Product (mathematics)

A product is the result of multiplying two or more numbers or mathematical expressions. Multiplication also denotes the operation that produces it.

Multiplication: An arithmetic operation that combines quantities according to scaling and repeated-grouping rules. It is the operation whose result is a product.
Long multiplication: A written algorithm for multiplying multi-digit numbers using place-value partial products. It calculates a product by combining contributions from each pair of digits.
Area: A measure of the size of a two-dimensional region, expressed in square units. The area of a rectangle is the product of its side lengths.
Sum: The result of adding two or more numbers or mathematical expressions. Addition combines quantities, while a product results from multiplication.
Factor (mathematics): A number or expression that is multiplied by another to form a product. Each input to a multiplication is a factor of its product.
Partial product: A product formed from selected parts of factors during a multiplication calculation. Long multiplication adds these intermediate products to obtain the final result.
Cartesian product: The set of all ordered pairs formed by choosing one element from each of two sets. Its name and size connect multiplication with counting combinations.
Quotient: The result of dividing one quantity by another. Division reverses multiplication: a quotient can recover a factor from a product.
Commutative property: A property stating that changing the order of operands does not change an operation's result. For ordinary numbers, swapping factors leaves their product unchanged.
Distributive property: The rule that multiplication distributes over addition, so a(b+c)=ab+ac. It expands products over sums and supports many multiplication algorithms.

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