How this works
Enter two fractions (numerator and denominator each), pick the operation, and the calculator returns the answer simplified to lowest terms — plus its decimal equivalent. Negatives are supported (use a negative numerator). Result auto-simplifies via the GCD of numerator and denominator, so e.g. 4/8 + 1/8 returns 5/8 directly rather than the unsimplified intermediate.
The formula
For + and − the common denominator is the simple product b·d (not the LCM, which would also be valid but adds complexity); the simplification step at the end produces the same final answer either way. Sign handling: any negative is carried on the numerator; the denominator is normalised to positive after simplification so the displayed form looks canonical.
Example calculation
- 1/2 + 1/3 with common denominator 6: 3/6 + 2/6 = 5/6
- 5/6 already in lowest terms (gcd(5, 6) = 1).
- Decimal: 5 ÷ 6 ≈ 0.8333...
- Sanity check: 0.5 + 0.333... = 0.833... ✓
Frequently asked questions
Why does the calculator show a fraction even when I add to a whole number?
It still shows the fraction form (e.g. "5/1" or "3/1") because the data is fractional internally — but for whole-number results the denominator collapses to 1, making the result trivially recognisable. The decimal line shows the value as a familiar number for confirmation.
How do I enter a mixed number like "2 1/3"?
Convert it to an improper fraction first: 2 + 1/3 = (2 × 3 + 1) / 3 = 7/3. Then enter 7 as the numerator and 3 as the denominator. The general rule is: whole part × denominator + fractional numerator, all over the same denominator.
Why does dividing by zero show an error?
Division by zero is mathematically undefined — there is no number that, multiplied by 0, gives anything other than 0. The calculator detects two ways this can happen: a 0 in any denominator (the input fraction is itself undefined), or a 0 numerator in fraction B during division (you'd be dividing by zero indirectly). Both surface as the same explicit error rather than NaN/Infinity.