multiplies

Multiplies is the third-person singular present tense of the verb multiply. In mathematics, to multiply two numbers or symbols is to form their product, typically by combining equal groups or by applying established rules of arithmetic. The operation is binary, taking two factors and producing a product, written in symbols as a × b = c or ab = c.

Notation and interpretation vary by context. Common symbols for multiplication include the times sign ×, a middle dot ·, or simple juxtaposition (writing ab). For nonnegative integers, multiplication can be interpreted as repeated addition: a × b equals the sum of a added to itself b times. In higher mathematics, multiplication extends to fractions, decimals, negatives, and abstract objects such as matrices, vectors, and functions, each with its own rules.

Key properties are widely used. The commutative property states that a × b = b × a. The associative property says (a × b) × c = a × (b × c). The distributive property over addition states a × (b + c) = a × b + a × c. The identity element for multiplication is 1: 1 × a = a, and multiplying by zero yields zero: a × 0 = 0.

Applications of multiplication are foundational in many fields. It is central to arithmetic, algebra, geometry (such as calculating areas), physics, computer science, and economics. In computation, multiplication is implemented by processors and algorithms of varying complexity, from simple long multiplication to more advanced methods like Karatsuba or lattice multiplication.

Notes: while the verb form multiplies is correct, everyday language more often uses multiply by or times in place of the present-tense form.