### 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.