How_To_Be_Good_At_Math

Arithmetic laws

Whenever we’re calculating, it helps to remember three basic

rules called the arithmetic laws. These are especially useful

when we’re working on a calculation with several parts.

Multiplication

Here we have 3 fish 2 times, giving

a total of 6 fish. If we have 2 fish 3 times,

we also have a total of 6 fish. It doesn’t

matter what order we multiply the

numbers, the product is the same.

We can partition 47 into 40 + 7.

If we work out this calculation,

the answer is 183.

We can move the brackets to make

the calculation simpler. Adding 136

and 40 first, then the 7, also gives 183.

Addition

Look at these fish. Adding 6 to 5

gives 11 fish. Adding 5 to 6 also gives

11 fish. We can add numbers in any

order and still get the same total.

Addition

The associative law helps us to add

together tricky numbers, like 136 + 47.

The commutative law

When we add or multiply two numbers,

it doesn’t matter which order we do it in

• the answer will be the same. This is
  called the commutative law.

The associative law

When we add or multiply

three or more numbers,

the way we group the

numbers doesn’t affect

the result. This is the

associative law.

5 + 6 = 11

3 × 2 = 6 2 × 3 = 6

136 + 47

136 + (40 + 7) = 183

6 + 5 = 11

• = +

154 CALCULATING •^ ARITHMETIC LAWS

3 fish 2 times,

or 3 × 2

2 fish 3 times,

or 2 × 3

(136 + 40) + 7 = 183

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