Subtraction = Taking One Number Away from Another


The opposite to “addition” is “subtraction” where we remove the value of one number from another to arrive at a new result which of course is (normally) less than we started with. “Subtraction” is all around us, income tax, mortgages, indeed any debt that we have involves the subtraction of money from our pockets leaving us with less than that we started with. Subtraction is yet again another skill which is worth mastering so that you can for example make sure that your monthly budget is on target by taking your routine and daily expenses away from the money you have in the bank. Of course a calculator is probably more critical in subtraction and you would probably default to a calculator straightaway as I believe most people would, but learning to do it on paper with a pen is a desirable skill which we will start to go through now.


Our first example will be very simple, 15 take away 4 equal 11. The first part involves the “taking away” of 4 from 5. If you line up for example 5 oranges and take 4 of them away it is quite obvious you are left with just one so in this case would put the one in the answer box (the rightmost number 1 of the two shown). The second operation would be to take something away from the 10, but as you can see there is nothing to take away from it, so we bring it down into the answer box unchanged.

In each individual column, where the number at the bottom is smaller than the one at the top, the subtraction is always quite straightforward. For example the above 5-4 is one, but what about if the 5 and 4 had been reversed?


This time the subtraction isn’t quite so straightforward, because in simplistic terms you can’t take 5 away from 4 (later on in the book you will find that in fact you can, but your answer will be negative and so is not to confuse the matter at the moment we won’t bother with those).


Consider for a moment if we want to buy something, but we have not got the money, what do we do? Well… We can consider a loan from the bank so in fact we “borrow” and we do exactly the same in this subtraction.


Study the question, we need to borrow 10 from the tens column to add to our 4, so that we can take away 5 from it. This time, because 4 is too small to do the subtraction I’ve borrowed a 10 from the tens column and so the tens column has had to be reduced by 1 to 0. I’ve placed the “borrowed” 10 near to the 4 making it 14, I have then taken away the 5 leaving 9, and this is our answer because we have nothing left in the tens column to do anything with.




The next example I’m going to go through will contain some hundreds, and will be a little bit more complicated than this first one but by the same token I hope it will make the processes a little bit clearer to you.


In this question we take away 187 from 455, leaving us with 268. There will be a couple of instances of “borrowing” during this question, but as always, we will take it step by step.

First of all look at the units, we can see straight away that we cannot ordinarily take 7 away from 5 so straight away we have to consider “borrowing” a 10 from the five 10s we have in the top line (the 50 component of 455).


We “borrow” 10 from the 50 in the 455 component of the question, making our units 15, from which we take away 7 leaving us with 8. The 5 in ‘455’ representing the tens is reduced by 1, temporarily making the number 445 as shown below:


Study the diagram in conjunction with the last few lines if you’re not sure where this has all come from.

If you’re satisfied to move on then you will see that 15 - 7 is indeed 8 and our five 10s has been reduced four 10s because we borrowed one.



Moving into the tens column we now need to subtract 8 from 4 and once again (ordinarily) we cannot do this without borrowing 100 from the hundreds column.  



We do this by borrowing 100 from the 400 and reducing it to 300, then we make our 4 in the tens column into a 14, we subtract 8 from it leaving 6 which were put in the answer box. Study the diagram for a while, you will see that it is in fact correct and that we now only have three 100s to play with not 4 because we borrowed 1.



The remaining step is quite simple, looking at the hundreds column 3 minus one equals 2 so the answer that we place in the answer box to the left of the 6 will be 2, giving us our final answer of 268.


So…