# Order of Functions

To ensure uniformity, and prevent mistakes, there are rules on the order to calculate maths problems and this is known as the order of functions.

Brackets in sums

Multiplication or Division

## What is the order of functions?

To ensure uniformity, and prevent mistakes, there are rules on the order to calculate maths problems and this is known as the order of functions.

In life you may come across a maths problem which looks something like this.

Example 1

12 + 4 X 5

This sum can be calculated in two ways. Either you add the 12 to the 4 equalling 16 and then multiply that by 5 giving the answer of 80.

Or you may multiply 4 X 5 which is 20 and then add the 12 giving the answer of 32.

So as you can see getting the correct order of functions is vital to getting the right answer, but which of these is correct? You may think the logical move would be to calculate as it is written i.e. left to right but this is not the correct order of functions.

## Brackets in sums

The rules for the order of functions are as follows. The first thing to look for in an equation is brackets. If part of the equation is in brackets then this needs to be calculated first.

Example 2

5 X (3 + 7)

So first you add the 3 and 7 which is 10 and then multiply by 5 giving the answer of 50.

## Multiplication or Division

If there are no brackets, or you have calculated the brackets, then the next functions to look for are multiplication or divisions in the sum. If these are present in the equation then they must be calculated first before any addition or subtraction functions.

Example 3

5 + 6 X 3

Here the 6 is multiplied by the 3 giving the answer of 18. Then you add the 5 making the complete answer 23.

## Addition and Subtraction

Addition or subtraction functions in a sum are calculated last of all.

But what if the sum only contains multiplication and division functions or addition and subtraction functions?

Well in this case you work left to right through the sum.

Example 4

4 – 3 + 6

Here you subtract the 4 from the 3 to make 1, then add the 6 giving an answer of 7

Example 5

10 X 5 ÷ 4

Here you would multiply the 10 and 5 to give you 50 and then divide by 4 giving you the answer of 12.5.

You may notice that the sum in example 5 is the same in either order (5 ÷ 4 is 1.25 and multiply that by 10 gives you 12.5) but this is not always the case.

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