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Ratio and Proportion Explained: Simplify, Scale, Share

Published October 3, 2026Written and reviewed by Mateuss M.

Ratio and Proportion Explained: Simplify, Scale, Share — illustration
In short: A ratio compares quantities: 12 : 18 simplifies to 2 : 3. A proportion says two ratios are equal, so 2 : 3 = 10 : x gives x = 15.

Simplifying a ratio

Divide every term by their greatest common factor, exactly like simplifying a fraction.

12 : 18
Answer2 : 3
  • Decimal ratio 0.666667
Step-by-step working 3 steps
  1. 1
    Write the ratio
    12 : 18
  2. 2
    Divide both by the GCF
    GCF(12, 18) = 6
12 ÷ 6 : 18 ÷ 6 = 2 : 3
  3. 3
    Other forms
    As a fraction: 2/3
As decimals: 1 : 1.5   or   0.666667 : 1

Solving a proportion

Cross-multiply: in a/b = c/x, a × x = b × c. A recipe uses 2 cups of rice for 3 people. For 10 people, write people : cups as 3 : 2 = 10 : x.

3 : 2 = 10 : x (people : cups)
Answerx = 6.666667
  • 3 : 2 = 10 : 6.666667
Step-by-step working 4 steps
  1. 1
    Set up the proportion
    3 / 2 = 10 / x
  2. 2
    Cross-multiply
    3 × x = 2 × 10 = 20
  3. 3
    Divide
    x = 20 ÷ 3 = 6.666667
  4. 4
    Check
    3 ÷ 2 = 1.5   and   10 ÷ 6.666667 = 1.5

Sharing in a ratio

Split 100 in the ratio 2 : 3. There are 2 + 3 = 5 parts, so one part is 100 ÷ 5 = 20; the shares are 40 and 60.

Ratio vs fraction vs percent

2 : 3 means 2 of 5 parts = 2/5 = 40% and 3/5 = 60%. Use the ratio calculator and the simplify fractions calculator.

Frequently asked questions

What is the difference between a ratio and a proportion?

A ratio compares two quantities; a proportion states that two ratios are equal.

How do I check a proportion?

Cross-multiply both sides; the products should be equal.

Written and reviewed by Mateuss M.

Mateuss M. writes and reviews mathematical content for CalcSolver, focusing on online calculators, formulas, equations, and practical math tools. He reviews calculator functionality, calculation methods, formulas, examples, and explanations to help ensure that each tool is clear, useful, and easy to understand.

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