Operation that, to each pair of numbers called the factors of the multiplication, associates a new number called the product of these factors.

The inverse operation of multiplication is division.

### Symbol

The symbol of multiplication is “×” which is read as “**multiplied by**“.

### Properties

- (a) Multiplication is a commutative operation.

Example : 12 × 15 = 15 × 12 - (b) Multiplication is an associate operation.

Example : (12 × 15) × 10 = 12 × (15 × 10) - (c) Multiplication has an identity element.

Example : 12 × 1 = 1 × 12 - (d) Any number multiplied by 0 gives 0 as a result.

Example : 12 × 0 = 0 × 12 = 0

### Example

Consider this multiplication of whole numbers: 5 × 7 = 35

The numbers 5 and 7 are called the factor of the multiplication.

The number 35 is the product.

In this multiplication, we sometimes call the number 12 the multiplicand and the number 15 the multiplier.

### Educational Note

The symbol “×” appeared in a text by the mathematician William Oughtred called *Clavis Mathematicae* in 1631. The same year, mathematician Thomas Harriot (1560-1621) used a large dot “.” as a symbol of multiplication. In fact, Harriot used this dot to separate a coefficient from a variable, as in “6 . y .”