## Step 1: Find the greatest common factor

Look for the greatest common factor (GCF) shared by the values of the ratios. If we want to simplify 56:70, we’ll need to determine the value of its GCF.

## Step 2: Divide by the greatest common factor

Divide all the values by the GCF. So, for our example, we can divide 56 and 70 by 14.

## Step 3: Rewrite with simplified values

Once the values are simplified, rewrite the ratio with the simplified values. This means that:

## Examples of how to simplify ratios

**Q1) Simplify the following ratios.**
a. 80:90 b. 64:144 c. 128:160

Determine the greatest common factor shared by the values found on each of the ratios. 80=10×8 64=16×4 128=32×4 90=10×9 144=16×9 160=32×5

Once we have the GCF shared by the values on each ratio, we divide the values by the GCF.

80÷10=8 64÷16=4 128÷32=4 90÷10=9 144÷16=9 160÷32=5

Write the ratios with their simplified ratios.

a. 80:90=8:9 b. 64:144=4:9 c. 128:160=4:5

**Q2) Jenny allots $1430 for her monthly utility bills and $4400 for her monthly rent. What is the ratio of the amount that she spends on monthly utility bills to her monthly rent?**

We want to find the simplified ratio of $1430 for utility bills and $4400 for monthly bills.

1430:4400

First, let’s determine the greatest common factor (GCF) shared by the values.

1430=110×13 4400=110×40

Divide both values by 110 to find the simplified form of the ratio.

1430÷110=13 4400÷110=40

So, rewriting the ratio, we have 1430:4400=13:40

This means that the ratio that Jenny pays for her utility bills to the amount she spends on rent is 13:40.