Fraction Calculator

How This Calculator Works

Adding, subtracting, multiplying, or dividing two fractions combines them into a single simplified result. Enter two fractions and choose an operation, and this calculator returns the simplified result, its decimal equivalent, and a mixed-number form when the result is an improper fraction (numerator larger than denominator). Each fraction also has an optional whole-number field, so a mixed number like 1 1/2 can be entered directly instead of converting it to the improper fraction 3/2 first.

A second mode, “Convert a decimal to a fraction,” goes the other direction: enter any decimal and get back its simplest equivalent fraction — useful for turning a measurement or a calculator’s decimal output into a fraction you can actually mark on a tape measure or a recipe.

The Formula

Adding or subtracting first finds a common denominator by cross-multiplying:

$$\frac{\vA{a}}{\vB{b}} + \frac{\vC{c}}{\vD{d}} = \frac{\vA{a} \times \vD{d} + \vC{c} \times \vB{b}}{\vB{b} \times \vD{d}}$$

Multiplying multiplies straight across:

$$\frac{\vA{a}}{\vB{b}} \times \frac{\vC{c}}{\vD{d}} = \frac{\vA{a} \times \vC{c}}{\vB{b} \times \vD{d}}$$

Dividing multiplies by the second fraction’s reciprocal:

$$\frac{\vA{a}}{\vB{b}} \div \frac{\vC{c}}{\vD{d}} = \frac{\vA{a} \times \vD{d}}{\vB{b} \times \vC{c}}$$

Every result is then reduced to its simplest form by dividing both the numerator and denominator by their greatest common divisor.

Converting a decimal to a fraction uses a continued-fraction expansion — the standard method for finding the simplest fraction that closely approximates a given decimal, rather than just reading off digits after the decimal point (which would turn a repeating decimal like 0.333333 into an ugly fraction like 333333/1000000 instead of the actual 1/3 it’s approximating).

Worked Example

Adding 1/2 and 1/3:

1. Common denominator: $2 \times 3 = 6$.
2. Numerator: $1 \times 3 + 1 \times 2 = 5$.
3. Result: $\frac{5}{6}$ (already in simplest form) — about 0.8333.

Adding 1/2 and 2/3 instead gives an improper fraction: $\frac{7}{6}$, which this calculator also shows as the mixed number 1 1/6.