Subtraction - how do you do it?

As our daughters move through school - we as parents are re-learning things with them that we studied ourselves in primary school.

One of the really basic things we are 'learning' is subtraction - in particular taking larger numbers away from smaller numbers. Euan and I both learned different methods of subtraction - and the method I learned is different to that being taught to our daughters, so I am having to re-learn how to subtract!

Take the above problem for example.  You would start on the right, with 2-7, which doesn't work, so what do you do..??

The method I learned - The Austrian 

So first I start with 2-7    .

This can't be done, so I add ten to the top and ten to the bottom.

In the top row, I add the 10 in the 'ones' , and in the bottom I add the 10 in the tens column, like this:

So now I have 12 - 7 = 5
and then            5 - 2  = 3

The problem works as you add an extra ten on both sides of the subtraction.  So long as you remember to mark the extra ten on both the top and the bottom!

The other method - what our daughters are learning!

This method only alters the numbers on the top row and involves crossing numbers out.  So here instead of adding numbers, you borrow from another column!  You borrow ten from the tens column and put that ten in the ones column, so:

So your problem now looks like this:

And then you have:

                       12 - 7 = 5
and then            4 - 1  = 3

Two different methods to produce the same result.

Now for me - of course the first method is easier - as that is what I was taught as a child.

But although I may be biased, I still think this method is easier and also neater than borrowing and crossing out, particularly when you have larger sums and you have to borrow from the hundreds or even the thousands column!  See the two different methods on this problem:

Of course it doesn't matter which method you use, or which your children learn.  It's probably best not to confuse them with both methods though!  And since our girls school is teaching the method of borrowing and crossing out, then when I help them with their homework, I need to help them using this method too!

What method do you use? and are your kids learning the same method? 


  1. I learned the same method that your daughters are learning, but my children learned it the other way.

    1. It's confusing isn't it! I never thought something so simple could be so confusing. I never really 'thought' about it before - just one of those things you do automatically!

  2. Wow! I never ever heard of the Australian method. I went to school a lot of places (not in Australia, though) and never saw anyone do it like that. I have to admit, I kind of like it. AND, it is neater!

  3. There are lots of different ways to do addition and subtraction (as well as other operations). I think it's better to teach kids the principles actually going on with the math so that they can understand multiple methods and then do whichever works best for them. However, schools tend to just teach rote memorization of algorithms instead, like what you discussed. This doesn't really result in mathematical literacy, which is why I think so many people hate math. They end up just solving equations rather than understanding them.

    1. I agree that whichever works for kids is what is best for them. Everyone is different and sees things in a different way. The important thing is to make sure kids get the basics - whichever method it takes!


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