Question

A quantity a varies directly as a quantity b, if, when b changes, a changes in the same ratio. What happens to the quantity a if the quantity b doubles in value?

Answer 1

This means that if b doubles, then a will become half as large. For the inverse of the ratio 2 to 1 ("doubles") is the ratio 1 to 2 ("half"). The terms are exchanged; the inverse of the ratio a : b is the ratio b : a. When a varies inversely as b, we say that a is inversely proportional to b.