Fraction Calculator
Add, subtract, multiply, divide or compare fractions, mixed numbers, whole numbers and decimals exactly, with the common denominator and cancelling shown.
The result in lowest terms, as a mixed number and as a decimal, the operands in lowest terms, and each step — common denominator, invert-and-multiply, cross-multiplication, cancelling.
Example: 1/2 + 1/3: common denominator 6 gives 3/6 + 2/6 = 5/6; 1 3/4 × 2/3 = 14/12 = 7/6 = 1 1/6; 5/8 vs 7/12 cross-multiplies to 60 vs 56, so 5/8 is larger.
Common denominators,
shown not hidden.
How each operation is carried out exactly, how mixed numbers and decimals are read, and what the steps show.
The operations
Addition and subtraction go over the least common denominator; multiplication multiplies across; division inverts the second fraction and multiplies; comparison cross-multiplies. The result is reduced by the greatest common divisor and given as an improper fraction, a mixed number and a decimal. Every intermediate value is an exact integer.
Reading the operands
n/d, whole numbers, mixed numbers such as 1 3/4, negative values, and decimals — a decimal is read as the fraction it writes (0.75 = 3/4, 2.5e1 = 25), so a rounded decimal input carries its rounding into the answer. The operands are shown in lowest terms first when they were not.
Limits
Two operands per calculation; for a chain, feed the result back. The decimal column is rounded to twelve places and marked with an ellipsis when the exact value does not terminate. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Exact integer arithmetic on numerators and denominators: a/b ± c/d over lcm(b, d), a/b × c/d = ac/bd, a/b ÷ c/d = ad/bc, reduced by the GCD; comparison by cross-multiplication
Last reviewed 21 September 2026. How results are checked: How we verify.