Simple Subtraction

Sooner or later, your child is going to want to understand the concept of subtraction. While this is – essentially – the reverse of addition, it somehow feels more complicated, perhaps due to having found teaching methods at primary school rather confusing. Remember that, as in all basic maths, it is far more important for your child to understand the principles involved than to remember number ‘facts’.

So take it slowly, and make sure that your child – whatever age – understands and is familiar with the first ten numbers and the ways they can be combined. The page number bonds tells you how to introduce this, if your child has not already figured it out on his own. It is also worth making sure that he is confident about adding numbers, and writing them down if he cannot do a sum in his head or on his fingers.

Starting subtraction

It is a good idea to use the idea of subtraction in everyday life, when appropriate. For instance: ‘I cooked 10 sausages, and we ate four of them. How many do you think are left?‘ If your child’s curiosity is piqued, you could show him how to calculate something like this on his fingers, or by using buttons or lego bricks to represent sausages. There are several ways to do even a simple calculation such as this: for instance, you could count out ten, then count six of them and move them away, and count the remaining four. Or you could count backwards from ten while removing one at a time. Or you could move them into two piles of five each, and then move one piece into the other pile.  There are no ‘wrong’ methods, and the vital thing is to see that this kind of problem is just another way of looking at the basic number bonds.

As with addition, simple subtraction of larger numbers will not necessarily pose a problem if he understands how to count in tens, and sees that (for instance) taking 4 from 10 is related to taking 24 from 30, or 94 from 100. A child who likes patterns and is quick to grasp them may then see that if 4 taken from 10 is 6, 4 taken from 20 must be 16.

However, until your child wants to write numbers down, and is confident doing so, it’s best to keep this kind of thing conversational, and to make a game of it. You can show your child where subtraction is used day to day – when looking at a thermometer for instance, to see how much colder it is. Or when he buys something at a shop and gets ‘change’ – it’s very useful to learn to check whether the correct amount has been given. This may be a good opportunity to talk about subtraction from 100, if he has paid for something with a pound (or euro or dollar…) and has been given some change. Encourage him to use a calculator, if you have one handy (perhaps on your phone) so that he becomes familiar with the process and the minus sign that looks like a hyphen.

Place value

Sooner or later, your child will want to learn how to write down a subtraction problem himself. Before you try to teach a method of subtracting on paper, it would be a good idea to read the page on . Understanding the significance of digits and what zero means is vital before children can do subtraction on paper. Make sure that he is able to subtract 20 from 30 as easily as 2 from 3, and that he is comfortable, too, with hundreds and thousands, and the concept of zero.

Two digit subtraction

First of all, choose numbers such that digits of the larger one are each bigger than those of the smaller number. Remind him about the conventions of writing numbers in columns, as explained on the page about addition, and tell him the ‘minus’ or ‘subtraction’ symbol, -, with the underline to show that the answer will be underneath:

Remind him that 34 means three lots of ten, and four ones, while 76 means seven tens and six ones. So to subtract them, you can first subtract the ones – which we call ‘units’ – to give two ones (ie 6 – 4 = 2). You can then subtract the multiples of ten, giving four tens (ie 70 – 30 = 40). We write this as:

If your child is skeptical, write it out as an addition sum (ie 34 + 42) to check that the result is indeed 76. Show him, too, that 76 – 42 = 34. This is an important principle that many small children fail to grasp, leading to difficulties – later on – with algebra. If he understands this immediately, try a couple more similar subtraction problems, using three digits if you like.

Don’t make this a drill; just play around with one or two problems like this at a time. If you have numerical fridge magnets, try using them. If you have foggy windows, try writing with your fingers on them. You can do simple maths like this on the beach, drawing in the sand, or using chalks on a blackboard, or glitter pens on paper… whatever appeals.

Subtraction with re-grouping (‘borrowing’)

At some point, your child will realise that there is a problem if one of the digits to be subtracted is bigger than the one above it. If, for instance, he wants to take 36 away from 54, it becomes more complicated. You can, first of all, show him that it can be done by counting in tens on your fingers and then the units – or perhaps remind him that it’s essentially the same as taking 6 from 24, and physically count out buttons to find the answer.

But eventually your child will want to see it on paper. So:

Some children, if taught by rote, will see that 6 cannot be taken from 4, so will take 4 from 6 instead. However, if a child fully understands the concepts, and what he is trying to do, this should not be a problem (if it is, put it aside and wait a few months before trying again). Years ago, we were taught that in a situation like this, we could ‘borrow’ from the tens column. This led to a great deal of confusion, so today the same technique is known as ‘regrouping’. What happens is that instead of thinking of – in this case – 54 as five tens and four ones, we think of it as four tens and fourteen ones. We can clearly take 6 away from 14, giving 8, and can then take thirty from forty, giving the result of 18.

To show how to do this kind of thing visually, you can watch the short video demonstrations on this page about subtraction with regrouping on the ‘maths is fun’ site. This is not the only way to think of subtraction of this kind, but it’s the most commonly taught. You can find other methods with examples, if you prefer, at the coolmath4kids site.

Subtraction with bigger numbers

Once your child is familiar with subtraction and re-grouping, you can play around with more problems, including larger and larger numbers if your child is intrigued by them. Just follow the same principles, subtracting one column at a time, regrouping if necessary – which is why it is vital to remember what each digit refers to. If your problem is to subtract something like 367 from 542, you will have to regroup twice,  remembering that 500 is the same as 400 plus 100.

Keep a calculator handy to check your answers and encourage your child to do the same.

If your child gets in a muddle with a lot of zeroes – and it can be daunting having to regroup 10000 or even 100 – a ‘trick’ which he may spot himself, or which you can point out, is to subtract from the number that is one lower (ie 9999 or 99 in the above examples) – and then add one on again at the end. You can demonstrate this by asking him to work out 99 – 27, and then 100 – 27. If he simply tells you the answer to the second question without writing it down, he has grasped this ‘trick’ intuitively.

Examples to try: 98-43; 432 -332; 656 – 547; 10000 – 2345; 100-9.

Other basic maths for young children:

Maths for toddlers
Beginning multiplication
Fractions for four-year-olds
Prime numbers and factors