Denominator

The denominator is the bottom part of a fraction, the number after the slash, and it represents the number of equal parts into which the whole is divided. It also serves as the divisor in the division that defines the fraction.

In a fraction a/b, a is the numerator and b the denominator. Examples: 3/4, 7/10. The denominator cannot be zero, because division by zero is undefined.

Denominators have implications for decimal representations: a fraction with a denominator whose reduced form has prime factors other than 2 or 5 will have a repeating decimal; fractions with denominators of the form 2^m 5^n terminate in base 10.

In arithmetic and algebra, the denominator is a target for operations: to add fractions you need a common denominator; to simplify you cancel common factors from numerator and denominator; in algebra the denominator can be an expression such as x+1, with the caveat of domain restrictions (denominator ≠ 0).

Beyond fractions, the concept appears in ratios and rates where the denominator represents the total amount being measured; in rational functions the denominator is the polynomial that can create undefined points (poles) when it equals zero.

Etymology: denominator comes from Latin denomināre meaning to name or distinguish; opposite of numerator, which comes from Latin numerāre for counting. The denominator is a foundational concept in arithmetic and mathematics.