# How to Find Proportional Ratios

Learn what proportion is and how to write and create a proportion in few simple steps.

## Step by step guide to creating proportional ratios

• A proportion means that two ratios are equal. It can be written in two ways:
$$\frac{a}{b}=\frac{c}{d} , a∶b=c∶d$$
• The proportion $$\frac{a}{b}=\frac{c}{d}$$ can be written as: $$a \ × \ d=c \ × \ b$$

### Proportional Ratios – Example 1:

Solve this proportion for $$x$$. $$\frac{2}{4} = \frac{3}{x}=$$

Solution:

Use cross multiplication: $$\frac{2}{4}=\frac{3}{x} ⇒2 \ × \ x=3 \ × \ 4⇒2 \ x=12$$
Divide to find $$x$$: $$x=\frac{12}{2} ⇒x=6$$

### Proportional Ratios – Example 2:

If a box contains red and blue balls in the ratio of $$2:5$$ red to blue, how many red balls are there if $$60$$ blue balls are in the box?

Solution:

Write a proportion and solve. $$\frac{2}{5}=\frac{x}{60}$$
Use cross multiplication: $$2 \ × \ 60=5 \ × \ x⇒120=5 \ x$$
Divide to find $$x$$: $$x=\frac{120}{5}⇒x=24$$

### Proportional Ratios – Example 3:

Solve this proportion for $$x$$. $$\frac{4}{8}=\frac{5}{x}$$

Solution:

Use cross multiplication: $$\frac{4}{8}=\frac{5}{x } ⇒4×x=5×8⇒4x=40$$
Divide to find $$x: x=\frac{40}{4} ⇒x=10$$

### Proportional Ratios – Example 4:

The ratio of boys to girls in a school is $$2: 3$$. How many boys are in the school if there are $$90$$ girls in the school?

Solution:

Write a proportion and solve. $$\frac{2}{3}=\frac{x}{90}$$
Use cross multiplication: $$2×90=3×x⇒180=3x$$
Divide to find $$x:x=\frac{180}{3}⇒x=60$$

There are $$60$$ boys in the school.

## Exercises for Finding Proportional Ratios

### Solve each proportion.

1. $$\color{blue}{\frac{2}{4}=\frac{8}{x},x=}$$
2. $$\color{blue}{\frac{1}{2}=\frac{6}{x},x=}$$
3. $$\color{blue}{\frac{2}{3}=\frac{12}{x},x=}$$
4. $$\color{blue}{\frac{1}{4}=\frac{x}{20},x=}$$
5. $$\color{blue}{\frac{3}{4}=\frac{x}{8},x=}$$
6. $$\color{blue}{\frac{1}{4}=\frac{18}{x},x=}$$

1. $$\color{blue}{16}$$
2. $$\color{blue}{12}$$
3. $$\color{blue}{18}$$
4. $$\color{blue}{5}$$
5. $$\color{blue}{6}$$
6. $$\color{blue}{72}$$

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