How Can We Tell the Difference Between Direct and Inverse Proportions?

Knowing how to tell direct proportions from inverse proportions is really important in math, especially when we talk about ratios and relationships. Let’s break it down in simple terms!

Direct Proportion

In a direct proportion, when one thing goes up, the other thing goes up too. They both change together in the same way. Here’s an example:

• Example: If we buy more apples, the total cost goes up. If 3 apples cost £3, then 6 apples will cost £6. We can write this relationship as:

  $\text{Cost} \propto \text{Number of Apples}$

This means that if you double the apples, you also double the cost!

Inverse Proportion

Now, with inverse proportion, when one thing goes up, the other thing goes down. They change in opposite ways. Let’s look at this example:

• Example: If we have a set amount of work to do, the more people we have, the less time it takes. For instance, if 4 workers can finish a job in 2 hours, then 8 workers would finish it in just 1 hour. We can show this relationship as:

  $\text{Time} \propto \frac{1}{\text{Number of Workers}}$

Here, when the number of workers doubles, the time needed is cut in half!

Summary

To sum it all up, figuring out if a relationship is a direct or inverse proportion is easy if you watch how one thing reacts when the other changes:

• Direct Proportion: Both go in the same direction (either both go up or both go down).
• Inverse Proportion: They go in opposite directions (one goes up while the other goes down).

Keep these ideas in mind, and you’ll do great with problems about ratios and proportions!