Fraction Calculator

Add, subtract, multiply, or divide two fractions and get the simplified result.

How this works

Enter two fractions (numerator and denominator each), pick the operation, and the calculator returns the answer simplified to lowest terms — plus its decimal equivalent. Negatives are supported (use a negative numerator). Result auto-simplifies via the GCD of numerator and denominator, so e.g. 4/8 + 1/8 returns 5/8 directly rather than the unsimplified intermediate.

The formula

a/b + c/d = (a·d + c·b) / (b·d) a/b − c/d = (a·d − c·b) / (b·d) a/b × c/d = (a·c) / (b·d) a/b ÷ c/d = (a·d) / (b·c) Then simplify: divide num and den by gcd(num, den).

For + and − the common denominator is the simple product b·d (not the LCM, which would also be valid but adds complexity); the simplification step at the end produces the same final answer either way. Sign handling: any negative is carried on the numerator; the denominator is normalised to positive after simplification so the displayed form looks canonical.

Example calculation

  • 1/2 + 1/3 with common denominator 6: 3/6 + 2/6 = 5/6
  • 5/6 already in lowest terms (gcd(5, 6) = 1).
  • Decimal: 5 ÷ 6 ≈ 0.8333...
  • Sanity check: 0.5 + 0.333... = 0.833... ✓

Frequently asked questions

Why does the calculator show a fraction even when I add to a whole number?

It still shows the fraction form (e.g. "5/1" or "3/1") because the data is fractional internally — but for whole-number results the denominator collapses to 1, making the result trivially recognisable. The decimal line shows the value as a familiar number for confirmation.

How do I enter a mixed number like "2 1/3"?

Convert it to an improper fraction first: 2 + 1/3 = (2 × 3 + 1) / 3 = 7/3. Then enter 7 as the numerator and 3 as the denominator. The general rule is: whole part × denominator + fractional numerator, all over the same denominator.

Why does dividing by zero show an error?

Division by zero is mathematically undefined — there is no number that, multiplied by 0, gives anything other than 0. The calculator detects two ways this can happen: a 0 in any denominator (the input fraction is itself undefined), or a 0 numerator in fraction B during division (you'd be dividing by zero indirectly). Both surface as the same explicit error rather than NaN/Infinity.

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