Explain what is meant by the phrase ' \(a\) is inversely proportional to \(b\) '.

In mathematics, two variables are said to be inversely proportional if one of the variables is directly proportional to the reciprocal of the other variable. It means that when one variable increases, the other variable decreases, and vice versa. In other words, the product of the two variables remains constant. This can be represented as: a ∝ 1/b or ab = k, where k is a constant.

Let's take an example to better understand the concept of inverse proportionality. Suppose we have a fixed amount of money, \(60, and we want to buy chocolates that cost \)3 per piece. The number of chocolates we can buy (a) is inversely proportional to the price of each chocolate (b). As the price of each chocolate (b) increases, the number of chocolates (a) we can buy with the fixed amount of money decreases, and vice versa. This can be represented as: a ∝ 1/b or ab = 60 If the price per chocolate (b) is $3, then the number of chocolates (a) we can buy is 20: a = 60 ÷ 3 = 20 If the price per chocolate (b) is $6, the number of chocolates (a) we can buy is 10: a = 60 ÷ 6 = 10 This example demonstrates how an increase in one variable (price per chocolate) leads to a decrease in the other variable (number of chocolates) and vice versa, illustrating the concept of inverse proportionality.