Standard arithmetic on two fractions — addition, subtraction, multiplication, or division — with the result automatically simplified.
How it works
Addition and subtraction find a common denominator by cross-multiplying; multiplication multiplies numerators and denominators directly; division multiplies by the reciprocal of the second fraction. Every result is reduced to lowest terms.
What this does not include
This does not include converting a single fraction to a decimal — for that, use this site’s fraction-to-decimal calculator instead. This tool combines two fractions together.
How to use this calculator
- Enter both fractions and choose an operation.
A worked example
Addition: 1/2 + 1/3 → common denominator 6 → 3/6 + 2/6 = 5/6.
Multiplication: 2/3 × 3/4 = 6/12, simplified to 1/2.
Division: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2, simplified to 2.
What the operations do
| Operation | Method |
|---|---|
| Addition / subtraction | Cross-multiply to a common denominator, then combine numerators |
| Multiplication | Multiply numerators together and denominators together |
| Division | Multiply by the second fraction’s reciprocal |
Edge cases worth knowing
A zero denominator anywhere is invalid. Fractions with a zero denominator aren’t defined, so this calculator won’t produce a result for one.
Dividing by zero fails the same way, even as a fraction. A second fraction of 0/n has no reciprocal, since flipping it would put zero in the denominator — division by that fraction is undefined.
Frequently asked questions
Why do addition and subtraction need a common denominator?
Fractions can only be directly added or subtracted when they represent parts of the same-sized whole — cross-multiplying the denominators creates that common basis before combining the numerators.
Why is dividing by a fraction the same as multiplying by its reciprocal?
Dividing by a number undoes multiplying by it — flipping the second fraction and multiplying achieves exactly that inverse operation.
Is the result always shown in simplest form?
Yes — every result is automatically reduced by its greatest common divisor, so 2/4 always displays as 1/2.
