➗ Fraction Calculator
1 1/2 + 3/4 = 9/4 = 2 1/4, exactly, with the steps shown. Fractions, mixed numbers and decimals in; simplified fraction, mixed number and decimal out.
Accepts fractions (3/4), mixed numbers (1 2/3), integers and decimals (2.5).
9/4
exact fraction
2 1/4
mixed number
2.25
decimal (exact)
Working
- Write both fractions over the common denominator 4: 3/2 = 6/4 and 3/4 = 3/4
- Add the numerators: 6 + 3 = 9, giving 9/4
- Simplify to lowest terms: 9/4
Computed with exact integer arithmetic, no floating-point rounding, ever. Runs locally.
How the fraction calculator works
Every input, a fraction like 3/4, a mixed number like 1 2/3, an integer or a decimal, is converted to an exact rational number (a pair of arbitrary-precision integers), and the arithmetic happens on those. Addition and subtraction go through the least common denominator, multiplication multiplies straight across, division multiplies by the reciprocal, and each route shows its working as numbered steps, the way it's taught. The result appears three ways at once: simplified fraction, mixed number, and decimal (marked exact when it terminates, rounded when it doesn't).
Why exact matters: a floating-point calculator answering 1/3 + 1/3 + 1/3 gets 0.9999999999999999, close, but wrong, and visibly wrong when the numbers feed a recipe scale-up or a homework answer. Rational arithmetic has no such drift: thirds stay thirds. The steps display doubles as a checking aid for schoolwork, the answer alone teaches nothing; the working is the point.
Frequently asked questions
What input formats are accepted?
Proper and improper fractions (3/4, 7/2), mixed numbers with a space (1 2/3), negative values (-5/6), whole numbers, and decimals (2.5 becomes 5/2 exactly). Both operands accept any of these, mixed freely.
How do you add fractions with different denominators?
Rewrite both over the least common denominator, then add numerators. 1/2 + 1/3 → 3/6 + 2/6 = 5/6. The tool shows exactly this working for your numbers.
Why does my calculator show 0.9999999999 for 1/3 + 2/3?
Because it computes in binary floating point, which cannot represent 1/3 exactly, so tiny errors accumulate. This tool keeps numbers as exact fractions, 1/3 + 2/3 is exactly 1.
Does it simplify to lowest terms?
Always, results are reduced by the greatest common divisor and shown as a fraction, a mixed number (when the value exceeds 1), and a decimal marked exact or rounded.
Is my input sent anywhere?
No, all arithmetic runs in your browser and the page works offline.