# Into Math Grade 5 Module 16 Lesson 1 Answer Key Represent Decimal Multiplication

We included HMH Into Math Grade 5 Answer Key PDF Module 16 Lesson 1 Represent Decimal Multiplication to make students experts in learning maths.

## HMH Into Math Grade 5 Module 16 Lesson 1 Answer Key Represent Decimal Multiplication

I Can find the product of two decimals to the tenths place by using a decimal model.

Mr. Kasim has a collection of 100 coins from around the world. Of the 100 coins, 0.7 are in the shape of a circle. Of these circular coins, 0.3 have holes. How many coins in his collection are in the shape of a circle and have holes?

Number of coins in his collection are in the shape of a circle = 70.
Number of coins in his collection are having holes = 30.

Explanation:
Number of coins are in the shape of a circle  = 0.7 of the 100 coins
Number of coins are having holes = 0.3 of the 100 coins
Number of coins in his collection are in the shape of a circle = (Number of coins are in the shape of a circle × 100)
= (0.7 × 100)
= 70.
Number of coins in his collection are having holes = (Number of coins are having holes × 100)
=  (0.3 × 100)
=  30.

Turn and Talk How can you tell whether the product of 0.7 and 0.3 is greater than or less than each factor?
Well, we can say whether the product of 0.7 and 0.3 is greater than or less than each factor by checking the digits values in the given number.

Explanation:
Well, we can say whether the product of 0.7 and 0.3 is greater than or less than each factor by checking the digits values in the given number.
=> 0.7 is greater than 0.3.
=> product of 0.7 is greater than the product of 0.3.

Build Understanding
Question 1.
Mrs. Varga has a collection of postage stamps. Of her stamps, 0.6 are from a country outside of the United States Of those stamps, 0.8 are from the last 5 years. What decimal represents the part of her collection that is from outside of the United States and from the last 5 years?

Use the decimal model.
A. What multiplication expression models the situation?
Number of stamps are from the last 5 years = 0.48.

Explanation:
Number of stamps are from a country outside of the United States = 0.6.
Number of stamps are from the last 5 years = 0.8 × Number of stamps are from a country outside of the United States
=> 0.8 × 0.6.
=> 0.48.

B. Think about what each column of the decimal model represents.

How can you use the decimal model to show 0.6?
We can use to represent decimal point in the column by marking or coloring the number after point.

Explanation:
We can use to represent decimal point in the column by marking or coloring the number after point.

Explanation:
Number of squares are shaded = 6.

C. How do you represent 0.8 of 0.6 in the decimal model?

Explanation:
We can represent the multiplication of 0.8 by 0.6 by figuring them in separate columns and product in other column.

D. How many squares are shaded to represent 0.8 × 0.6?
Number of squares are shaded to represent 0.8 × 0.6 = 4 + 8 = 12.

Explanation:
Product of 0.8 and 0.6:
0.8 × 0.6 = 0.48.

E. What part of Mrs. Varga’s collection is from outside of the United States and from the last 5 years?
Part of Mrs. Varga’s collection is from outside of the United States and from the last 5 years = 0.48.

Explanation:
Part of Mrs. Varga’s collection is from outside of the United States and from the last 5 years = 0.48.

Turn and Talk How can you use your decimal model for 0.8 × 0.6 to find the product 0.8 × 1.2?
0.8 × 1.2 = (0.8 × 0.6) + (0.8 × 0.6) = 0.96.

Explanation:
Product of:
0.8 × 0.6 = 0.48.
0.8 × 1.2 = 0.8 ( 0.6 + 0.6)
= (0.8 × 0.6) + (0.8 × 0.6)
= 0.48 + 0.48
= 0.96.

Question 2.
Hakeem also collects postage stamps. One of his stamps shows an older model telephone. What is the area of the stamp?

A. What multiplication expression models the area?
Area of the of the postage stamp = 1.08 in.

Explanation:
Length of the postage stamp = 0.9 in.
Width of the postage stamp = 1.2 in.
Area of the of the postage stamp = Length of the postage stamp × Width of the postage stamp
= 0.9 × 1.2
=  1.08 inches.

B. How can you represent 1.2 in the decimal model?

Explanation:
We can represent 1.2 decimal on column chart by 1 ones on one full column and 2 Oneth in other column.

C. How many squares are shaded?
Number of squares are shaded for 1.2 = 102.

Explanation:
Number of squares are shaded 1.2 = (10 × 10) + 2
= 100 + 2
= 102.

D. How do you represent 0.9 of 1.2 in the decimal model?
Representation of 0.9: 9 square shade.
Representation of 1.2:  102 square shade.

Explanation:
Representation of 0.9: 9 square shade.
Representation of 1.2:  102 square shade.

E. What is the area of the stamp?
Area of the of the postage stamp =1.08 inches.

Explanation:
Length of the postage stamp = 0.9 in.
Width of the postage stamp = 1.2 in.
Area of the of the postage stamp = Length of the postage stamp × Width of the postage stamp
= 0.9 × 1.2
=  1.08 inches.

Check Understanding
Question 1.
Jason has a silver dollar that weighs 0.9 ounce. He has a nickel that weighs 0.2 of the weight of the silver dollar. How much does the nickel weigh? Use the decimal model.

Weight of a nickel that he has = 0.306 ounces.

Explanation:
Weight of a silver dollar that Jason has = 0.9 ounce.
Weight of a nickel that he has = 0.2 of the weight of the silver dollar.
1 nickle = 0.17 ounces
=> (0.2 × 0.17) × Weight of a silver dollar that Jason has
=> 0.034 × 0.9
=> 0.0306 ounces.

Question 2.
Kali has a banner with a width of 0.3 meter and a length of 1.5 meters. What is the area of the banner? Use the decimal model.

Area of the banner = 0.45 square meters.

Explanation:
Width of a banner Kali has = 0.3 meter.
Length of a banner Kali has = 1.5 meters.
Area of the banner = Width of a banner Kali has × Length of a banner Kali has
= 0.3 × 1.5
=  0.45 square meters.

Question 3.
Model with Mathematics Carter has a bottle of detergent that holds 1.8 liters. He fills a container that is 0.4 the size of the bottle. How much detergent is in the smaller container?
Write a multiplication expression that models the situation. Use the decimal model. Then explain how you used the model.

Number of liters detergent is in the smaller container has = 0.72.

Explanation:
Number of liters  a bottle of detergent Carter has = 1.8 liters.
He fills a container that is 0.4 the size of the bottle.
=> Number of liters detergent is in the smaller container has = 0.4 × Number of liters  a bottle of detergent Carter has
= 0.4 × 1.8
= 0.72.

How much detergent is in the smaller container?
Number of liters detergent is in the smaller container has = 0.72.

Explanation:
Number of liters detergent is in the smaller container has = 0.4 × Number of liters  a bottle of detergent Carter has
= 0.4 × 1.8
= 0.72.

Find the area of the rectangle described. Use the decimal model.
Question 4.
length = 0.8 cm
width = 0.3 cm

area = ___________
Area = 0.24 sq cm.

Explanation:
Length = 0.8 cm
Width = 0.3 cm
Area = Length × Width
= 0.8 × 0.3
= 0.24 sq cm.

Question 5.
length = 0.5 cm
width = 1.3 cm

area = ___________
Area = 0.65 sq cm.

Explanation:
Length = 0.5 cm
Width = 1.3 cm
Area = Length × Width
= 0.5 × 1.3
= 0.65 sq cm.

Question 6.
Open-Ended Write a word problem that can be represented by the decimal model shown.

Area = 0.50.

Explanation:
Length = 0.25.
Width = 0.2
Area = Length × Width
= 0.25 × 0.2
= 0.50.

I’m in a Learning Mindset!
How effective for me was it to use decimal models for understanding decimal multiplication?