Proportion simply means that two ratios are equal. Creating a proportion means creating two equal ratios or fractions.

## Step by step guide to creating a proportion

- A proportion contains two equal fractions! A proportion simply means that two fractions are equal.
- To create a proportion, simply find (or create) two equal fractions.

### Example 1:

Express ratios as a Proportion and solve.

\(180\) miles on \(9\) gallons of gas, how many miles on \(1\) gallon of gas?

**Solution:**

First create a propotion: \(\frac{9}{180}=\frac{1}{x}→9 \ × \ x=180 \ × \ 1→x=20\). Then: \(20\) miles per gallon

### Example 2:

State if this pair of ratios form a proportion. \(\frac{2}{3}\) and \(\frac{13}{30}\)

**Solution:**

Use cross multiplication: \(\frac{2}{3}=\frac{12}{30}→2 \ × \ 30=12 \ × \ 3→60=36\), which is not correct. Therefore, this pair of ratios doesn’t form a proportion.

### Example 3:

Express ratios as a Proportion.

\(120\) miles on \(4\) gallons of gas, how many miles on \(1\) gallon of gas?

**Solution:**

First create a fraction: \(\frac{120 \ miles}{4 \ gallons}\), and divide: \(120÷4=30 \)

Then: \(30\) miles per gallon

### Example 4:

State if this pair of ratios form a proportion. \(\frac{3}{5}\) and \(\frac{24}{45}\)

**Solution:**

Use cross multiplication: \(\frac{3}{5}=\frac{24}{45}→3×45=5×24→135=120\), which is not correct. Therefore, this pair of ratios doesn’t form a proportion.

## Exercises

### Create proportion from the given set of numbers.

- \(\color{blue}{1, 6, 2, 3}\)
- \(\color{blue}{12, 144, 1, 12}\)
- \(\color{blue}{16, 4, 8, 2}\)
- \(\color{blue}{9, 5, 27, 15}\)
- \(\color{blue}{7, 10, 60, 42}\)
- \(\color{blue}{8, 7, 24, 21}\)

## Answers

- \(\color{blue}{1 : 3 = 2 : 6}\)
- \(\color{blue}{12 : 144 = 1 : 12}\)
- \(\color{blue}{2 : 4 = 8 : 16}\)
- \(\color{blue}{5 : 15 = 9 : 27}\)
- \(\color{blue}{7 : 42, 10 : 60}\)
- \(\color{blue}{7 : 21 = 8 : 24}\)