# Lesson 6

Methods for Multiplying Decimals

### Problem 1

Find each product. Show your reasoning.

- \((1.2) \boldcdot (0.11)\)
- \((0.34) \boldcdot (0.02)\)
- \(120 \boldcdot (0.002)\)

### Solution

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### Problem 2

You can use a rectangle to represent \((0.3) \boldcdot (0.5)\).

- What must the side length of each square represent for the rectangle to correctly represent \((0.3) \boldcdot (0.5)\)?
- What area is represented by each square?
- What is \((0.3) \boldcdot (0.5)\)? Show your reasoning.

### Solution

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### Problem 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.

- How much does one gallon of gas cost in Toronto? Round your answer to the nearest cent.
- Is the cost of gas greater in Buffalo or in Toronto? How much greater?

### Solution

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### Problem 4

Calculate each sum or difference.

\(10.3 + 3.7\)

\(20.99 - 4.97\)

\(15.99 + 23.51\)

\(1.893 - 0.353\)

### Solution

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(From Unit 5, Lesson 2.)### Problem 5

Find the value of \(\frac{49}{50}\div\frac{7}{6}\) using any method.

### Solution

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(From Unit 4, Lesson 11.)### Problem 6

Find the area of the shaded region. All angles are right angles. Show your reasoning.

### Solution

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(From Unit 1, Lesson 1.)### Problem 7

- Priya finds \((1.05) \boldcdot (2.8)\) by calculating \(105 \boldcdot 28\), then moving the decimal point three places to the left. Why does Priya’s method make sense?
- Use Priya’s method to calculate \((1.05) \boldsymbol \boldcdot (2.8)\). You can use the fact that \(105 \boldcdot 28 = 2,\!940\).
- Use Priya’s method to calculate \((0.0015) \boldcdot (0.024)\).

### Solution

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