Inverse Variation

48 sweets are shared equally among some children. With 3 children each gets 16; with 6 children each gets 8. Double the children and each share halves: the share varies inversely with the number of children.

In symbols, $y = \frac{k}{x}$, with k fixed. Here $y = \frac{48}{x}$, and the product $xy$ is always 48: 3 times 16, and 6 times 8. To use the rule, put x in: with 6 children, $y = \frac{48}{6}$, which is 8.

Compare the two kinds. In direct variation y over x stays fixed, and with a positive k, y grows with x. In inverse variation x times y stays fixed, and with a positive k, y shrinks as x grows. x can never be 0: nothing is shared among no children.