Ø5

×5 denotes the operation of multiplying a number by five, read as “times five” or “multiplied by five.” It is a binary arithmetic operation that scales its input by a factor of five. In algebra, this multiplication is commutative with other multiplications, so a × 5 = 5 × a, and it interacts with addition and other operations through standard arithmetic laws.

Calculating products with five can be done in several ways. In decimal arithmetic, 5 × n is equal to (10 × n)/2; if n is even this can be computed quickly as (n/2) × 10. A common mental math rule is to compute 5 × n as 4 × n + n, using doubling and addition. In binary, multiplying by five can be implemented as (n << 2) + n, i.e., shifting left by two places and adding the original number.

Properties of the operation include linearity: the map n → 5n is a linear transformation on integers or real numbers, preserving both addition and scalar multiplication. The set of multiples of five is closed under this operation, producing results that are all divisible by five.

Examples illustrate the concept: 5 × 7 = 35, 5 × 0 = 0, and 5 × (−3) = −15. Beyond pure arithmetic, multiplying by five serves in scaling quantities, unit conversions, and in contexts such as computing fivefold increases or determining prices or measurements that are five times larger.

Notation and usage: The × symbol is widely used to denote multiplication in many educational settings, though in programming languages the asterisk (*) is more common. The symbol × originated as a multiplication sign in early modern mathematical notation and is read as “times.” The expression ×5 is a standard shorthand for multiplying a value by five.