Remainder - GCSE Maths Definition

In GCSE Mathematics, the remainder is the value leftover when one number is divided by another. A very simple example of this would be 5 ÷ 2 = 2 r 1; so the remainder is 1. You may recall writing remainders in this way from primary school but, at this level, when working with remainders we are likely to write them in a more useful, mathematical way.

One such way is to write improper fractions as mixed numbers. For example, 17 ÷ 5 = 3 r 2. "3" is the whole part (also called quotient) and "2" is the remainder. As a mixed number, we would write this as ("three and two-fifths"). The remainder becomes the numerator of the fractional part of the mixed number, where the denominator is the value we were dividing by in the first place (called the divisor).