BIDMAS

(Sometimes referred to as BODMAS or PEDMAS)

BIDMAS is the order you need to complete the operations in (+ - x and ÷ are the operations). It is a way of remembering the correct order:

 B = Brackets

I = Indices

D = Division

M = Multiplication

A = Addition

S = Subtraction

With BIDMAS is it best to write down each calculation as you go. Children can be reluctant to show their working out, but I've found most of the time this is because they are unsure how to. In the following examples I've shown how they can do this wherever possible. The calculations they write down as part of this may seem obvious at first, but if they get into this habit it will help them immensely with more complicated equations later on (particularly in Algebra). 

The following is an explanation of how to complete each step:

BRACKETS

If you had a sum such as 2 + (10 - 6), you need to complete the equation in the brackets first.

If there is more than one set of brackets, work out each set in turn:

E.g. 4 + (30 - 20) + 5 + (10 - 2)

INDICES

Indices are square roots, square numbers, cubed numbers, powers, etc. The following is a reminder of each of these:

Square Roots The following are examples of how square roots are written (sometimes the lines may look like this in a text book: √ This means the square roots shown below will look like this: √16 and √25 ).

If you are asked to find √16 (which is the square root of 16), you are being asked to find the number that, when multiplied by itself, gives the answer of 16: 4 x 4 = 16, so this means the square root of 16 = 4.

therefore √16 = 4

If you are asked to find √25, then 5 x 5 = 25, so the square root of 25 = 5.

therefore √25 = 5

Square Numbers are numbers the answer when a number is multiplied by itself.

For instance, 4 is a square number as 2 x 2 = 4. This is written as 2² .

9 is a square number as 3 x 3 = 9 . This is written as 3² .

Cubed Numbers are numbers that are multiplied by themselves, then multiplied by themselves again.

For instance, 2 x 2 x 2 = 8

(work from left to right along the equation: 2 x 2 = 4 ; 4 x 2 = 8).

This is written as 2³: the small number is ³ because 2 has been multiplied three times.

Powers These are a continuation of square numbers and cubed numbers.

2 x 2 x 2 x 2 is '2 to the power of 4'. It is written as 2⁴ as 2 has been multiplied 4 times.

2 x 2 x 2 x 2 = 16

therefore 2⁴ = 16

Always remember to work from left to right when multiplying, as follows:

Another example is 3 x 3 x 3 x 3 x 3, which is '3 to the power of 5'. It is written as 3⁵ as 3 has been multiplied by itself 5 times.

3 x 3 x 3 x 3 x 3 = 243

therefore 3⁵ = 243

Multiplying from left to right, the sum is calculated like this:

It is also worth noting:

a² is a x a

b³ is b x b x b

c⁴ is c x c x c x c and so on.

DIVISION AND MULTIPLICATION

Once you have calculated the brackets and indices, then work out the multiplication and division. Sometimes there will be an x and ÷ sign in the equation and you need to work from left to right, through the equation (as shown in the section on Indices).

For instance, the equation 12 ÷ 3 x 2 is completed as follows:

12 ÷ 3 is completed first, as this appears first in the equation.

12 ÷ 3 = 4

Then multiply 4 by the 2:

4 x 2 = 8, so the answer is 8.

If you complete the multiplication first, you will get the wrong answer: always work from left to right.

(3 x 2 would be 6 and 12 ÷ 6 = 2, which gives the wrong answer.)

Another example is: 16 ÷ 8 x 2

16 ÷ 8 = 2 and 2 x 2 = 4, so the answer is 4.

(If you do not work from left to right, you will get the following answer which is wrong: 8 x 2 = 16 and 16 ÷ 16 = 1).

MULTIPLICATION

If a number is on its own outside the brackets, without a + , - , x or ÷ sign then it needs to be multiplied. (There is more about this in the 'Multiplication sign' section in algebra.)

Example 1: Solve: 2(4 x 5)

Example 2: Solve 3(2² x 6)

3(2² x 6) is the same as 3 x (2² x 6)

To solve the equation, work out the equation in the brackets first: 2² x 6 is the same as 4 x 6 which is 24.

Then multiply by the 3 outside the brackets: 3 x (24) = 72

DIVISION

It is worth noting that the ÷ sign is not always used, sometimes only the 'line' is used.

For instance:

ADDITION AND SUBTRACTION

Once you have calculated the brackets, then the indices, then any multiplication and division, you can then calculate the addition and subtraction. Again, make sure you work from left to write, as shown above in the section on multiplication and division.

EXAMPLES OF THIS PUT INTO PRACTICE:

(I encourage my students to highlight parts of the sum in different colours in the following way, to help them keep track.)