November 2008
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Division – Partial Quotients Method

We are under way with unit 4 focused on Division. There is more than one way to divide and the partial quotients method is one that is new to me. I have copied this link from Mr. Hossack to put on this site so that you may get a better understanding of how this method works and teach your parents because I’m sure that one or two of them will not have seen this method. It really doesn’t matter what method you use, as long as the one you use works for you. There is also no harm in learning a new method if you already know how to divide.  Here is an example taken from this useful math site called Math Corner.

Division Methods

Our favorite way to introduce multi-digit division is by alerting kids to the fact that they merely need to know how to multiply (and subtract and add) in order to divide. We teach our students how to use the partial- quotients method, which is a most forgiving method for division. At each step, the student finds a partial answer and at the end, these partial answers are added to find the quotient.

Study the example below delineating how partial quotients can be used to find the answer to 94 ÷ 6.

6        94

 Think: How many 6s are in 94?

               (At least 10)

                The first partial quotient is 10

(10 x 6 = 60)

Subtract 60 from 94

Think:  How many 6s in 34?

                At least 5 [6s] or 30

The second partial quotient is 5

(5 x 6 =30)

Subtract. Add partial quotients

  Total: 15  with a remainder of 4

The partial quotients method works just as well if the divisor is a 2-digitnumber. It often helps students to write down some easy facts for the divisor first. For example: In solving a problem such as 400 ÷ 22; some facts for 22 would be

22 x 2 = 44

22 x 5  = 110

22 x 10 = 220

22              400

10              ( 10  [22s] in

5                ( 5 [22s] in 180)

2                (2 [22s] in 70)

1                 (1 [22] in 26)

 Total        18  remainder 4

The reason this method is easy to use is that the student can choose the numbers he or she feels most comfortable working with. There are different ways to find the partial quotients and yet all these ways lead to the right answer. Study the example below to see the different ways three students approached the problem 371 ÷ 4.

Work out the following questions on scratch paper using the partial quotients method for homework tonight. Remember to show your working out.

  • 279 ÷ 6 =
  • 557 ÷ 4 =
  • 734 ÷ 7 =
  • 492 ÷ 5 =
  • 631 ÷ 9 =

Mr. T

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