# times

Multiplication (often denoted by the cross symbol “×”, or by the absence of symbol) is one of the four elementary, mathematical operations of arithmetic; with the others being addition, subtraction and division. When two numbers and are multiplied, the result is called their product and and the factors. In the case where and are whole numbers, the product can be interpreted as the number of objects in groups of objects each. By arranging the objects in a rectangular array and viewing the “groups” as either the rows or the columns, it can be seen that , known as the commutative property, a relation that also holds when multiplying other kinds of numbers. The relationship between multiplication and addition is specified by the distributive property: This relationship can be used to convert products of sums into sums of products, or vice versa. For example, the sum can be rewritten using the distributive property as the product , and the whole-number product can be written as Multiplication can be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have given lengths. The area of a rectangle does not depend on which side is measured first, which illustrates the commutative property. In general, multiplying two measurements gives a new type, depending on the measurements. For instance: : : The inverse operation of the multiplication is the division. For example, since 4 multiplied by 3 equals 12, then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number (since the division of a number other than 0 by itself equals 1). Multiplication is also defined for other types of numbers, such as complex numbers, and more abstract constructs, like matrices. For these more abstract constructs, the order that the operands are multiplied sometimes does matter.