Multiplication - Notation and Terminology

Notation and Terminology

Multiplication is often written using the multiplication sign "×" between the terms; that is, in infix notation. The result is expressed with an equals sign. For example,

(verbally, "two times three equals six")

There are several other common notations for multiplication. Many of these are intended to reduce confusion between the multiplication sign × and the commonly used variable x:

• Multiplication is sometimes denoted by either a middle dot or a period:

The middle dot is standard in the United States, the United Kingdom, and other countries where the period is used as a decimal point. In other countries that use a comma as a decimal point, either the period or a middle dot is used for multiplication.

• The asterisk (as in 5*2) is often used in programming languages because it appears on every keyboard. This usage originated in the FORTRAN programming language.

• In algebra, multiplication involving variables is often written as a juxtaposition (e.g., xy for x times y or 5x for five times x). This notation can also be used for quantities that are surrounded by parentheses (e.g., 5(2) or (5)(2) for five times two).

• In matrix multiplication, there is actually a distinction between the cross and the dot symbols. The cross symbol generally denotes a vector multiplication, while the dot denotes a scalar multiplication. A similar convention distinguishes between the cross product and the dot product of two vectors.

The numbers to be multiplied are generally called the "factors" or "multiplicands". When thinking of multiplication as repeated addition, the number to be multiplied is called the "multiplicand", while the number of multiples is called the "multiplier". In algebra, a number that is the multiplier of a variable or expression (e.g., the 3 in 3xy2) is called a coefficient.

The result of a multiplication is called a product, and is a multiple of each factor if the other factor is an integer. For example, 15 is the product of 3 and 5, and is both a multiple of 3 and a multiple of 5.