Lesson 18
Using Long Division
Let’s divide whole numbers.
Problem 1
Andre and Jada both found \(657 \div 3\) using the partial quotients method, but they did the calculations differently, as shown here.
![Andre and Jada's calculation of a partial product problem, 657 divided by 3.](https://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141638Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0db31cc443ad3bc6a03b61b18cd6565206d58bffe006bb7ae34b21f779961a59)
![Andre and Jada's calculation of a partial product problem, 657 divided by 3.](https://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141638Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0db31cc443ad3bc6a03b61b18cd6565206d58bffe006bb7ae34b21f779961a59)
- How is Jada's work the same as Andre’s work? How is it different?
- Explain why they have the same answer.
Problem 2
Here is a long-division calculation of \(917 \div 7\).
![Example division problem 917 divided by 7.](https://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141638Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=781803c5838ddff380a612f51f4305f1fcb7fa518016090e0b8678efb4a4d731)
- 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 \(9-7\)?
Problem 3
Han's calculation of \(972 \div 9\) is shown here.
![Student work of division problem.](https://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141638Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a57c6cede71c25f99cf1250c2aef66a6cea0474fde8192415aa9448b67739d08)
- 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.
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141638Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=12b96616a90274184024d1b67d5347c766588c3868a8e36c04ab261146984080)
Problem 5
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.
Problem 6
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?