fraction

A fraction expresses a part of a whole or a ratio between two integers. It is written as a/b, where a is the numerator and b the denominator. The denominator is a nonzero integer, and the fraction is interpreted as the quotient a divided by b.

Fractions can be proper (a < b), improper (a >= b), or represented as mixed numbers (for example, 2 and 1/3). Fractions can be negative when either the numerator or the denominator is negative. Denominators are never zero.

Fractions can be simplified by dividing numerator and denominator by their greatest common divisor, producing an equivalent fraction with no common factors other than 1. For example, 6/8 simplifies to 3/4. Any fraction can be converted to an equivalent one by multiplying numerator and denominator by the same nonzero integer.

Operations: to add or subtract fractions, find a common denominator and combine the numerators. To multiply, multiply numerators and denominators. To divide, multiply by the reciprocal of the second fraction. After each operation, simplify.

Fractions relate to decimals and percentages. They form the set of rational numbers. Some fractions have terminating decimal representations (e.g., 1/2 = 0.5); others repeat (e.g., 1/3 = 0.333…).

Fractions appear in many contexts, including measurements, proportions, and probability, and are used to describe parts of a whole, ratios, and fractions of a quantity.