Primary mathematics/Subtracting numbers

first 5-2=3 second 40-30=10

 45
-32
===
  3
 10

then add

 45
-32
===
  3
 10
===
 13

To get the answer.

When this is grasped move on to harder problems:

 52
-35
====

There are 2 methods that I would like to illustrate, the first uses carrying:

Start by saying that 5 is bigger than 2 so we take 10 from the 50 and add it to the 2 to get 12

 5412
- 3 5
======

Is the usual way of writing this.

Now subtract 5 from 12 to get 7. This is another 'pair' that needs to be taught - all the numbers up to 10 subtracted from all larger numbers up to 20 are 'required', or it is possible to say that 12-2 is 10 and that 5-2 is 3 and 10-3 is 7, which is how I do it, but is not necessarily the 'easiest' way. Different children will want to do this in different ways and will often develop their own methods for mental subtraction (i.e. when you don't write it down). For instance I do this: 56-38 becomes 50-40+6+2 : note that I have used both the fact that 56=50+6 and that 38=40-2 (this is why I personally feel that every child needs to know the pairs that sum to 10) and that a+b-(c-d) = a-c+b+d although you can 'see' this as the 'big chunk' from 40 to 50 and then the two small end bits added on (6 and 2) without explaining using algebra, again teachers should remember this general truth (that addition can be re-ordered and that minus minus = plus) in order to answer questions and with a view to the child learning it in this form.

To continue:

 5412
- 3 5
======
    7

Then we take 30 from 40 (remember that it is now 40 since we gave the other 10 to the units) to get 10

 5412
- 3 5
======
    7
   10

And finally add these two together

 5412
- 3 5
======
    7
   10
======
   17

To give the answer.

This is the method I was taught. I was introduced to this second method by being told that a young boy had used it without prompting, proving that young children can (and do) understand negative numbers if told about them:

The same sum:

 52
-35
====

This time we will take 30 from 50 first (working left to right here - much more 'obvious') to get 20

 52
-35
====
 20

Then we will take 5 from 2 to get -3

 52
-35
====
 20 
 -3

Then we take the 3 from the 20

 52
-35
====
 20 
 -3
====
 17

To finish the sum. Here students need to know what 20-3 is: This is easiest to look at as 10+10-3 and then know that 10-3 is 7 (again, numbers adding to 10).