How to Create a Proportion? (+FREE Worksheet!)

Related Topics

• How to Simplify Ratios
• How to Find Proportional Ratios
• How to Find Similarity and Ratios

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.

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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: $\frac{9}{180}=\frac{1}{x}→9 \ × \ x=180 \ × \ 1⇒ 9x=180$

Divide to find $?$$:x= \frac {180}{9} →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 $\frac{12}{30}$

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 proportion: $\frac{4}{120}=\frac{1}{x}→4 \ × \ x=120 \ × \ 1 ⇒ 4x=120$

Divide to find $?$$:x= \frac {120}{4} →x=30$.

Then: $30$ miles per gallon

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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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