How_To_Be_Good_At_Math

We can break 15 into its factors 5 and 3. If we

then work out this calculation, the answer is 90.

The associative law allows us to move the

brackets to make it easier. If we find 6 × 5

before multiplying by 3, the answer is still 90.

Multiplication

The associative law is also helpful when we

need to multiply by a tricky number, like 6 × 15.

The distributive law

Multiplying a number by some numbers

added together will give the same answer

as multiplying each number separately.

We call this the distributive law.

6 × 15 =?

6 × (5 × 3) = 90

(6 × 5) × 3 = 90

When a calculation has numbers in

brackets, work out the part in the

brackets first. We looked at the order

of operations on pages 152-53.

CALCULATING • ARITHMETIC LAWS 155

It’s quite a hard calculation if we don’t know

our multiplication tables for 3 all the way

to 14, so let’s split 14 into 10 + 4, which is easier

to work with.

Next, we can make the calculation simpler

to work out by distributing the number 3

to each of the numbers in the brackets.

Now we can solve the two brackets before

adding them together:

(3 × 10) + (3 × 4) = 30 + 12 = 42

So, by breaking 14 into simpler numbers

and distributing the 3 between them,

we’ve found that 3 × 14 = 42

Let’s see how the distributive law

can help us to find 3 × 14.

3 × 14 =?

3 × 14 = 42

3 × (10 + 4) =?

(3 × 10) + (3 × 4) =?

30 + 12 = 42

154-155_Arithmetic_laws.indd 155 29/02/2016 18:57