Lesson 10
Using Long Division
Problem 1
Kiran is using long division to find \(696 \div 12\).
![Long division. 696 divided by 12.](https://cms-im.s3.amazonaws.com/hASGxYzUx5WtmjDLALbvvHWZ?response-content-disposition=inline%3B%20filename%3D%226.5.D2.Image.04.1_1366.png%22%3B%20filename%2A%3DUTF-8%27%276.5.D2.Image.04.1_1366.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=20240630T143431Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=933a732a265d87a797cb0c50f2fa449cea1d3cb9fe8646e7082cf8b531178d08)
He starts by dividing 69 by 12. In which decimal place should Kiran place the first digit of the quotient (5)?
Hundreds
Tens
Ones
Tenths
Solution
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Problem 2
Here is a long-division calculation of \(917 \div 7\).
![Example division problem 917 divided by 7.](https://cms-im.s3.amazonaws.com/SxRBwFioGWjBB1ghncp8jf7R?response-content-disposition=inline%3B%20filename%3D%226-6.5.PP.Image.55.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.PP.Image.55.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=20240630T143431Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=43f54b02279103e361b1af2b8b7a05e628adc47d2c15453dc7bbf2bc3bfcc005)
- There is a 7 under the 9 of 917. What does this 7 represent?
- What does the subtraction of 7 from 9 mean?
- Why is a 1 written next to the 2 from \(9-7\)?
Solution
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Problem 3
Han's calculation of \(972 \div 9\) is shown here.
![Student work of division problem.](https://cms-im.s3.amazonaws.com/g7AcZBF1A3cBtqXFadR266HZ?response-content-disposition=inline%3B%20filename%3D%226-6.5.PP.Image.56.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.PP.Image.56.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=20240630T143431Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3f61b0273aef7832a977d39c16876b7366bdc1c982339872d84fc7d3108ed3a0)
- Find \(180 \boldcdot 9\).
- Use your calculation of \(180 \boldcdot 9\) to explain how you know Han has made a mistake.
- Identify and correct Han’s mistake.
Solution
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Problem 4
Find each quotient.
![Three long divisions, a, b, c. a, 465 divided by 5. b, 924 divided by 12. c, 1,107 divided by 3.](https://cms-im.s3.amazonaws.com/YQoXMJYuSeSBAESQyqd488aR?response-content-disposition=inline%3B%20filename%3D%226-6.5.D.PP.New.Image.22.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.D.PP.New.Image.22.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=20240630T143431Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9a200c13c3ff5f5e5c3e4cef6443376bded062d31979f8183860db925a3ec532)
Solution
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Problem 5
One ounce of a yogurt contains of 1.2 grams of sugar. How many grams of sugar are in 14.25 ounces of yogurt?
0.171 grams
1.71 grams
17.1 grams
171 grams
Solution
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(From Unit 5, Lesson 7.)Problem 6
The mass of one coin is 16.718 grams. The mass of a second coin is 27.22 grams. How much greater is the mass of the second coin than the first? Show your reasoning.
Solution
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(From Unit 5, Lesson 4.)