How this calculator works
Convert each mixed number to an improper fraction. Multiply the denominators to obtain a common denominator, scale each numerator, then add or subtract the scaled numerators. The greatest common divisor reduces the answer exactly. Whole-number components must be safe integers.
Formula
a/b ± c/d = (ad ± bc)/(bd). A mixed number w n/d has magnitude |w| + n/d and the sign of w.
Worked example
1/2 + 1/3 = 3/6 + 2/6 = 5/6. For mixed numbers, 2 1/4 - 1 1/2 = 9/4 - 6/4 = 3/4.
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Frequently asked questions
Can denominators be negative?
Yes in simple-fraction mode. Mixed-number denominators must be positive, and results always use a positive denominator.
Why are there two answer forms?
A reduced fraction is useful for further arithmetic. A mixed number makes the whole and remaining fractional portions easier to read.
Are answers rounded?
No. The integer numerator and denominator calculations are exact. Each input component is limited to the safe integer range.