Proportional Ratios

Proportional Ratios

Learn what proportion is and how to write and create a proportion in few simple steps.

Step by step guide to create proportional ratios

  • A proportion means that two ratios are equal. It can be written in two ways:
    \(\frac{a}{b}=\frac{c}{d} , a∶b=c∶d\)
  • The proportion \(\frac{a}{b}=\frac{c}{d}\) can be written as: \(a \ × \ d=c \ × \ b\)

Example 1:

Solve this proportion for \(x\). \(\frac{2}{4} = \frac{3}{x}=\)

Solution:

Use cross multiplication: \(\frac{2}{4}=\frac{3}{x} ⇒2 \ × \ x=3 \ × \ 4⇒2 \ x=12\)
Divide to find \(x\): \(x=\frac{12}{2} ⇒x=6\)

Example 2:

If a box contains red and blue balls in ratio of \(2:5\) red to blue, how many red balls are there if \(60\) blue balls are in the box?

Solution:

Write a proportion and solve. \(\frac{2}{5}=\frac{x}{60}\)
Use cross multiplication: \(2 \ × \ 60=5 \ × \ x⇒120=5 \ x\)
Divide to find \(x\): \( x=\frac{120}{5}⇒x=24\)

Example 3:

Solve this proportion for \(x\). \(\frac{4}{8}=\frac{5}{x}\)

Solution:

Use cross multiplication: \(\frac{4}{8}=\frac{5}{x } ⇒4×x=5×8⇒4x=40\)
Divide to find \(x: x=\frac{40}{4} ⇒x=10\)

Example 4:

The ratio of boys to girls in a school is \(2: 3\). How many boys are in the school if there are \(90\) girls in the school?

Solution:

Write a proportion and solve. \(\frac{2}{3}=\frac{x}{90}\)
Use cross multiplication: \(2×90=3×x⇒180=3x\)
Divide to find \(x:x=\frac{180}{3}⇒x=60\)

There are 60 boys in the school.

Exercises

Solve each proportion.

  1. \(\color{blue}{\frac{2}{4}=\frac{8}{x},x=}\)
  2. \(\color{blue}{\frac{1}{2}=\frac{6}{x},x=}\)
  3. \(\color{blue}{\frac{2}{3}=\frac{12}{x},x=}\)
  4. \(\color{blue}{\frac{1}{4}=\frac{x}{20},x=}\)
  5. \(\color{blue}{\frac{3}{4}=\frac{x}{8},x=}\)
  6. \(\color{blue}{\frac{1}{4}=\frac{18}{x},x=}\)

Download Proportional Ratios Worksheet

Answers

  1. \(\color{blue}{16}\)
  2. \(\color{blue}{12}\)
  3. \(\color{blue}{18}\)
  4. \(\color{blue}{5}\)
  5. \(\color{blue}{6}\)
  6. \(\color{blue}{72}\)

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