Unit 5, Lesson 6
Methods for Multiplying Decimals
Grade 6
6.2
Activity
Elena and Noah used different methods to compute . Both calculations were correct.
Elena's method. 0 point 2 3 times 100 equals 23. 1 point 5 times 10 equals 15. 23 times 15 equals 345. 345 divided by 1000 equals 0 point 3 4 5. Noah's method. 0 point 2 3 equals the fraction 23 over 100. 1 point 5 equals the fraction 15 over 10. The fraction 23 over 100 times the fraction 15 over 10 equals the fractions 345 over 1000. The fraction 345 over 1000 equals 0 point 3 4 5.
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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 ?
- What might Noah do to compute ?
- Will the two methods result in the same value?
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Compute each product using the equation and what you know about fractions, decimals, and place value. Explain or show your reasoning.
6.3
Activity
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In the diagram, the side length of each square is 0.1 unit.
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Explain why the area of each square is not 0.1 square unit.
- Explain how you can use the area of each square to find the area of the rectangle.
- What does the equation represent in this situation?
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Label the squares with their side lengths so the area of this rectangle represents .
- What is the area of each square?
- Use the squares to help you find . Be prepared to explain your reasoning.
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Label the squares with their side lengths so the area of this rectangle represents .
Next, use the diagram to help you find . Be prepared to explain your reasoning.
Student Lesson Summary
Here are three other ways to calculate a product of two decimals, such as .
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First, we can multiply each decimal by the same power of 10 to obtain whole-number factors.
Because we multiplied both 0.04 and 0.07 by 100 to get 4 and 7, the product 28 is times the original product, so we need to divide 28 by 10,000.
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Second, we can write each decimal as a fraction and multiply them.
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Third, we can use an area diagram. The product can be thought of as the area of a rectangle with side lengths of 0.04 unit and 0.07 unit.
In this diagram, each small square is 0.01 unit by 0.01 unit. The area of each square, in square units, is therefore , which is .
Because the rectangle is composed of 28 small squares, the area of the rectangle, in square units, must be:
All three calculations show that .
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