Fractions Calculator
Add, subtract, multiply, and divide fractions and mixed numbers with exact arithmetic. Fill the numerator and denominator boxes (switch to Mixed Fractions for whole parts), pick + − × ÷, and read the reduced fraction, the mixed number, the decimal, and the calculation steps. A second box evaluates full fraction expressions like 1/2 + 1 1/3 × 2. Everything runs locally in your browser.
Enter the two numbers
Each number is a whole number, a fraction a/b, or a mixed number W a/b. In Simple Fractions mode fill numerator and denominator only; switch to Mixed Fractions to reveal the whole-part boxes. A minus sign on the whole part negates the whole number: -2 1/2 means -(2 + 1/2). A bare negative fraction like -1/2 or 1/-2 also works.
Pick the operator
Choose + (add), − (subtract), × (multiply), or ÷ (divide) from the dropdown, then press Calculate — or just press Enter. Press Reset to clear the form, results, and steps. Dividing by zero and a denominator of 0 are rejected with a clear message.
Read the result and steps
The answer is reduced to lowest terms: 1/2 + 1/3 gives 5/6 = 0.833333, and 1/2 ÷ 1/3 gives 3/2 = 1 1/2 = 1.5. Whenever the reduced absolute value is greater than 1, a mixed form appears too (7/1 even shows 7). Press "View Calculation steps" for the lcm-based working, including the decimal to 6 places.
How fraction arithmetic works
- Adding and subtracting
- Rewrite both fractions over the least common multiple of the denominators, then add or subtract the numerators: 1/2 + 1/3 = 3/6 + 2/6 = 5/6 and 1/2 - 1/3 = 3/6 - 2/6 = 1/6. The steps panel prints exactly this working, headed by the lcm line.
- Multiplying and dividing
- Multiply straight across: 1/2 × 1/3 = (1×1)/(2×3) = 1/6. To divide, multiply by the reciprocal: 1/2 ÷ 1/3 = (1×3)/(2×1) = 3/2, written as the mixed number 1 1/2. Zero denominators and division by zero are refused rather than printed as garbage.
- Reducing, mixed numbers, and decimals
- Every result is divided by the greatest common divisor of its parts, so 4/6 + 1/3 reduces 6/6 to 1/1. The mixed form appears only when the reduced absolute value exceeds 1 — 1/1 stays hidden while 7/1 shows 7 — and negative mixed numbers keep the minus on the whole part: -2 1/2 - 1/3 = -17/6 = -2 5/6. The decimal is rounded half-up to 6 places with trailing zeros trimmed (0.5, not 0.500000); these display choices are this calculator's own convention.
- The fraction expression box
- Below the form you can type a whole expression — whole numbers, decimals (0.25), fractions (1/4), mixed numbers (1 1/2), + - × ÷, parentheses, and a leading minus — with ordinary precedence: (1/2 + 1/3) × 6 - 1 = 4 and 1/2 + 1/3 × 1/6 = 5/9. Decimals and mixed numbers become exact fractions first, so results never drift. Each success appends "expression = fraction = decimal" to the results list; typing * shows ×. This box implements a documented fraction grammar of its own — it is not a general math engine (sin(1) and 2(3) are rejected).
- What inputs does the calculator reject?
- Empty or half-filled numbers (whole + numerator without denominator, numerator without denominator), any non-integer text in the boxes (2.5, abc), signs inside a mixed number's fraction part (2 -1/2), a denominator of 0, division by zero, and any number part longer than 15 digits. All arithmetic uses arbitrary-precision integers, so even 999999999999999/2 × 1 stays exact: 499999999999999 1/2.
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.