Enter fractions and mixed numbers
Choose Two fractions for addition, subtraction, multiplication or division. Each number has a separate sign, an optional whole part, a numerator and a denominator. Leave the whole part blank for a simple fraction. Enter a zero numerator when you need a whole number or zero; the denominator is still required.
The sign applies to the entire mixed number: selecting Negative with whole part 1 and fraction 1/2 means −(1 + 1/2) = −3/2. Do not type minus signs into the integer fields. Improper fractions, such as 8/3, are allowed.
Choose Simplify one fraction to reduce a single number. Try example fills values without calculating. Changing the task or operation clears affected values and the result. Reset returns to an empty addition form. Editing removes the previous result and copy action.
Exact formulas and examples
Convert a mixed number to an improper fraction: whole × denominator + numerator, then apply its sign. For signed fractions a/b and c/d:
- Addition:
(ad + bc) / bd. - Subtraction:
(ad − bc) / bd. - Multiplication:
ac / bd. - Division:
ad / bc, where c is nonzero.
After the operation, divide the numerator and denominator by their greatest common divisor. The denominator of the result stays positive. Working shown with the result names the operation and reduced operands.
| Calculation | Exact answer | Mixed number |
|---|---|---|
| 3/4 + 1/6 | (18 + 4)/24 = 11/12 | 11/12 |
| 2/3 ÷ 4/5 | 10/12 = 5/6 | 5/6 |
| 1 1/2 + 3/4 | 6/4 + 3/4 = 9/4 | 2 1/4 |
| −1 1/2 + 3/4 | −6/4 + 3/4 = −3/4 | −3/4 |
| 3/4 − 3/4 | 0 | 0 |
Precision and limits
Every whole part, numerator and denominator accepts a nonnegative integer up to 1,000,000,000,000. A denominator cannot be zero. Dividing by a fraction whose value is zero is also rejected. Decimal inputs and scientific notation are not accepted in these fields.
Exact answers use BigInt rational arithmetic and are never rounded. The mixed number is another exact representation. The decimal is explicitly an approximation, shown to at most 12 decimal places; recurring decimals may be rounded. For example, 11/12 is approximately 0.916666666667. Large exact results may have more digits than any individual input. Steps are kept short rather than expanding arbitrary expressions.
This page handles one operation on two numbers or simplification of one number. It does not parse expressions or solve algebra. Use the Ratio Calculator for proportions, the Average Calculator for a list of numbers, or the Percentage Calculator for a percentage of a number.