 ## Content description

Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

These rules apply to multiplication.

In general, if a and b are numbers,

a × b = b × a  (commutative law for multiplication)

For example, 7 × 8 = 8 × 7.

(a × b) × c = a × (b × c)  (associative law for multiplication)

For example,    (7 × 5) × 6 = 7 × (5 × 6).

In general, if a, b and c are numbers,

a × (b + c) = a × b + a × c   and

(b + c) × a = b × a + c × a

Both of these are called the distributive law for multiplication over addition.

For example, 7 × (6 + 3) = 7 × 6 + 7 × 3.

It is not necessary for students to use the names of the laws or identify when a rule is being employed. Students should be aware of the properties and use them for mental and written computation.

Students should be aware of the properties and use them for mental and written computation.

These rules are also important in algebra.   