# How to Create a Proportion

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.

### Create a Proportion – 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

### Create a Proportion – 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.

### Create 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

### Create a Proportion – 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 for Creating a Proportion

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

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

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