The reciprocal, and the rule for dividing

In a division, the number being divided is the dividend, the number you divide by is the divisor, and the answer is the quotient.

In every example, the first step was: find what makes 1 when multiplied by the divisor. It's always the divisor flipped upside down. For 3/5 it's 5/3. This is the reciprocal. A number times its reciprocal is always 1.

The second step: multiply the dividend by that reciprocal. 2/3 ÷ 3/5 → 2/3 × 5/3 = 10/9.

In general:

a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)

To divide by a fraction, multiply by its reciprocal. People say flip and multiply, but now you know why it works.

This general rule for dividing fractions was also first written down by Brahmagupta in 628 CE.