Fractions and mixed numbers

The numerator counts selected parts; the denominator says how many equal parts make the whole. Proper fractions are below one, while improper fractions may be one or more.

A mixed number combines a whole number and a proper fraction, such as 2 1/3.

Simplifying divides numerator and denominator by the same common factor. Expanding multiplies both by the same number and leaves the value unchanged.

Addition and subtraction require a common denominator before the numerators are combined.

For multiplication, multiply numerators together and denominators together. For division, multiply by the reciprocal of the second fraction.

A fraction can be approximated as a decimal or shown as a percentage. Some decimals recur: 1/3 is 0.333… but remains exact as a fraction.

Fractions are useful when a ratio should remain exact instead of being rounded early.

Do not add denominators when adding fractions. Division by a fraction whose numerator is zero is undefined.

A displayed decimal may only be an approximation of an exact fraction.

Our calculator accepts whole parts, numerators and denominators and supports addition, subtraction, multiplication and division. It normalizes signs, simplifies with the greatest common divisor and shows mixed numbers where appropriate.

Core calculations use integers so ordinary fractions are not distorted by binary floating-point arithmetic. Decimal output is supplementary.