Fraction Calculator

What this fraction calculator does

This calculator performs addition, subtraction, multiplication, and division on two fractions and reduces the result to lowest terms. It also shows a mixed number and a decimal approximation.

A fraction represents a part of a whole: the numerator is the top number and the denominator is the bottom number. The denominator cannot be zero.

How to use this calculator

1. Enter the numerator and denominator of the first fraction.
2. Choose the operation.
3. Enter the numerator and denominator of the second fraction.
4. Click Calculate.

The default example is 2/7 + 3/8.

Fraction formulas

a/b + c/d = (ad + bc) / bd
a/b − c/d = (ad − bc) / bd
a/b × c/d = ac / bd
a/b ÷ c/d = ad / bc

After the operation, divide the numerator and denominator by their greatest common divisor to simplify.

What the results mean

For the default example, 2/7 + 3/8 = 37/56, which is about 0.6607. The fraction is already in lowest terms, so the mixed-number form is the same as the improper fraction.

A mixed number has a whole part and a fraction, such as 1 1/2. The calculator converts an improper result to that form.

Assumptions and limitations

The calculator accepts integer numerators and denominators. It does not accept mixed-number input directly, and it does not simplify algebraic fractions. Division by a zero fraction is rejected.

The decimal result is rounded for display; the fraction is exact for the integers you enter.

Frequently asked questions

How do I add fractions with different denominators?

Find a common denominator, convert each fraction, then add the numerators. The formula above does this in one step.

Why is the denominator not allowed to be zero?

Division by zero is undefined. A fraction with a zero denominator has no meaning.

Can the result be negative?

Yes. A negative numerator or denominator produces a negative fraction. The calculator normalizes the sign into the numerator.

Does the calculator reduce the fraction?

Yes. The result is divided by the greatest common divisor of the numerator and denominator.

Source

Reference: Wolfram MathWorld — Fraction.

Disclaimer

This calculator is for educational purposes. Verify results for homework, engineering, or financial calculations with an appropriate method.