By Mark Zegarelli

Division is different from addition, subtraction, and multiplication in that having a remainder is possible. A remainder is simply a portion left over from the division. For example, suppose you’re a parent on a picnic with your three children. You’ve brought along 12 pretzel sticks as snacks, and want to split them fairly so that each child gets the same number (don’t want to cause a fight, right?).

Each child gets four pretzel sticks. Whichever way you write it, the idea is the same: When you divide 12 pretzel sticks equally among three people, each person gets four of them.

But suppose that you want to divide seven candy bars between two people without breaking any candy bars into pieces (too messy). So each person receives three candy bars, and one candy bar is left over. This problem shows you the following:

7 / 2 = 3 with a remainder of 1, or 3r1

The letter r indicates that the number that follows is the remainder.

In long division, the remainder is the number that’s left when you no longer have numbers to bring down. The following equation shows that 47 / 3 = 15r2:


Note that when you’re doing division with a small dividend and a large divisor, you always get a quotient of 0 and a remainder of the number you started with: