Percentages & Fractions

How to Simplify Fractions Step by Step

By Math Solving Space · · 2 min read

On this page
  1. What "simplest form" means
  2. Step-by-step method
  3. Worked example 1: 18/24
  4. Worked example 2: 84/126 with prime factors
  5. How to check your answer
  6. Common mistakes
  7. Practice questions
  8. Frequently asked questions

To simplify a fraction, divide the top and bottom by their greatest common factor (GCF). For example, the GCF of 18 and 24 is 6, so 1824=34\frac{18}{24} = \frac{3}{4}. The fraction is fully simplified when the top and bottom share no factor other than 1.

What "simplest form" means

Equivalent fractions show the same amount with different numbers: 12\frac{1}{2}, 24\frac{2}{4} and 50100\frac{50}{100} are all one half. The simplest form is the version with the smallest whole numbers.

You can divide the numerator and denominator by the same number without changing the value, because you are really dividing by kk=1\frac{k}{k} = 1.

Step-by-step method

  1. List the factors of the numerator and the denominator.
  2. Find the greatest factor they share (the GCF).
  3. Divide both numbers by the GCF.

Worked example 1: 18/24

Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.

The greatest common factor is 6.

1824=18÷624÷6=34\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}

Worked example 2: 84/126 with prime factors

Listing factors gets slow for bigger numbers, so use prime factors instead.

84=22×3×7126=2×32×784 = 2^2 \times 3 \times 7 \qquad 126 = 2 \times 3^2 \times 7

Take each shared prime the fewest number of times it appears: one 2, one 3 and one 7.

GCF=2×3×7=42\text{GCF} = 2 \times 3 \times 7 = 42
84126=84÷42126÷42=23\frac{84}{126} = \frac{84 \div 42}{126 \div 42} = \frac{2}{3}

How to check your answer

Two quick checks:

  • No shared factors: 2 and 3 have no common factor except 1, so 23\frac{2}{3} is fully simplified.
  • Same value: 84÷12684 \div 126 and 2÷32 \div 3 both equal 0.666…0.666\ldots

Common mistakes

Mistake Fix
Dividing only the top or only the bottom Always divide both by the same number.
Stopping too early, e.g. 1824→912\frac{18}{24} \to \frac{9}{12} Check again: 9 and 12 still share 3, so carry on to 34\frac{3}{4}.
Subtracting instead of dividing 18−624−6\frac{18 - 6}{24 - 6} changes the value. Only divide (or multiply).

Practice questions

  1. Simplify 3648\frac{36}{48}.
  2. Simplify 35105\frac{35}{105}.
  3. Simplify 5672\frac{56}{72}.

Answers: 1) 34\frac{3}{4} 2) 13\frac{1}{3} 3) 79\frac{7}{9}

Frequently asked questions

Can every fraction be simplified?

No. If the numerator and denominator share no factor other than 1, such as 5/8, the fraction is already in its simplest form.

Do I simplify improper fractions the same way?

Yes. For example, 20/8 simplifies to 5/2, which you can also write as the mixed number 2½.

What if the numerator is zero?

Zero divided by any non-zero number is 0, so the fraction simplifies to 0.

Open the calculator →

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