Pythagorist
Fractions

Simplifying Fractions Calculator

Reduce any fraction to its simplest form. The calculator finds the greatest common divisor (GCD) using the Euclidean algorithm and shows every step.

Enter a fraction

Simplest form

3/4

= 0.75

Step-by-step working

  1. Find the GCD

    GCD(6, 8)=2\text{GCD}(6,\, 8) = 2

    The greatest common divisor of 6 and 8 is 2. Using the Euclidean algorithm.

    Result:2

  2. Divide by the GCD

    68=6÷28÷2=34\frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}

    Divide both numerator and denominator by 2.

    Result:3/4

The formula

ab=a÷gcd⁡(a,b)b÷gcd⁡(a,b)\frac{a}{b} = \frac{a \div \gcd(a,b)}{b \div \gcd(a,b)}
aaNumerator
bbDenominator
gcd⁡(a,b)\gcd(a,b)Greatest common divisor of a and b

Example substitution

1218=12÷618÷6=23\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}

GCD(12, 18) = 6. Divide both by 6.

Worked examples

Simplify 6/8

  1. 1
    GCD(6,8): = 2
  2. 2
    Divide numerator: 6 ÷ 2 = 3
  3. 3
    Divide denominator: 8 ÷ 2 = 4
Answer: 3/4

Simplify 15/25

  1. 1
    GCD(15,25): = 5
  2. 2
    Divide numerator: 15 ÷ 5 = 3
  3. 3
    Divide denominator: 25 ÷ 5 = 5
Answer: 3/5

Simplify 24/36

  1. 1
    GCD(24,36): = 12
  2. 2
    Divide numerator: 24 ÷ 12 = 2
  3. 3
    Divide denominator: 36 ÷ 12 = 3
Answer: 2/3

Frequently asked questions

How do you simplify a fraction?+

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. Repeat until no common factor remains.

What does simplest form mean?+

A fraction is in simplest form (or lowest terms) when the numerator and denominator share no common factor other than 1.

How do you find the GCD?+

The Euclidean algorithm is the most efficient method: divide the larger number by the smaller, take the remainder, and repeat until the remainder is 0. The last non-zero remainder is the GCD.

Is 1/2 the same as 2/4?+

Yes — they are equivalent fractions. 2/4 simplifies to 1/2 because GCD(2,4) = 2. Simplified fractions are always the preferred form in exam answers.

Related calculators

Fraction Calculator

Add, subtract, multiply and divide fractions instantly

Adding Fractions Calculator

Add any two fractions with step-by-step working

Comparing Fractions Calculator

Find which fraction is larger with full working shown