Numbers
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# Order of Operations

Suppose we wish to evaluate

To evaluate the above, we need to perform the operations in the correct order.
We do evaluate Brackets first, then we evaluate Orders which includes powers, indices, square roots, etc. Then we evaluate Division, followed by Multiplication, Addition and finally Subtraction.

This is easily remembered from the ‘word’ BODMAS, where
B stands for Brackets
O for Orders
D for Division
M for Multiplication
S for Subtraction

So, for our problems we should first perform , that gives us
So that, we now have

Next, we take down the orders, we have which is .
So, now we have

After Division, comes Multiplication. So, evaluate and 3\times 2=6

Following the rule of BODMAS, we now perform the addition.

Finally, we have
Therefore

We notice that Addition and Subtraction are given the same priority in the order of operation. So we could have done in the above first and then add

## Examples

##### Find the value of:

Find the value of
since is done first.

Find the value of
First

• Bracket first

Evaluate

If we have more brackets within brackets, then we perform the innermost brackets first and move outwards. For example, to evaluate

We do first to have .
This brings us to

Next we take , so that now we have

Now

Evaluate .
(Power first);
(Division, )
(Multiplication)