Fraction Calculator

How it works

Each fraction is first turned into an improper fraction: a mixed number w n/d becomes (w × d + n)/d, so 2 1/2 is 5/2. A negative mixed number carries its sign on the whole number, so −1 1/2 means −(1 + 1/2) = −3/2.

To add or subtract, both fractions are put over the common denominator b × d: a/b ± c/d = (a × d ± b × c)/(b × d). To multiply, numerators and denominators multiply straight across. To divide, the second fraction is flipped and the two are multiplied.

The raw result is then reduced by dividing numerator and denominator by their greatest common divisor, and shown three ways: as a fraction in lowest terms, as a mixed number when it is bigger than one, and as a decimal. The working line shows every step so you can follow or check it by hand.

Formula

w n/d = (w × d + n) / d                 (mixed number to improper)
a/b + c/d = (a × d + b × c) / (b × d)
a/b − c/d = (a × d − b × c) / (b × d)
a/b × c/d = (a × c) / (b × d)
a/b ÷ c/d = (a × d) / (b × c)
reduce: divide top and bottom by gcd(numerator, denominator)

Example

1/2 + 1/3 = (1×3 + 2×1)/(2×3) = 5/6, which is 0.833333 as a decimal.

7/12 + 5/18 = (7×18 + 12×5)/(12×18) = 186/216 = 31/36, after dividing top and bottom by 6.

2 1/2 + 1 3/4: 2 1/2 = 5/2 and 1 3/4 = 7/4, so (5×4 + 2×7)/(2×4) = 34/8 = 17/4 = 4 1/4, or 4.25.

3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1 1/8 = 1.125.

Assumptions and limitations

• Whole numbers, numerators and denominators must be integers; denominators must be positive. Enter 1/−2 as −1/2 (numerator −1, denominator 2).
• A negative mixed number is entered with the minus sign on the whole number (−1 1/2), never on the numerator; the numerator of a mixed number must be 0 or more.
• The common denominator used in the working is b × d, not the least common denominator, so the raw fraction may be larger than the one you would write by hand before reducing. The reduced result is the same.
• Arithmetic is exact. The decimal is rounded to six places for display.

Frequently asked questions