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Math · Fractions

Fraction Calculator

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Fraction Calculator

Enter both fractions and an operation, then calculate.

Mixed Numbers

Enter two mixed numbers and an operation, then calculate.

Simplify a Fraction

Enter a fraction to reduce it to lowest terms.

Decimal to Fraction

Enter a decimal number to convert it to a fraction.

Fraction to Decimal

Enter a fraction to convert it to a decimal.

How these calculations work

Add, subtract, multiply, or divide fractions — plus mixed numbers, simplifying, and decimal conversion. For two fractions a/b and c/d: addition is (a×d + c×b) / (b×d); subtraction is (a×d − c×b) / (b×d); multiplication is (a×c) / (b×d); division is (a×d) / (b×c). Every result is then reduced to lowest terms by dividing both the numerator and denominator by their greatest common divisor — the same steps shown above for your own numbers once you calculate.

Examples

1/2 + 1/3 = 5/6. 3/4 − 1/2 = 1/4. 2/3 × 9/4 = 3/2, or 1 1/2. 5/6 ÷ 10/9 = 3/4.

About these formulas

These are standard fraction arithmetic rules from elementary mathematics — no external source citation is needed for them.

Related tools

More calculators are on the way — browse everything planned on the Home page.

Frequently asked questions

Can numerators and denominators be negative?

Yes — a negative numerator or denominator is accepted and normalized so the sign always ends up on the numerator of the result. The only values that are never allowed are a zero denominator, or a non-whole (decimal) numerator or denominator.

Why does the calculator say my input is invalid?

Either a field is empty or contains something other than a whole number, a denominator is zero (which makes a fraction undefined), or you chose division with a second fraction whose numerator is zero (dividing by zero).