# Operations

Operations are actions you can use on numbers.  The four most common operations are addition, subtraction, multiplication and division.  You can use these operations on any numbers, whether they are fractions, whole numbers, or even decimal numbers.

## Order of Operations

Say I have the following question and I want to find an answer:

3 × 5 + 4

There are two operations in this question, a multiplication and an addition.  Now, the answer that you get depends on what order you do these operations in.  Let’s try doing it in two different orders.

First we’ll try doing the multiplication part first:

This time we get 27 as the answer!  How can this be?  Can both 19 and 27 be the correct answer?

The answer to this is no!  When you have more than one operation in a question, you need to do the operations in the correct order.  So what’s this order of operations?  Well, here it is:

Brackets – do the calculations for anything inside brackets first.

Next do the ‘Of’ operations – such as “the square root of”.

Multiplication and division – do these calculations next. Do them from left to right.

So back to:

Need to do the multiplication first

So 19 was the correct answer for that question.  Here’s a more complicated question:

First we do anything with brackets around it:

Remember that you can remove the brackets when they are around just a single number, like the ‘(3)’ above.

Next we do anything with multiplication or division.  We’ve got both a division and multiplication, so we’ll do it from left to right:

The last step is any addition or subtraction:

And there’s the answer – quite easy when you break it down into simple steps.  You can get really nasty questions like:

(5 × (2 – 4))

This question has more than 1 set of brackets – so just work from the inside outwards:

So, doing the inside brackets first we get:

And then the multiplication: