Fraction Calculator

Fraction operation formulas

Fractions use different formulas depending on the operation. Addition uses a common denominator: a/b + c/d = (ad + bc)/bd. Subtraction is similar: a/b − c/d = (ad − bc)/bd. Multiplication is direct: a/b × c/d = ac/bd. Division flips the second fraction and multiplies: a/b ÷ c/d = ad/bc. This calculator applies those rules and then reduces the answer so the numerator and denominator are as small as possible.

Simplifying is done with the greatest common divisor. If the raw result is 50/100, both numbers share a greatest common divisor of 50, so the simplified result is 1/2. Negative signs are kept on the numerator, and denominators are normalized to positive values. If the result is larger than one, the page also shows a mixed-number version for easier reading.

Using the decimal output

The decimal output helps compare fractions or transfer the answer to a calculator, spreadsheet or measurement. Some fractions terminate, such as 1/4 = 0.25. Others repeat, such as 1/3, so the widget rounds the displayed decimal to a practical number of digits. The exact simplified fraction remains the primary result when precision matters.

Validation and privacy

A denominator cannot be zero because division by zero is undefined. Dividing by a zero fraction is also blocked for the same reason. The input fields are intended for integer numerators and denominators; mixed numbers should be converted to improper fractions first. All arithmetic runs locally in your browser and does not upload homework, recipes, measurements or other values.

If you are comparing recipe quantities, construction measurements or classwork, keep the simplified fraction as the exact answer and use the decimal only when an approximate value is acceptable.

Worked examples

To add 1/3 + 1/4, use the formula: (1 × 4 + 3 × 1) / (3 × 4) = 7/12, which is already simplified. Subtracting 3/4 − 5/6 gives (18 − 20) / 24 = −2/24, which reduces to −1/12. Multiplying 2/3 × 9/10 gives 18/30 = 3/5. Dividing 3/4 ÷ 3/8 gives (3 × 8) / (4 × 3) = 24/12 = 2.

The most common mistake is adding numerators and denominators directly: 1/2 + 1/3 is 5/6, not 2/5. You do not need to find the least common denominator yourself, because the calculator works with the product of the denominators and then reduces the answer. To enter a mixed number such as 2 1/3, convert it first: 2 × 3 + 1 = 7, so type 7/3. A whole number can be entered as a fraction over 1.