Division algorithm

The division algorithm involves repeatedly subtracting large chunks from a number, which are multiples of the number we are dividing by, and keeping track of how many multiples.

Background material that will assist teachers to explain division to students can be found in the module for Division of whole number (Years 4–7)

If we want to know how many 'lots of' 3 apples we can make from 47 apples we can draw a picture.

We can see that there are 15 lots of 3 and 2 left over. We write 47 ÷ 3 = 15 remainder 2.

We could set this out using the division algorithm. We set the question out as follows:

		1	5	rem	2
3	)	4	7
		3	0
		1	7
		1	5
			2

We say '3 goes into 4 once', so we write a '1' above the line.

3 × 10 = 30, so we subtract 30 from 47.

We say '3 goes into 17 five times', so we write a '5' above the line.

3 × 5 = 15, so we subtract 15 from 17.

There is a remainder of 2, so we write 'rem 2' above the line.