Multiplicand

Multiplicand is a term used in arithmetic to refer to the quantity that is multiplied by another quantity. In a multiplication expression such as a × b = c, the multiplicand is the number that is being multiplied, and the other factor is called the multiplier. The product is the result of multiplying the two factors. Although multiplication is commutative for ordinary numbers, distinguishing the multiplicand from the multiplier helps describe the operation, especially in procedural contexts like long multiplication.

In common usage, the multiplicand is described as the number that is to be multiplied, while the multiplier is the number by which it is multiplied. This distinction is particularly useful when explaining the steps of a calculation or when describing algorithms that build the product by multiplying the multiplicand by every digit of the multiplier and summing the shifted partial products.

Examples illustrate the convention: in 7 × 5 = 35, 7 is the multiplicand and 5 the multiplier. If the order is reversed to 5 × 7, the roles can be described similarly, though the specific designation may vary by textbook. In long multiplication, the process involves multiplying the multiplicand by each digit of the multiplier in turn.

Notes and scope: the term is mainly used for scalar multiplication. In higher mathematics, including vector, matrix, or abstract algebra contexts, the factors or operands are often described without specific labels like multiplicand or multiplier. Etymologically, multiplicand derives from Latin for something that is to be multiplied.