 × 0.6 = 0.42.
0.7 × 0.7 = 0.49.
0.7 × 0.8 = 0.56.
0.7 × 0.9 =0.63.
0.7 × 1 = 0.7
0.7 × 1.1 = 0.77.
0.7 × 1.2 = 0.84.
0.7 × 1.3 = 0.91.
0.7 × 1.4 = 0.98.

C. For what other numbers on the wheel will Taylor not win a prize?
Other numbers on the wheel will Taylor not win a prize are:
0.7 × 0.5 = 0.35.
0.7 × 0.6 = 0.42.
0.7 × 0.7 = 0.49.
0.7 × 0.8 = 0.56.
0.7 × 0.9 =0.63.
0.7 × 1.1 = 0.77.
0.7 × 1.2 = 0.84.
0.7 × 1.3 = 0.91.
0.7 × 1.4 = 0.98.

Explanation:
Other numbers on the wheel will Taylor not win a prize are:
0.7 × 0.5 = 0.35.
0.7 × 0.6 = 0.42.
0.7 × 0.7 = 0.49.
0.7 × 0.8 = 0.56.
0.7 × 0.9 =0.63.
0.7 × 1.1 = 0.77.
0.7 × 1.2 = 0.84.
0.7 × 1.3 = 0.91.
0.7 × 1.4 = 0.98.

D. Which numbers on the wheel will result in Taylor winning a prize?
0.7 × 1.1 = 0.77 and 0.7 × 1 = 0.7 numbers on the wheel will result in Taylor winning a prize.

Explanation:
0.7 × 1.1 = 0.77 and 0.7 × 1 = 0.7 numbers on the wheel will result in Taylor winning a prize.

Turn and Talk Suppose the numbers on the wheel change. How can you tell whether a player will win a prize or not win a prize?
If the numbers on the wheel change,  the product of the numbers will be changed and she can win if it is more than the number and vise verse.

Explanation:
If the numbers on the wheel change,  the product of the numbers will be changed and she can win if it is more than the number and vise verse.

Check Understanding
Question 1.
There are also 4 sticker packs on the prize table. The value of each is $0.46. Javier claims that the total value is less than$2.00. Is his claim reasonable? Explain.
Yes, total cost of sticker packs = $1.84 his claim is reasonable as its less than$2.00.

Explanation:
Number of sticker packs on the prize table = 4.
Cost of each = $0.46. Total cost of sticker packs = Number of sticker packs on the prize table × Cost of each = 4 ×$0.46
= $1.84. Javier claims that the total value is less than$2.00.

Determine whether the statement is true or false.
Question 2.
6 × o.52 < 3
Its false 6 × o.52 < 3.

Explanation:
6 × o.52 = 3.12.

Question 3.
4 × 0.61 > 2
Its true 4 × 0.61 > 2.

Explanation:
4 × 0.61 = 2.44.

Question 4.
7 × 0.87 > 7
Its false 7 × 0.87 > 7.

Explanation:
7 × 0.87 = 6.09.

Question 5.
STEM Human hair grows about 0.43 millimeter each day. Is it reasonable to expect that hair grows more than 3.5 millimeters in one week? Explain. No, it  is not reasonable to expect that hair grows more than 3.5 millimeters in one week because number of millimeters hair grows in a week = 3.01.

Explanation:
Number of millimeter each day Human hair grows = 0.43.
Number of days in a week = 7.
Number of millimeters hair grows in a week = Number of millimeter each day Human hair grows × Number of days in a week
= 0.43 × 7
= 3.01.

Determine whether the statement is true or false.
Question 6.
2 × 0.51 > 1
Its false 2 × 0.51 > 1

Explanation:
2 × 0.51 = 1.02.

Question 7.
4 × 0.49 > 2
Its true 4 × 0.49 > 2.

Explanation:
4 × 0.49 = 1.96

Question 8.
5 × 0.97 > 5
Its false 5 × 0.97 > 5.

Explanation:
5 × 0.97 = 4.85.

Question 9.
Jan goes to the grocery store to buy apples and oranges. Jan buys 5 apples. Is it reasonable that the apples weigh less than 5 pounds? Explain how you know.
Yes, its reasonable that the apples weigh less than 5 pounds because Weight of 5 apples = 3.71 lb.

Explanation:
Number of apples Jan buys = 5.
Weight of each apple = 0.74 lb.
Weight of 5 apples = Number of apples Jan buys × Weight of each apple
= 5 × 0.74 lb
= 3.70 lb.

Jan buys 6 oranges. Is it reasonable that the oranges weigh less than 3 pounds? Explain how you know.

Explanation:
Number of oranges Jan buys = 6.
Weight of each orange = 0.55 lb.
Weight of 5 oranges = Number of oranges Jan buys × Weight of each orange
= 5 × 0.55 lb
= 2.75 lb.

Question 10.
Reason Suppose you multiply 4 and 0.____7. What are the possible values of the unknown digit if the product is less than 1? Explain.
The possible values of the unknown digit if the product is less than 1 are 4 × 0.07 = 0.28 and
4 × 0.17 = 0.68.

Explanation:
Let the missing number be from 0 to 9:
4 × 0.07 = 0.28.
4 × 0.17 = 0.68.
4 × 0.27 = 1.08.
4 × 0.37 = 1.48.
4 × 0.47 = 1.88.
4 × 0.57 = 2.28.
4 × 0.67 = 2.68.
4 × 0.77 = 3.08.
4 × 0.87 = 3.48.
4 × 0.97 = 3.88.

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