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                          Long Division:  Partial Quotients Method


This method of long division "makes sense".

It can be used by any student who knows only their 1,2, 5 and 10 times tables.

I don't know why one has to teach the traditional method but if you do I would teach this method first.

Let's take the problem 789 divided by 9.

Have the class make up a word problem for this question.

For example Nine students wanted to share 789 marbles.

We can give each student 50 marbles.


If each student has 50 marbles we will have shared 450 marbles and have 339 left over.

(Here is why I like this method. Instead of dividing 9 into 78

 I am working with "real " numbers.

 Can I give each student 100 marbles?  No, so what's a number I'm comfortable with?

I chose 50 but someone with stronger skills could  have chosen 70 .)



If we give each student 20 more  marbles

 we will have shared 9 x 20 = 180 more marbles


We have 159 marbles left. Can we give each student 10 more?

Subtract 90 from 159 and we have 69 marbles left.

Now we can give each one 5 marbles. We have 24 marbles left to share.


Each student can have 2 more and we will have 6 marbles left over.



We now add our numbers  on the right and find we can give each student 87 marbles .


The great advantage with this method is that student can work through the problem at their own level of understanding.

They don't have to have mastered all the times table to do long division .

 A weak student might take longer to solve the problem but they can do it. 

There are always students who can find  a faster way by

using this method .




Web Pages

Double Division

Partial Quotient Method  Video

Snork's Long Division Game

Coolmath's Long Division Lessons

BBC Division

Acronym for Long Division

                                                                                              Partial Quotient: Slide Share



Thank you for visiting the Long Division page.

I last edited this page on April 27  2010

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Last updated: 01/02/13.