 ## Multiplication

Any two numbers can be multiplied together. The result is called the product of the numbers.

#### Example 3

3 × 5 = 5 × 3 = 15

3 × 5 × 6 = 15 × 6 = 3 × 30 = 90

Using pronumerals this becomes:

$$x\times y = y × x$$

$$x\times y\times z=(x\times y)\times z=x\times(y\times z)$$

Both these examples illustrate the any-order property for multiplication. It states that a list of numbers can be multiplied together in any order to give the product of the numbers.  This property summarises the commutative and associative laws for multiplication.

Multiplication is distributive over addition and subtraction.

#### Example 4

(20 + 1) × 36 = 20 × 36 + 1 × 36 = 720 + 36 = 756

(30 − 2) × 36 = 30 × 36 − 2 × 36 = 1080 − 72 = 1008

Using pronumerals this becomes:

$$(x+y)\times z=x\times z+y\times z=xz+yz$$

$$(x-y)\times z=x\times z-y\times z=xz-yz$$

$$(x+2y)\times x=x\times x+2\times y\times x=x^2+2xy$$

Note that we usually write the product of pronumerals in alphabetical order.   