Lesson 9

Using the Partial Quotients Method

The practice problem answers are available at one of our IM Certified Partners

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. 

Problem 2

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.

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.

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.

Problem 5

Use the partial quotients method to find \(1,\!032 \div 43\).

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.

(From Grade6, 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.

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

  2. How many meters wider?
(From Grade6, Unit 5, Lesson 4.)