# The Basics of Inverse Proportion

In the **previous post**, we have discussed the basics of direct proportions. Recall that when two quantities and change and if changes n times, then changes n times, then we can say that is directly proportional to . In this post, we are going to learn about inverse proportions.

**Problem**

A rectangle has area 24 square units. Find the possible areas if the length and width are both whole numbers.

**Solution and Discussion**

The table shows the pairs of length and width that has area of 24 square units.

Let us consider the first column as a reference pair. Notice that when the length becomes 2 times (see second column), then the width becomes ½ times (24 becomes 12). When the length becomes 3 times (1 becomes 3), then the width becomes 1/3 times (24 becomes 8). Verify if this is true with the others.

When two quantities and change, and if changes 2 times, 3 times 4 times, and so on, and y changes ½ times, 1/3 times, and ¼ times, then we can say that is inversely proportional to .

Notice that the area of the rectangle above is constant, so the product of length and width is always constant. Therefore, if is directly proportional to , then , where is a constant. We can also derive the formula .

As show in the previous post, the graph of a direct proportion lies on a straight line. Notice that the graph of inverse proportion is a curve which is high near the y-axis and approaches the x-axis as x-increases.