Fraction Calculator
Add, subtract and reduce fractions automatically.
Reduced fraction
5/6
What is the Fraction Calculator?
This tool computes the sum, difference, product or quotient of two fractions, then automatically reduces the result using the greatest common divisor (GCD) to its lowest terms. If the result is an improper fraction, a mixed-number and decimal form are also shown.
How to use it
Enter the numerator and denominator for both fractions, choose an operator (+, −, ×, ÷), then press Calculate. A denominator of 0 is not allowed, and dividing by a fraction with a zero numerator is treated as an error.
How reduction works
Addition/subtraction use a common denominator (a/b ± c/d = (ad ± bc) / bd), multiplication multiplies numerators and denominators directly, and division multiplies by the reciprocal. The resulting fraction is reduced by dividing both terms by their GCD, found via the Euclidean algorithm.
Why some fractions terminate as decimals and others repeat
Whether a reduced fraction (one already in lowest terms) becomes a terminating decimal depends entirely on the prime factors of its denominator. If the denominator is built only from powers of 2 and 5 (e.g. 2, 4, 5, 8, 10, 20…), the decimal always terminates. If any other prime factor (3, 7, 11…) is present, the decimal repeats forever.
For example, 1/8 has denominator 8=2³ — only powers of 2 and 5 — so it ends exactly at 0.125. But 1/3 has only the prime 3 as its denominator, so it repeats endlessly as 0.3333…, and 1/6 has denominator 6=2×3, where the 3 forces it to repeat as 0.1666… even though the 2 alone would be fine. Try entering a fraction with 3 or 7 in the denominator into this calculator's decimal output to see the repeating pattern directly.
The addition mistake that happens when you skip finding a common denominator
The most common mistake when adding fractions with different denominators is to simply add the numerators together and the denominators together. Adding 1/2 + 1/3 this incorrect way gives (1+1)/(2+3) = 2/5 = 0.4.
But fraction addition always requires finding a common denominator first. The correct calculation is (1×3 + 1×2) / (2×3) = 5/6 ≈ 0.8333 — more than double the incorrect result of 0.4. Entering 1/2 and 1/3 into this calculator's addition (+) mode confirms the correct answer is exactly 5/6, making it clear how far off skipping the common-denominator step can be.