shumëzimin

Shumëzimi is the arithmetic operation that combines two numbers, a and b, to produce their product, written as ab or a × b. In Albanian mathematics, shumëzimi is a binary operation that is fundamental to arithmetic and algebra.

The product is defined for natural numbers and extended to integers, rational numbers, real numbers, and complex numbers, maintaining the same basic rules. For natural numbers, the product a × b can be interpreted as repeated addition of a to itself b times. In higher algebra, multiplication is extended to various structures, while preserving its core properties.

Key properties include commutativity (a × b = b × a), associativity ((a × b) × c = a × (b × c)), and distributivity over addition (a × (b + c) = ab + ac). The number 1 acts as the multiplicative identity (a × 1 = a), and 0 annihilates the product (a × 0 = 0).

Common computational methods include the standard algorithm of long multiplication, as well as visual methods like lattice multiplication. In computing, multiplication also forms part of binary arithmetic and is implemented in processor instructions.

Shumëzimi is applied across mathematics, science, and everyday life, including calculating areas and volumes, scaling quantities, solving algebraic equations, and in probability and statistics.