Lesson 13
Dividing Decimals by Decimals
Problem 1
A student said, “To find the value of \(109.2 \div 6\), I can divide 1,092 by 60.”
- Do you agree with her? Explain your reasoning.
-
Calculate the quotient of \(109.2 \div 6\) using any method of your choice.
Solution
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Problem 2
Here is how Han found \(31.59 \div 13\):
![Long division of 31 point 5 9 divided by 13. 8 rows.](https://cms-im.s3.amazonaws.com/gW5WTJWzE35htGvFpBAGqkkk?response-content-disposition=inline%3B%20filename%3D%226-6.5.PP.Image.65.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.PP.Image.65.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=20240630T142820Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e9aafb15c0984af983658de0b4ef2d225043b3af365a94604ca08a84614c0fe7)
- At the second step, Han subtracts 52 from 55. How do you know that these numbers represent tenths?
- At the third step, Han subtracts 39 from 39. How do you know that these numbers represent hundredths?
- Check that Han’s answer is correct by calculating the product of 2.43 and 13.
Solution
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Problem 3
- Write two division expressions that have the same value as \(61.12 \div 3.2\).
- Find the value of \(61.12 \div 3.2\). Show your reasoning.
Solution
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Problem 4
A bag of pennies weighs 5.1 kilograms. Each penny weighs 2.5 grams. About how many pennies are in the bag?
20
200
2,000
20,000
Solution
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Problem 5
Find each difference. If you get stuck, consider drawing a diagram.
Solution
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(From Unit 5, Lesson 3.)Problem 6
Plant B is \(6\frac23\) inches tall. Plant C is \(4\frac{4}{15}\) inches tall. Complete the sentences and show your reasoning.
- Plant C is _______ times as tall as Plant B.
- Plant C is _______ inches ____________ (taller or shorter) than Plant B.
Solution
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(From Unit 4, Lesson 12.)Problem 7
At a school, 460 of the students walk to school.
- The number of students who take public transit is 20% of the number of students who walk. How many students take public transit?
- The number of students who bike to school is 5% of the number of students who walk. How many students bike to school?
- The number of students who ride the school bus is 110% of the number of students who walk. How many students ride the school bus?
Solution
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(From Unit 3, Lesson 15.)