Ohio Assessments for Educators (OAE) Mathematics Practice Exam

In which situation would you describe a relationship as an inverse proportion?

1. Both quantities increase together

2. One quantity increases while the other decreases

3. The ratio remains constant

4. Both quantities show exponential growth

The correct answer is: One quantity increases while the other decreases

A relationship is described as an inverse proportion when one quantity increases while the other decreases. This means that as one variable becomes larger, the other must compensate and become smaller, maintaining a constant product between the two quantities. In inverse proportionality, the mathematical relationship can often be expressed as \( y = \frac{k}{x} \), where \( k \) is a constant. This illustrates that if \( x \) increases, \( y \) must decrease in such a way that the product \( xy \) remains constant. For instance, if you have a fixed number of hours to complete tasks, as you take longer to finish one task, you will have less time available for others. This demonstrates how the two quantities of time spent on tasks are inversely related. Such a relationship reflects the balancing act between two variables where one must decrease to allow for the increase of the other. In contrast, when both quantities increase together, the relationship is called direct variation rather than inverse. A constant ratio implies a proportional relationship but does not capture the essence of inverse proportion. Exponential growth indicates that both variables are increasing in a more complex manner but does not denote an inverse relationship.