Fraction Addition Calculator
Add two integer fractions, simplify the resulting numerator and denominator, and display the unsimplified intermediate fraction.
Add and simplify two fractions
How this tool works
Adding fractions requires a common denominator before their numerators can be combined. This calculator uses cross-products, then applies the greatest common divisor so the final fraction is expressed in lowest integer terms.
For a/b plus c/d, the unsimplified result is (a×d + c×b)/(b×d). Dividing both parts by their greatest common divisor produces the reduced fraction.
How to use it
- Enter integer numerator and non-zero denominator values for the first fraction.
- Enter the second fraction in the same way.
- Read the simplified result and inspect the unsimplified intermediate value.
Worked examples
Different denominators
- Input
- 1/3 + 1/6
- Output
- 1/2
Cross-multiplication gives 6/18 plus 3/18, or 9/18. Dividing numerator and denominator by their common divisor nine gives one half.
Improper result
- Input
- 3/4 + 5/6
- Output
- 19/12
The common cross-product numerator is 18 plus 20, while the denominator is 24. Reducing 38/24 by two produces 19/12.
Limitations
- The tool currently adds two fractions and does not provide subtraction or mixed-number input.
- Very large integers may exceed JavaScript safe-integer precision.