Simplify Fractions
The calculator reduces a fraction to lowest terms: it finds the GCD with the Euclidean algorithm, divides the numerator and denominator by it and writes a mixed number.
The simplify fractions calculator reduces a fraction to lowest terms: it finds the GCD of the numerator and denominator with the Euclidean algorithm, divides both by it and, if needed, writes the result as a mixed number.
What it means to simplify a fraction
To simplify (reduce) a fraction means to divide the numerator and the denominator by the same non-zero number. The value of the fraction does not change, only the way it is written:
6/8 = 6 ÷ 2/8 ÷ 2 = 3/4
A fraction that cannot be simplified any further is in lowest terms: its numerator and denominator have no common divisors other than 1.
How to simplify in one step
- Find the greatest common divisor (GCD) of the numerator and the denominator.
- Divide the numerator and the denominator by the GCD.
Example. Simplify 84/126.
Euclidean algorithm: 126 = 84 · 1 + 42; 84 = 42 · 2 + 0, so GCD(84, 126) = 42.
84/126 = 84 ÷ 42/126 ÷ 42 = 2/3
How to simplify step by step
If you do not want to find the GCD, you can simplify gradually using divisibility rules:
- both numbers are even — divide by 2;
- the digit sum of each number is divisible by 3 — divide by 3;
- both numbers end in 0 or 5 — divide by 5;
- both end in zeros — cross out the same number of zeros.
Example. 84/126 = 42/63 (by 2) = 14/21 (by 3) = 2/3 (by 7)
Common mistakes
- You can cancel factors, not terms: in 2 + 3/2 the twos cannot be cancelled.
- Divide both the numerator and the denominator, and by the same number.