Those of us of a certain age will remember the ‘borrow the one, pay back the one’ rule for subtraction.  It works well because, even though we didn’t understand the actual mathematical reasoning behind it, as children we understood the concept of borrowing something & returning it.  It was the rule and you just did it.

Today, that little rule has been replaced with the concept of Renaming or Regrouping and it causes untold confusion for parents – particularly when the numbers get bigger and there is a zero in the midst of it; by the way regrouping and renaming is the same thing!

When the Romans created their army, they based everything on tens and units. It made sense – we have ten fingers so it was an easy concept understand and replicate. A centurion was in charge of one hundred soldiers, made up of ten groups of soldiers, with each group consisting of ten individual soldiers (unit).

Modern maths continues to use this concept of hundreds, tens and units.  When written down the units are always on the left, the tens to the right of them and so on.  So the number 42 is made up of 2 units and 4 groups of ten units. The number 942 is made up of 2 units and 4 groups of ten units and 9 groups of one hundred units.

So how does this help with subtraction?

Let’s take a sum as an example;   82 – 39

Under the ‘borrow 1 /pay back 1’ rule we would say “nine from two I cannot do, borrow the one. Nine from twelve is three. Pay back the one. Three plus one is four, four from eight is four. The answer is forty three”.  When doing this, what we were in fact doing was borrowing ten units and then repaying ten units.

Under the new method, we are no longer borrowing ten units; we are simply regrouping the number.  So the number 82, usually 2 units and 8 tens, is regrouped or renamed as twelve units and 7 tens. We can then easily subtract 39 as follows; nine units from twelve units is three units. Three tens from seven tens is four tens. The answer is 4 tens and 3 units or 43.

If the top line number includes a zero. E.g. 900 – 107, then let’s look at the top number first.  There are no units and there are no tens but there are 9 one hundreds.  So firstly we regroup the 9 one hundreds into 8 one hundreds and 10 tens, but we still have no units. So we then regroup again into 8 one hundreds, 9 tens and 10 units.  We can then easily subtract 7 units from ten units, no tens from 9 tens and 1 one hundred from 8 one hundreds giving an answer of 7 hundreds, 9 tens and 3 units or 793.

The beauty is that all the changes are only ever made to the top number, which improves accuracy.

Why not have a go at the sums below?  Do the question both ways.  There are always a number of ways to approach a maths question, just as there are many ways to approach any problems.

37-18=?                193-75=?              604-397=?           470-299=?           800-488=?

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