How to Create a Proportion? (+FREE Worksheet!)
Proportion simply means that two ratios are equal. Creating a proportion means creating two equal ratios or fractions.
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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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