Fraction calculator
Add, subtract, multiply, divide. Simplified, decimal, and mixed-form output.
How we simplify
We keep the answer as a single integer over an integer, then divide both by their greatest common divisor. So 4/8 → 1/2, 6/4 → 3/2, 15/45 → 1/3. The sign always moves to the numerator so denominators stay positive — this is the convention most textbooks follow.
Common-denominator addition
For + and −, we use the cross-multiplication method: a/b + c/d = (a·d + b·c) / (b·d). This always works but doesn't produce the lowest common denominator — that's why we simplify at the end. The result is mathematically identical either way.
Mixed numbers
When the numerator's magnitude exceeds the denominator (an improper fraction), we also show the mixed form — a whole number plus a proper fraction. So 7/2 shows as 3 1/2. Mixed form is friendlier for cooking and measurements; improper form is friendlier for further math.
Looking for percentages or ratios?
For percentage math (% of, % change, etc.), use the percentage calculator. For solving proportions like A:B = C:D, use the ratio calculator.