Fraction Calculator
Add, subtract, multiply, or divide two fractions and get the simplified result.
How fraction operations work
Adding or subtracting fractions requires a common denominator: cross-multiply so both fractions share the same denominator, then add or subtract the numerators.
Multiplying fractions is more direct — multiply the numerators together and the denominators together. Dividing is the same as multiplying by the reciprocal (flip the second fraction).
Worked example
1/2 + 1/3: cross-multiplying gives a common denominator of 6, so this becomes 3/6 + 2/6 = 5/6, which is already in its simplest form.
What the tool does with your numbers
- Enter whole numbers in the numerator and denominator boxes. Mixed numbers must be converted first, so 2 1/3 is typed as 7 over 3. A decimal in any box is refused with a message asking for whole numbers.
- Addition and subtraction cross-multiply, so the working denominator is d₁ × d₂. The result is then reduced with the greatest common factor.
- The answer is always shown as an improper fraction such as 8 / 3, followed by a decimal rounded to four places with trailing zeros removed.
- A negative sign is moved onto the numerator. A result of zero is shown as 0 / 1.
- A zero denominator, an empty box or a non-number gives an error. In division, a second fraction whose numerator is zero is also refused.
More worked examples
3/4 − 5/6: the cross-multiplied result is 18 − 20 = −2 over 24, which reduces to −1 / 12, a decimal of −0.0833.
2/3 ÷ 4/9 flips the second fraction: 18 over 12 reduces to 3 / 2, or 1.5. And 3/8 × 4/5 is 12 over 40, which reduces to 3 / 10, or 0.3.
1/3 + 1/6 cross-multiplies to 9 over 18 rather than using the smaller denominator 6, but reduction brings it back to 1 / 2. The answer is correct even when the intermediate denominator is larger than needed.
Rounding and limits
The decimal line is shortened to four places, so 1/7000 reads 0.0001 even though the fraction stays exact as 1 / 7000. Only two fractions can be combined at a time; for a longer sum, feed each result back in as the next first fraction.
Frequently asked questions
Why does the calculator simplify the answer?
Fractions are conventionally given in their lowest terms — the largest common factor of the numerator and denominator is divided out so the fraction can't be reduced any further.
Can I use negative numbers?
Yes. A negative numerator or denominator is handled correctly, and the sign is normalised onto the numerator in the simplified result.
How do I enter a mixed number like 2 1/3?
Convert it first: multiply the whole part by the denominator and add the numerator, so 2 × 3 + 1 = 7. Enter 7 and 3. The answer comes back as an improper fraction.
Why does the answer for 1/3 + 1/6 not show 3/6?
The tool always reduces to lowest terms. The sum works out to 9/18 and then to 1/2.
Can I add three fractions?
Do it in two steps. Add the first two, then use the simplified result as the first fraction and enter the third as the second.