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.
![A rectangle area model. The rectangle is partitioned into 15 identical squares. There are 5 rows of 3 squares in each row.](https://cms-im.s3.amazonaws.com/Vgc1qkr59cEZnL5bLX53Ei1A?response-content-disposition=inline%3B%20filename%3D%226-6.5.C2.Image.07.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.C2.Image.07.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T143507Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=96d3b11a59d0caf876fd19c6daab4cf23efb6eaa01926bad287d364b808b7183)
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.
![A multi-sided figure.](https://cms-im.s3.amazonaws.com/DhqcDGtYtF2joLoyUSU9fG77?response-content-disposition=inline%3B%20filename%3D%226-6.1.A.PP.New.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.A.PP.New.Image.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T143507Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c26b6512f99c126b5bea48ee0782cc66275ed2329bf82d8a51d4e138e763d68b)
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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