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How to use
This fraction calculator performs the four basic operations on two fractions and reduces the exact result to lowest terms. Improper results are also shown as mixed numbers, with a decimal value for quick comparison.
- Enter the numerator and non-zero denominator for each fraction.
- Choose add, subtract, multiply or divide.
- Calculate to see the reduced fraction, mixed-number form and decimal value.
How it is calculated
Example
Example: 3/4 + 5/6 = (18 + 20) / 24 = 38/24, which reduces to 19/12 = 1 7/12 ≈ 1.5833.
Important notes
The tool validates integer inputs, zero denominators and division by a zero-valued fraction. It is useful for checking work, but it does not replace any steps your class or exam may require.
Worked examples and interpreting results
Adding fractions requires a common denominator; multiplying fractions multiplies the numerators and denominators directly. One half plus one third is five sixths, not the result of simply adding both denominators.
| Case | Calculation | Result |
|---|---|---|
| Addition: 5/6 | 1/2 + 1/3 = (3 + 2)/6 | 0.833333 |
| Multiplication: 1/6 | 1/2 × 1/3 = 1/6 | 0.166667 |
| Division: 3/2 | 1/2 ÷ 1/3 = 1/2 × 3/1 | 1.5 |
How to check the result
The decimal in the table is rounded; the fraction 5/6 is exact. A denominator cannot be zero, and the divisor fraction cannot be zero. Reduce the numerator and denominator by a common factor after calculating.
Frequently asked questions
How do I add fractions with different denominators?
Cross-multiply to form a common denominator, combine the adjusted numerators, then reduce the result.
Why is the result simplified?
The numerator and denominator are divided by their greatest common divisor so the fraction is in lowest terms.
Can the answer be negative?
Yes. Negative results keep the sign in the reduced fraction, mixed form and decimal output.