Fraction Calculator
Add, subtract, multiply or divide two fractions and reduce the result.
Result
Simplified result: 19/12
The fraction is reduced by the greatest common factor of its terms.
- Decimal value
- 1.583333
- Reduced numerator
- 19
- Reduced denominator
- 12
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Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Fraction Calculator
- Enter the numerator and denominator of each positive fraction.
- Choose addition, subtraction, multiplication or division.
- Read the reduced exact fraction and its decimal equivalent.
Exact fraction arithmetic
Addition and subtraction use a shared denominator. Multiplication combines numerators and denominators directly, while division multiplies by the reciprocal:
a/b + c/d = (ad + bc) / bda/b × c/d = ac / bda/b ÷ c/d = ad / bcThe resulting terms are divided by their greatest common factor. The decimal is displayed for convenience; the reduced fraction is the exact result.
With your numbers
- The selected add operation produces 19/12.
- Decimal value = 1.58333333.
Quick reference
The fraction is reduced by the greatest common factor of its terms.
| Example | Simplified result |
|---|---|
| 3/4 plus 5/6 | 19/12 |
| 7/8 minus 1/3 | 13/24 |
| 2/5 times 3/7 | 6/35 |
| 4/9 divided by 2/3 | 2/3 |
| 1/2 plus 1/2 | 1 |
| 5/6 minus 5/6 | 0 |
Common questions about the Fraction Calculator
- How are fractions reduced?
- The numerator and denominator are divided by their greatest common factor until no common factor remains.
- Why do addition and subtraction use a common denominator?
- The parts must have the same size before their numerators can be combined. Multiplication and division do not require that step.
- How is division performed?
- The first fraction is multiplied by the reciprocal of the second.
- Why are the inputs limited to whole numbers?
- A numerator and denominator define an exact rational number. Decimal inputs would first need a separate conversion rule.