In general, we say that when we are adding, it doesn’t matter what way we group the numbers before we add them.
This is known as the associative property of addition. This also works with multiplication, as shown.
The word ‘associative’ comes from ‘associate’, which means ‘to group together’. So, the associative property is the rule that refers to grouping.
(2 × 4) × 3 = 8 × 3 = 24
=
2 × (4 × 3) = 2 × 12 = 24
The associative property states that how we group numbers (put them into brackets) does not matter. Discuss and discover
Working with the person beside you, pick any three numbers and investigate if the associative property works for (i) addition
(ii) subtraction (iii) division
Distributive property Consider how we can calculate the following: 3 × (2 + 4) Using the array model: 3 × (2 + 4) = 18
2 3 4 6 12
Using the order of operations rule the solution to this question works out as follows. 3 × (2 + 4) (brackets fi rst) = 3 × (6) = 18
(then multiplication)
Now consider what would happen if we did the multiplication fi rst and then the addition. 3 × (2 +4)
= (3 × 2) + (3 × 4) = 6 + 12 = 18
2
3 6
4 12
From this example, we can see that 3 × (2 + 4) = (3 × 2) + (3 × 4). This is called the distributive property of multiplication.
3 groups of (2 + 4) is the same as 3 groups of 2 plus 3 groups of 4 3 × (2 + 4)
The distributive property states that multiplying a number by a group of numbers added together is the same as doing each multiplication separately and then adding the results.
Discuss and discover
Working with the person beside you and using any three numbers of your own choosing, investigate whether the distributive property works for subtraction.
3 × 2 + 3 × 4
Distributive comes from the word ‘distribute’, which means ‘to spread out’.
= (iv) multiplication
Section A Introducing concepts and building skills