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a/b + c/d, exactly

Fraction calculator

Four operations on fractions with an exact result: simplified fraction, mixed number and decimal, plus the step that produced it.

Short answer: 2/3 + 1/6 = 1/2, exactly. Subtract 1/4 from 3/4 and you get 1/2; multiply 2/3 by 3/4 and you get 1/2; divide 1/2 by 3/4 and you get 2/3, which is 0.666… and repeats.

Why exactness matters

A calculator that converts to decimals and back will show 1/3 + 1/6 as 0.4999999999999999 or round it to 0.5 without telling you which. Keeping the numerator and denominator as integers until the final reduction avoids the question: the answer is a fraction, and 1/2 is the answer.

Worked example

3/8 + 1/6: the common denominator is 24, giving 9/24 + 4/24 = 13/24, which does not simplify (13 is prime and does not divide 24). As a decimal that is 0.5416…, a repeating decimal, so the fraction is the honest answer.

Fraction questions

Why is the answer exact?

The numerator and denominator are handled as whole numbers and the result is simplified by their greatest common divisor, so 1/3 + 1/6 is exactly 1/2. Converting to decimals first and adding would give 0.4999999 and lose the point.

How do I add fractions with different denominators?

Cross-multiply: a/b + c/d = (a×d + c×b) ÷ (b×d), then simplify. The page does this and reduces the answer, so 2/3 + 1/6 comes back as 5/6 rather than 15/18.

Does it show repeating decimals?

Yes. A result is flagged as repeating when the simplified denominator has a prime factor other than 2 or 5 — 1/3, 2/7, 5/12 — because those have no finite decimal form and printing eight digits would be a rounding, not a value.

Can I enter decimals instead of fractions?

Yes, in the decimal field. 0.375 is converted to 3/8 first, so it can be added to 1/8 as fractions rather than as floats.

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