When you’re in Year 10 math class, it’s super important to know how to change ratios into proportions. But what do these terms really mean? Let’s break it down!

What Are Ratios?

A ratio is a way to compare two amounts.

For example, if you have a ratio of 2:3, it means that for every 2 of one thing, there are 3 of another.

You can also write ratios as fractions. So, the ratio 2:3 can be written as $\frac{2}{3}$.

What Are Proportions?

Proportions show that two ratios are equal.

For example, if we say that $\frac{2}{3} = \frac{4}{6}$, we are showing a proportion. This means that these two fractions represent the same relationship between their amounts.

How to Change Ratios into Proportions

To change a ratio into a proportion, just follow these steps:

1. Find the Ratio: Start with your ratio, like 4:5.

2. Turn it into a Fraction: Change your ratio into a fraction. So, 4:5 becomes $\frac{4}{5}$.

3. Set Up the Proportion: You can compare this fraction to another one. For instance, if you want to compare it to $\frac{8}{10}$, you write: $\frac{4}{5} = \frac{8}{10}$

Example

Let’s make this even clearer.

Imagine the ratio of boys to girls in one class is 3:4.

To show this as a proportion against another class with a ratio of 6:8, you can do this:

1. Write the ratios:
   • Class 1: $\frac{3}{4}$
   • Class 2: $\frac{6}{8}$
2. Show they are equal: $\frac{3}{4} = \frac{6}{8}$

This means that both classes have the same ratio of boys to girls!

By understanding how to change ratios into proportions, you can tackle many math problems, especially those involving these concepts.

Happy learning and solving!