How to simplify fractions

To simplify a fraction, divide the top and bottom by the same number until nothing but 1 divides both. Divide by the greatest common factor and it takes one step: 18/24 ÷ 6/6 = 3/4. This page shows why with fraction bars, has a tool to simplify any fraction, and covers the mistakes children make.

Simplifying fractions: the big idea

Simplifying is finding the equivalent fraction with the smallest numbers. 6/8 and 3/4 are the same amount; 3/4 just uses fewer, bigger pieces. A fraction is in simplest form when the top and bottom have no common factor except 1.

6/83/4
Same amount, bigger pieces.

How to simplify fractions, step by step

  1. Find the greatest common factor (GCF) of the numerator and denominator. For 18/24 it is 6.
  2. Divide both by it: 18 ÷ 6 = 3, 24 ÷ 6 = 4.
  3. Check: 3 and 4 share no factor but 1, so 3/4 is in simplest form.

Can’t find the GCF? Divide by any common factor (2, 3, 5…) and repeat until you can’t go further: 18/24 → 9/12 → 3/4.

Simplify any fraction

Type a fraction to see its GCF, the division and both as bars.

Worked examples

Example 1: 4/10

GCF 2: 2/5.

Example 2: 12/16

GCF 4: 3/4.

Example 3: 15/45

GCF 15: 1/3.

Example 4: 7/9

GCF 1: already in simplest form.

Example 5: 20/8

GCF 4: 5/2, which is 2 1/2 as a mixed number.

Common mistakes

6/8 = 3/8Divided only the top.Fix: divide top and bottom by the same number.
18/24 = 9/12, stoppedDidn’t finish simplifying.Fix: keep going until the only common factor is 1: 3/4.
12/16 = 6/10Subtracted 6 from both.Fix: subtraction changes the value; only divide.
Thinks 3/4 is smaller than 6/8Smaller numbers look like a smaller amount.Fix: compare the bars.

How to teach it at home

Share a chocolate bar

A bar with 12 squares, 8 eaten: 8/12. Group the squares in fours: 2/3 eaten.

Factor detective

Ask: what number goes into both? Use the divisibility rules for 2, 3 and 5.

Measuring cups

4/8 of a cup is 1/2 cup. Pour to check.

By grade

Worksheets and practice

Simplifying fractions worksheet, page 1

Simplifying fractions worksheet: printable PDF with an answer key. · Make a fresh test

Equivalent fractions · Factors and multiples · All fractions

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Questions parents ask

How do you simplify a fraction?

Divide the numerator and denominator by their greatest common factor. 18/24: the GCF is 6, so 3/4.

What is simplest form?

A fraction whose numerator and denominator have no common factor other than 1, like 3/4 or 2/5.

Does simplifying change the value of a fraction?

No. 6/8 and 3/4 are the same amount; simplifying just uses smaller numbers.

How do you simplify an improper fraction?

Simplify the same way, then change it to a mixed number if needed. 20/8 = 5/2 = 2 1/2.

What if I can’t find the GCF?

Divide by any common factor, like 2, and repeat until the fraction can’t be divided further.