# Lesson 6

Methods for Multiplying Decimals

### Problem 1

Find each product. Show your reasoning.

1. $$(1.2) \boldcdot (0.11)$$
2. $$(0.34) \boldcdot (0.02)$$
3. $$120 \boldcdot (0.002)$$

### Solution

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### Problem 2

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

1. What must the side length of each square represent for the rectangle to correctly represent $$(0.3) \boldcdot (0.5)$$?
2. What area is represented by each square?
3. 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.

1. How much does one gallon of gas cost in Toronto? Round your answer to the nearest cent.
2. 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

1. 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?
2. Use Priya’s method to calculate $$(1.05) \boldsymbol \boldcdot (2.8)$$. You can use the fact that $$105 \boldcdot 28 = 2,\!940$$.
3. Use Priya’s method to calculate $$(0.0015) \boldcdot (0.024)$$.

### Solution

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