Lesson 18

Using Long Division

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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.
  1. How is Jada's work the same as Andre’s work? How is it different?
  2. Explain why they have the same answer.

Solution

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Problem 2

Here is a long-division calculation of \(917 \div 7\).

Example division problem 917 divided by 7.
  1. There is a 7 under the 9 of 917. What does this 7 represent?
  2. What does the subtraction of 7 from 9 mean?
  3. 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.
  1. Find \(180 \boldcdot 9\).
  2. Use your calculation of \(180 \boldcdot 9\) to explain how you know Han has made a mistake.
  3. 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.

 

Solution

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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.

Solution

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(From Unit 3, Lesson 15.)

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.

  1. Which is wider, the spider web or the fiber? Explain your reasoning.

  2. How many meters wider?

Solution

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(From Unit 3, Lesson 15.)