Equivalent Fractions: Guides and Calculator

Equivalent fractions guides: how to find and check them, with lists, diagrams and practice problems.

What Are Equivalent Fractions?

Equivalent fractions are fractions that name the same amount with different numbers, such as 1/2, 2/4 and 4/8. You find them by multiplying or dividing the numerator and denominator by the same non-zero number. To check two fractions, cross-multiply: a/b = c/d when a × d = b × c. Every guide here lists the equivalent fractions of one fraction, with a diagram, a table, practice problems and sources.

In short: Multiply or divide the top and bottom by the same number to get an equivalent fraction. Never add or subtract.

Your Equivalent Fractions Learning Path

  1. Read the full guide to equivalent fractions: definition, three methods, simplest form and the cross-multiplication check.
  2. Pick a fraction below to see its equivalent fractions with a diagram and practice problems.
  3. Check your answers with the free equivalent fractions calculator, which shows every step.
  4. Move on to fractions as decimals and percents.

Equivalent Fractions of Common Fractions

Select a fraction to see all of its equivalent fractions.

Fraction First equivalent fractions
1/3 2/6, 3/9, 4/12
2/3 4/6, 6/9, 8/12
3/4 6/8, 9/12, 12/16
1/7 2/14, 3/21, 4/28
4/7 8/14, 12/21, 16/28
5/7 10/14, 15/21, 20/28
2/9 4/18, 6/27, 8/36
7/9 14/18, 21/27, 28/36
8/9 16/18, 24/27, 32/36
11/13 22/26, 33/39, 44/52
11/17 22/34, 33/51, 44/68
13/17 26/34, 39/51, 52/68

How to Find and Check Equivalent Fractions

  • Multiply: 2/3 × 2/2 = 4/6.
  • Divide: 12/18 ÷ 6/6 = 2/3.
  • Check: 3/5 and 9/15 are equivalent because 3 × 15 = 5 × 9 = 45.

Sources: Math is Fun, Equivalent Fractions and OpenStax Prealgebra 2e, Section 4.2.