Ratios and proportions, step by step

A ratio compares two quantities, and proportional reasoning is the grade-six skill that grows out of it.

The question

2 : 6 = 1 : 3

2 : 6
2 : 6both ÷ 2
2 : 6=1 : 3
  1. A ratio simplifies the same way a fraction does — divide BOTH sides by the same number, and it stays the same ratio.
  2. The biggest number that goes into both 2 and 6 is 2.
  3. 2 ÷ 2 = 1 and 6 ÷ 2 = 3, so 2 : 6 is 1 : 3. Same ratio, smaller numbers — nothing has changed except how it is written.

How it works.

  1. 01

    A ratio simplifies the same way a fraction does — divide BOTH sides by the same number, and it stays the same ratio.

  2. 02

    The biggest number that goes into both 2 and 6 is 2.

  3. 03

    2 ÷ 2 = 1 and 6 ÷ 2 = 3, so 2 : 6 is 1 : 3. Same ratio, smaller numbers — nothing has changed except how it is written.