# How to Find Proportional Ratios? (+FREE Worksheet!)

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

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## 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: \(a \ × \ d=c \ × \ b\)

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### Proportional Ratios – Example 1:

Solve this proportion for \(x\)**.** \(\frac{2}{4} = \frac{3}{x}=\)

**Solution:**

Use cross multiplication: \(\frac{2}{4}=\frac{3}{x} ⇒2 × x=3 \ × \ 4⇒2x=12\)

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: \(2 \ × \ 60=5 \ × \ x⇒120=5x\)

Divide to find \(x\): \( x=\frac{120}{5}⇒x=24\)

There are \(24\) red balls in the box.

### 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 \(x: x=\frac{40}{4} ⇒x=10\)

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### 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.

- \(\color{blue}{\frac{2}{4}=\frac{8}{x},x=}\)
- \(\color{blue}{\frac{1}{2}=\frac{6}{x},x=}\)
- \(\color{blue}{\frac{2}{3}=\frac{12}{x},x=}\)
- \(\color{blue}{\frac{1}{4}=\frac{x}{20},x=}\)
- \(\color{blue}{\frac{3}{4}=\frac{x}{8},x=}\)
- \(\color{blue}{\frac{1}{4}=\frac{18}{x},x=}\)

### Download Proportional Ratios Worksheet

## Answers

- \(\color{blue}{16}\)
- \(\color{blue}{12}\)
- \(\color{blue}{18}\)
- \(\color{blue}{5}\)
- \(\color{blue}{6}\)
- \(\color{blue}{72}\)

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