Math

Simplify Fraction Calculator (Reduce to Lowest Terms)

Enter the numerator and denominator to simplify the fraction.

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

Simplified fraction
Simplified fraction
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Greatest common divisor
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Mixed number
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Decimal
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Percentage
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Simplify Fraction Calculator (Reduce to Lowest Terms) by TheCalcTools

How the Simplify Fraction Calculator (Reduce to Lowest Terms) works

Divide the numerator and denominator by their greatest common divisor (GCD). The result is in lowest terms because no number above 1 divides both any more.

The GCD is found with Euclid’s algorithm: repeatedly replace the larger number by its remainder when divided by the smaller.

The formula

a/b = (a ÷ gcd) / (b ÷ gcd)

Worked example

Using the default values shown in the calculator:

Numerator84
Denominator126
  1. gcd(84, 126) = 42, so 84/126 = 2/3.
  2. As a decimal: 0.(6).

Result:

Simplified fraction2/3
Greatest common divisor42
Mixed number—
Decimal0.(6)
Percentage66.67%

Frequently asked questions

How do I simplify 84/126?

The GCD is 42, so 84/126 = 2/3.

Sources and further reading

Fraction CalculatorDo arithmetic with two fractions and see the answer in lowest terms GCD and LCM CalculatorEnter two whole numbers to find their greatest common divisor and least common multiple Decimal to Fraction CalculatorEnter a decimal number and, optionally, the largest denominator you want Fraction to Decimal Calculator (Repeating Decimals)Enter a numerator and denominator to see the exact decimal

More in Math · All calculators

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