## Wednesday, 23 July 2008

### Order of Precedence for Maths

In our daily life, we encounter many rules. The rules are in place to keep things in order.
Similarly in maths, we also do have rules to keep the mathematical computations in proper order.

This post is created for the sake of some learners of maths who even at high school or upper secondary level still has not master this.

The first important rule before learning maths, I believe , is to master the Order of Precedence.

What is this Order of Precedence?
It is the priority level of the elementary mathematical operators, +, -, / , x and ().

They are used in a certain pre-determined order.

Let's see some maths examples.

Example1: 3 + 4 x 2
Example2: (3 + 4) x 2
Example3: 6 / 2 + 3
Example4: 12 / (3 - 1)
Example5: 4 - 2 + 3 x 2

Order of Precedence:
1st priority of use: Brackets ( )
2nd Priority of use: Multiply "x" or Divide "/"
3rd priority of use: Add "+" or Subtract "-"

Let us analyse the above maths equations.

Example1: 3 + 4 x 2

Base on the Order of Precedence, we need to perform the maths operation "x" first.Why?

We need to know the exact meaning of the maths operator "x".

In a x 3, we mean it to be a + a + a , that is, to add "a" 3 times.

Therefore Example1 can be re-written 3 + 4 + 4 since ONLY 4 is x 2, which is 4 + 4.

If we do addition "+" first, followed by x 2, Example1 becomes 3 + 4 + 3 + 4 (which is wrong!).

The correct answer: 3 + 4 x 2 = 3 + 8 = 11

NOTE: If we desire to have 3 + 4 added twice, we then need the maths operator bracket ().
(3 + 4) x 2 ==> 3 + 4 + 3 + 4 .

The brackets isolate the (3 + 4) from the multiply operator.
This is the result for Example2 also.

Example3 is 6 / 2 + 3 and base on the Order of Precedence, we need to perform the maths operation Divide "/" first before the Addition operation "+".

6 / 2 = 3 (the sub-working) which makes Example3 become 3 + 3 = 6.

NOTE: Example3 does not have ( ). Therefore 6 / 2 is done first due to "/" having higher priority.

If Example3 is modified to 6 / (2 + 3), the maths equation has the result = 6 / 5 since ( ) gets done first.

This explains the result for Example4 is 12 / (3 - 1) = 12 / 2 = 6.

How about Example5? 4 - 2 + 3 x 2

Again the maths operation "x' has to be performed first ==> 3 x 2 = 3 + 3 = 6

Example5 becomes 4 - 2 + 3 x 2 = 4 -2 + 6 = 2 + 6 = 8 (answer).

Tip: Practice with the Order of Precedence in mind.

Through sincere constant practice, the concept and meaning of these maths operators will be understood and retained.

Only through strengthening this importance knowledge, you can then avoid many unnecessary maths errors,and move forward doing maths with ease.

:)

.

Anonymous said...

you got the order wrong.
here is what it should be.

1st priority of use: Brackets ( )
2nd Priority of use: Divide "/"
3rd priority of use: Multiply "x"
4th priority of use: Add "+"
3rd priority of use: Subtract "-"

EeHai said...

Thanks for the comment.

You have a point to split the priority. It may not be necessary for some operation though. See below case.

3 x 4
------
2 x 6

Which operation to be done first? "x" or the "/"?

I will do the "x" first.
You may do the "/" first, not wrong. It is difference in preference.

iamthejuggler said...

If you write it like this however:

3 x 4 / 2 x 6

then the '/' takes priority over the multiplication. So it essentially becomes

3 x (4 / 2 ) x 6

Which is very different from

(3 x 4) / (2 x 6)

It is not a difference in preference. It is a rule.

Anonymous said...

Sorry iamthejuggler - the rule for x/ and +- is left to right evaluation - there is no precedence of / over * etc.. This wiki page is pretty accurate: http://en.wikipedia.org/wiki/Order_of_operations

Anonymous said...

3 x 4
------
2 x 6

is equivalent to (3 x 4) / (2 x 6)

Am I wrong?

EeHai said...

Yes, it is correct. The brackets are good visual aids for maths.