Fraction Calculator (Add, Subtract, Multiply, Divide)

This fraction calculator adds, subtracts, multiplies or divides two fractions and simplifies the answer. A fraction calculator saves the fiddly work of finding common denominators and reducing answers. Enter two fractions, pick an operation, and this tool returns the result simplified, as a mixed number and as a decimal — with the intermediate steps shown so you can check the method.

How each operation works

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)

Addition and subtraction combine over the common denominator b × d; division flips the second fraction and multiplies.

Why the answer is always reduced

After combining, the numerator and denominator are divided by their greatest common divisor (Euclid's algorithm). That is why 2/4 returns as 1/2 and 6/8 as 3/4, with no manual simplifying.

Worked example

Adding 1/4 and 1/6:

common denominator = b × d = 4 × 6 = 24
numerators         = 1×6 + 1×4 = 10
combined           = 10/24
GCD(10, 24)        = 2
reduced            = 5/12 ≈ 0.4167

Worth noticing: the tool combines over b × d = 24 rather than the least common multiple 12, so the intermediate fraction is larger than the one you would write by hand. It makes no difference to the answer, because reducing by the GCD at the end always lands on the same lowest terms — 10/24 and 5/12 are the same number — and using the product avoids computing an LCM before every operation.

Division, and the inputs with no answer

Dividing flips the second fraction: a/b ÷ c/d becomes a/b × d/c = (a·d)/(b·c). So 3/4 ÷ 2/5 = (3×5)/(4×2) = 15/8, which is 1 7/8 as a mixed number and 1.875 as a decimal.

Three inputs return no result at all, and the tool shows nothing rather than inventing a number. A zero denominator in either fraction is undefined, because division by zero has no value. A zero numerator in the second fraction makes the divisor itself zero, which is the same problem wearing a disguise. Everything else resolves, including negatives — the sign is carried on the numerator so the denominator stays positive, which is why −3/4, 3/−4 and −(3/4) all come back as −3/4.

Mixed numbers and real measurements

An improper fraction has a numerator larger than its denominator; a mixed number splits the whole part back out. 15/8 is 1 7/8, and both forms are shown, because different contexts want different ones — arithmetic is easier in improper fractions while measuring is easier in mixed numbers.

That is why this tool turns up well outside homework. Imperial measurements are fractions: a spanner is 3/8 in, a board is cut at 5 1/2 in, a recipe wants 2/3 of a cup. Adding 1 3/4 in to 2 5/8 in by hand means finding a common denominator and carrying the whole numbers, and getting it wrong costs a piece of timber. Decimal to Fraction Converter handles the opposite direction, since digital calipers and metric tape measures read in decimals, and Ratio Calculator is the right tool when you are scaling a recipe rather than combining quantities.

Private and instant

Everything runs in your browser using exact integer arithmetic. Nothing you type is uploaded, and there is no sign-up.