Probably better stated as a reciprocal proportion, the inverse proportions relates two quantities through factors that are multiplicative inverses. That is, through factors that are reciprocals, such as 3 and 1/3.

For example, let us say that you are driving a car and you are going to travel 60 miles. Consider this to be a constant distance throughout the following discussion.

Case #1:

Suppose that you spent 1 hour driving. Your average speed would be 60 mph.

Case #2:

Suppose that you spent 2 hours driving. Your average speed would be 30 mph.

So, changing the number of hours that you drive will change the average speed that you will travel.

Notice that the number of hours, the time, that is, changed by a factor of 2, since 1 hour times 2 is 2 hours.

Also, notice that the speed at which you were traveling changed by a factor of 1/2, since 60 mph times 1/2 is 30 mph.

The two quantities, time and speed, changed by reciprocal factors. Time changed by a factor of 2; speed changed by a factor of 1/2.

When quantities are related this way we say that they are in inverse proportion. That is, when two quantities change by reciprocal factors, they are inversely proportional.

In the above example the time is in inverse proportion to the average speed. One could also say that the average speed was in inverse proportion to the time.

The formal definition of inverse proportion:

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