# Illustrative Mathematics Unit 6.5, Lesson 6: Methods for Multiplying Decimals

Learning Targets:

• I can use area diagrams to represent and reason about multiplication of decimals.
• I know and can explain more than one way to multiply decimals using fractions and place value.

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Illustrative Math

#### Lesson 6: Methods for Multiplying Decimals

Let’s look at some ways we can represent multiplication of decimals.

Illustrative Math Unit 6.5, Lesson 6 (printable worksheets)

#### Lesson 6 Summary

The following diagram shows how to multiply decimals using fractions, place value and area diagrams.

#### Lesson 6.1 Which One Doesn’t Belong: Products

Which expression doesn’t belong? Explain your reasoning.
A. 2 · (0.3)
B. 2 · 3 · (0.1)
C. 6 · (0.1)
D. (0.1) · 6

#### Lesson 6.2 Using Properties of Numbers to Reason about Multiplication

1. Elena and Noah used different methods to compute (0.23) · (1.5). Both computations were correct.
Analyze the two methods, then discuss these questions with your partner.
• Which method makes more sense to you? Why?
• What might Elena do to compute (0.16) · (0.03)? What might Noah do to compute (0.16) · (0.03)? Will the two methods result in the same value?
1. Compute each product using the equation 21 · 47 = 987 and what you know about fractions, decimals, and place value. Explain or show your reasoning.
a. (0.16) · (0.03)
b. (0.16) · (0.03)
c. (0.16) · (0.03)

#### Lesson 6.3 Using Area Diagrams to Reason about Multiplication

1. In the diagram, the side length of each square is 0.1 unit.
a. Explain why the area of each square is not 0.1 square unit.
b. How can you use the area of each square to find the area of the rectangle? Explain or show your reasoning.
c. Explain how the diagram shows that the equation (0.4) · (0.2) = 0.08 is true.
2. Label the squares with their side lengths so the area of this rectangle represents 40 · 20.
a. What is the area of each square?
3. Label the squares with their side lengths so the area of this rectangle represents (0.04) · (0.02).

#### Lesson 6 Practice Problems

1. Find each product. Show your reasoning.
a. (1.2) · (0.11)
b. (0.34) · (0.02)
c.. 120 · (0.002)
2. You can use a rectangle to represent (0.3) · (0.5).
a. What must the side length of each square represent for the rectangle to correctly represent (0.3) · (0.5)?
b. What area is represented by each square?
c. What is (0.3) · (0.5)? Show your reasoning.br>
3. One gallon of gasoline in Buffalo, New York costs \$2.29. In Toronto, Canada, one liter of gasoline costs \$0.91. There are 3.8 liters in one gallon.
a. How much does one gallon of gas cost in Toronto? Round your answer to the nearest cent.
b. Is the cost of gas greater in Buffalo or in Toronto? How much greater?
4. Calculate each sum or difference.
a. 10.3 + 3.7
b. 20.99 - 4.97
c. 15.99 + 23.51
d. 1.893 - 0.353
5. Find the value of 49/50 ÷ 7/6 using any method.
6. Find the area of the shaded region. All angles are right angles. Show your reasoning.
7. a. Priya finds (1.05) · (2.8) by calculating 105 · 28, then moving the decimal point three places to the left. Why does Priya’s method make sense?
b. Use Priya’s method to calculate (1.05) · (2.8). You can use the fact that 105 · 28 = 2,940.
c. Use Priya’s method to calculate (0.0015) · (0.024).

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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