Lesson 9
Using the Partial Quotients Method
Problem 1
Here is one way to find \(2,\!105 \div 5\) using partial quotients. Show a different way of using partial quotients to divide 2,105 by 5.
![Partial quotient method of 2,105 divided by 5.](https://cms-im.s3.amazonaws.com/ehfknAP5PyApaFzQdtSC7iSS?response-content-disposition=inline%3B%20filename%3D%226-6.5.D.PP.New.Image.17.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.D.PP.New.Image.17.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=20240630T142809Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5f0a4f8ea3dd95f9a37f366e798d7b362dfc897ec6dbaf5158913ce4b702c611)
Solution
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Problem 2
![Andre and Jada's calculation of a partial product problem, 657 divided by 3.](https://cms-im.s3.amazonaws.com/dhfv6AJVsDv13svoC8ypHdx7?response-content-disposition=inline%3B%20filename%3D%226-6.5.PP.Image.49.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.PP.Image.49.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=20240630T142809Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=39c55fc89a61202ee98ff75736408be6610cb5a38ae3dd9c9512878c973227af)
- How is Jada's work the same as Andre’s work? How is it different?
- Explain why they have the same answer.
Solution
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Problem 3
Which might be a better way to evaluate \(1,\!150 \div 46\): drawing base-ten diagrams or using the partial quotients method? Explain your reasoning.
Solution
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Problem 4
Here is an incomplete calculation of \(534\div 6\).
Write the missing numbers (marked with “?”) that would make the calculation complete.
![An incomplete partial quotient calculation of 534 divided by 6.](https://cms-im.s3.amazonaws.com/bh9gTKxJxHhpbAKZKmkDRF1z?response-content-disposition=inline%3B%20filename%3D%226-6.5.D.PP.New.Image.18.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.D.PP.New.Image.18.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=20240630T142809Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=fdaaf654c5cd350434ac395e76f47e47c344d57ba07333cce580d88f7b4bca65)
Solution
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Problem 5
Use the partial quotients method to find \(1,\!032 \div 43\).
Solution
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Problem 6
Which of the polygons has the greatest area?
A rectangle that is 3.25 inches wide and 6.1 inches long.
A square with side length of 4.6 inches.
A parallelogram with a base of 5.875 inches and a height of 3.5 inches.
A triangle with a base of 7.18 inches and a height of 5.4 inches.
Solution
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(From Unit 5, Lesson 8.)Problem 7
One micrometer is a millionth of a meter. A certain spider web is 4 micrometers thick. A fiber in a shirt is 1 hundred-thousandth of a meter thick.
-
Which is wider, the spider web or the fiber? Explain your reasoning.
- How many meters wider?
Solution
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(From Unit 5, Lesson 4.)