Once a number has more than one digit, the easiest way to subtract is to stack the two numbers — one above the other — and line them up by place value: ones above ones, tens above tens. Then we subtract one column at a time, starting from the ones on the right.

Working right to left keeps everything tidy: each column is just a small one-digit subtraction, and the digits stay under the place they belong to.

But there's a catch. To take 7 ones away from 2 ones, we don't have enough — 2 is too small. So we exchange (some people say borrow): we take one ten from the tens column and turn it into ten ones. Now the top number is rewritten as 4 tens and 12 ones — the same value, just carried differently — and 12 - 7 = 5 works.

Exchanging never changes how big the number is. It only moves value from one column to the next so the subtraction in the ones column becomes possible.

See it worked through

Watch the subtraction step by step. The ones column comes first; when the top digit is too small, one ten is exchanged for ten ones (shown in colour), and then both columns subtract cleanly. Step through it. Reload for a fresh example.

See it explained

Sal Khan works through a subtraction that needs borrowing, exchanging a ten for ten ones.