# How to Simplify Ratios

Learn how to simplify ratios in few simple and easy steps.

## Step by step guide to simplify ratios

• Ratios are used to make comparisons between two numbers.
• Ratios can be written as a fraction, using the word “to”, or with a colon.
• You can calculate equivalent ratios by multiplying or dividing both sides of the ratio by the same number.

### Simplifying Ratios – Example 1:

Simplify. $$4:2=$$

Solution:

Both numbers $$4$$ and $$2$$ are divisible by $$2 , ⇒ 4 \ ÷ \ 2=2, 2 \ ÷ \ 2=1$$,
Then: $$4:2=2:1$$

### Simplifying Ratios – Example 2:

Simplify. $$\frac{14}{24}=$$

Solution:

Both numbers $$14$$ and $$24$$ are divisible by $$2, ⇒ 14 \ ÷ \ 2=7, 24 \ ÷ \ 2=12$$,
Then: $$\frac{14}{24}=\frac{7}{12}$$

### Simplifying Ratios – Example 3:

Simplify. $$8:4=$$

Solution:

Both numbers $$8$$ and $$4$$ are divisible by $$4$$, $$⇒ 8÷4=2, 4÷4=1$$,
Then: $$8:4=2:1$$

### Simplifying Ratios – Example 4:

Simplify. $$\frac{12}{36}=$$

Solution:

Both numbers $$12$$ and $$36$$ are divisible by $$12$$, $$⇒ 12÷12=1, 36÷12=3$$,
Then: $$\frac{12}{36}=\frac{1}{3 }$$

## Exercises for Simplifying Ratios

### Reduce each ratio.

• $$\color{blue}{21:49}$$
• $$\color{blue}{20:40}$$
• $$\color{blue}{10:50}$$
• $$\color{blue}{14:18}$$
• $$\color{blue}{45:27}$$
• $$\color{blue}{49:21}$$

• $$\color{blue}{3:7}$$
• $$\color{blue}{1:2}$$
• $$\color{blue}{1:5}$$
• $$\color{blue}{7:9}$$
• $$\color{blue}{5:3}$$
• $$\color{blue}{7:3}$$

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