A number bond is a pair of numbers that add together to make a particular total. The most useful ones make 10, because ten is the number our whole counting system is built around.

Think of 10 as a single whole that splits into two parts. If one part is a, the other part is whatever is left over:

This is just addition seen the other way round: instead of asking "what is the total?", we fix the total at ten and ask "what two parts make it?".

See ten split apart

Watch a row of ten cells split into two coloured parts. The left part is a and the right part is 10 - a — together they always fill the whole ten. Step through it. Each visit shows a different bond.

The bonds to 10

There are only a handful of them, and they come in mirror pairs — once you know 3 + 7 you also know 7 + 3:

Learning these by heart is worth the effort: once the bonds to ten are instant, much of mental addition becomes fast, because you can always lean on a friendly ten.

Stretching to 20

The same idea works for any whole. The bonds to 20 split twenty into two parts in exactly the same way:

So 13 + 7 = 20 and 15 + 5 = 20. If you already know a bond to ten, you can often find the matching bond to twenty by adding ten to one of the parts.

See it explained

Sal Khan shows the different ways of making ten by filling in the missing part.