Sometimes a total won't share out evenly. When division leaves something behind, the left-over part is called the remainder.

Take 13 \div 4. You can make 4 full groups of 3, which uses up 12 — but 1 is left over with nowhere to go. So:

We read that as “three remainder one”: three in each group, and one left over.

Press play to deal a pile of dots out one at a time, round and round the groups. The groups fill up evenly — and the dots that can’t finish another full round are the remainder, glowing on their own.

Here’s the key idea: the remainder is always smaller than the number of groups. If it were as big as the number of groups, you could deal out one more full round! With 4 groups, the remainder can only be 0, 1, 2, or 3.

A remainder of 0 means the total shared out exactly — no left-overs at all. That’s just ordinary division with nothing to write after the “r”.

Khan Academy introduces remainders here: