dividing

Dividing is the process of determining how many times one quantity is contained in another, or of separating something into parts. It is a fundamental arithmetic operation used to allocate, measure, or compare quantities.

In mathematics, division is a binary operation that yields a quotient when a dividend is divided by a divisor. It is written as a ÷ b or a/b. The result is the quotient; when the divisor does not evenly divide the dividend, a remainder may exist. Division is the inverse of multiplication: if a × b = c, then c ÷ b = a.

Special cases include division by zero, which is undefined in standard arithmetic; zero divided by a nonzero number equals zero. The sign of the quotient follows the signs of the operands, so dividing two numbers with the same sign yields a positive result, while opposite signs yield a negative result.

In fractions, dividing by a fraction means multiplying by its reciprocal: a ÷ (c/d) = a × (d/c). In general, division is not commutative, and the order of operands matters (a ÷ b ≠ b ÷ a).

Division can be performed with algorithms such as long division, or estimated mentally. The quotient may be a finite decimal or an infinite repeating decimal, and division by a rational number produces a rational result.

Beyond mathematics, dividing means separating something into parts, such as dividing land or responsibilities. In biology, cell division refers to processes like mitosis and meiosis, in which a cell splits to form daughter cells.

Historically, the division symbol (÷) and the slash (/) have been used to denote division in various contexts, and division is a central concept in many programming languages as an operator for numeric computation.