Inverse Proportion
(Reference Copy)

Activity  12&13: Inverse Proportions

In previous activities, all the proportions that you studied were a special type of proportion called a direct proportion.   In direct proportions, when one row of a table shows that the proportion gets larger, the numbers in the other row or rows get "proportionally" larger.  You can always find the numbers in a row by multiplying the numbers in another row by some specific number.  In this lesson, you also learn about inverse proportions.  In these proportions, one row gets smaller at the same time that another gets larger.  For example, think of how long it would take you to paint your room.  How long would it take if you had one friend helping you?  How long would it take if you had two friends helping you?  The relation between the time it takes to paint your room and the number of people painting is an inverse proportion.  The more people you have, the less time it takes (or at least the less time it should take!)

Setting Up and Solving Inverse Proportions

Like direct proportions, inverse proportions can also be solved using the cross-multiply and divide method.  However, the proportion must be set up much differently to account for the fact that one term is increasing while the other is decreasing.  You must (1) make a ratio of one type of term ( persons, weight, etc.), (2) make a ratio of the second type of term (hours, distance, etc.), (3) invert one of the ratios (flip it upside down), and then (4) use the cross-multiply and divide procedure for direct proportions.  For example, we could make ratios of persons and hours to paint a room by doing the following: