How to Simplify Ratios Made Easy

Simplifying ratios is a great skill! It helps make numbers easier to understand. Ratios are just a way to compare two or more amounts. Let’s go through the steps together.

Step 1: Write Down the Ratio

First, write down your ratio. For example, let’s look at the ratio of apples to oranges, which is 12:8.

Step 2: Find the Greatest Common Factor (GCF)

The GCF is the biggest number that can divide both numbers in the ratio without leaving any leftovers.

1. List the factors:

   • For 12, the factors are: 1, 2, 3, 4, 6, 12
   • For 8, the factors are: 1, 2, 4, 8

2. Find the common factors: The numbers that are in both lists are 1, 2, and 4.

3. Pick the biggest: The greatest common factor is 4.

Step 3: Divide Both Parts of the Ratio by the GCF

Now, let’s take the original ratio 12:8 and divide both sides by the GCF, which is 4.

$$\text{New Ratio} = \left(\frac{12}{4}\right) : \left(\frac{8}{4}\right) = 3:2$$

Step 4: Check Your Work

To make sure the ratio is really simplified, see if there are any other common factors left. In 3:2, the only number they share is 1. This means it's in its simplest form!

Summary

Here’s a quick recap of how to simplify a ratio:

1. Write the ratio down.
2. Find the GCF of both numbers.
3. Divide both numbers by their GCF.
4. Check to see if it’s in its simplest form.

This process makes comparisons clearer and helps you work with numbers more easily!