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.

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 \(𝑥\)\(:x= \frac {180}{9} →x=20\).

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 propotion: \(\frac{4}{120}=\frac{1}{x}→4 \ × \ x=120 \ × \ 1 ⇒ 4x=120\)

Divide to find \(𝑥\)\(:x= \frac {120}{4} →x=30\).

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.

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

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