In division, the remainder is the number left when one number does not divide another number exactly. Remainders can be expressed in several ways.

Remainder as a whole number

Often the remainder in division is expressed as a whole number.
Floyd had 14 gumballs. He gave them to 4 friends. How many gumballs did each person receive?
14 ÷ 4 = 3, with a remainder of 2
Therefore each person received 3 gumballs, and there were 2 gumballs remaining. (Cutting gumballs into parts does not work very well!)

Remainder as a common fraction or decimal fraction

In many division problems, the remainder is expressed as a common fraction or a decimal fraction.
Jamie and Roger went on a 10-mile hike. If the trip lasted 4 hours, about how many miles did they hike per hour?
10 ÷ 4 = 2½ or 2.5
Thus, Jamie and Roger hiked about miles (or 2.5 miles) per hour. In this situation, the remainder is expressed as as ½ or 0.5.

Remainder ignored

In some problems, the remainder is ignored.
Bobbi was making bookshelves for her room. she had 8 feet of lumber for shelves, and each bookshelf was 3 feet long. How many shelves could she make?
8 ÷ 3 = 2, with 2 feet of shelving remaining.
She could make 2 shelves. The lumber she would have remaining after that is not enough for her to make another bookshelf.

Remainder as the next highest whole number

Sometimes a remainder requires the problem solution to be the next highest whole number.
Ken bought hot dog buns for the picnic. He needed 60 buns in all. The buns were packaged in bags containing 8 each. How many packages of buns did he need to buy?
60 ÷ 8 = 7, with a remainder of 4
If Ken buys 7 packages of hot dog buns, he will have only 58 buns, and he needs 60. He will need to buy a total of 8 packages of buns.

See also division, subtraction.