Adding Fractions Calculator
Add two fractions or mixed numbers exactly. Enter simple fractions with a slash (1/2 + 1/3) or mixed numbers with a space (2 1/2 + 1 1/3), press = and read the result as a reduced improper fraction, a mixed number, and a decimal. Every calculation runs locally in your browser with exact integer arithmetic.
Enter the first fraction
Type a simple fraction like 3/4, a whole number like 2, or a mixed number like 2 1/2 — the whole part and the fraction are separated by a single space. A leading minus sign makes the whole number negative: -2 1/2 means -(2 + 1/2).
Enter the second fraction
Type the second addend in the same format. Simple, whole, and mixed forms can be freely mixed — for example 1/2 + 2 1/3. Each number is limited to 15 digits per part, and a denominator of 0 is rejected.
Press = and read the sum
The result shows the reduced improper fraction, the mixed number when the value is greater than 1, and the decimal: 2 1/2 + 1 1/3 gives 23/6 = 3 5/6 = 3.833333. Press Clear to start over.
How to add fractions
- The rule for adding fractions
- Multiply across to get a common denominator, then add the numerators: a/b + c/d = (a·d + c·b) / (b·d). For example, 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6. The result is then divided by the greatest common divisor of its numerator and denominator to reduce it to lowest terms.
- Adding mixed numbers
- A mixed number like 2 1/2 first becomes the improper fraction (2×2 + 1)/2 = 5/2; then add as usual. For 2 1/2 + 1 1/3 this gives 5/2 + 4/3 = 23/6, which is written back as the mixed number 3 5/6 ≈ 3.833333.
- How the result is shown
- The sum is always given as a reduced improper fraction (even when it is a whole number — 1/2 + 1/2 shows 1/1 = 1). When the absolute value exceeds 1 and a remainder is left over, the mixed-number form appears too, and the decimal is rounded to 6 decimal places with trailing zeros trimmed. These display choices are this calculator's own convention.
- What about negative sums?
- Signs are carried exactly. -3/4 + 1/4 = -1/2, and -1 1/2 + 1/3 = -7/6 = -1 1/6, with the minus sign placed in front of the whole part. A leading plus sign (+1/2) is accepted and means the same as 1/2.
- What inputs does the calculator reject?
- Empty fields; anything that is not a whole number, a/b, or "W a/b" — including spaces inside a fraction (1 / 3), embedded signs (1/-2), multiple slashes (1/2/3), and decimal points (0.5); a denominator of 0; and any number part longer than 15 digits. All arithmetic is exact with arbitrary-precision integers, so large sums never suffer floating-point rounding.
More fraction tools and other math utilities live in the Math & Statistics category.
Privacy: every calculation runs in your browser tab — no value you type is sent anywhere, and nothing is stored after you close the page.