Principles of Mathematics

Rules of Precedence in Basic Maths

In basic maths, there are simple and basic rules that we need to follow in order that the maths computations are proper. The first important rules that, I believe , we need to master is the Rules of Precedence.
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.

What is this Rules of Precedence as applied in Basic Maths?
It is the priority of use for the mathematical operators +, -, / , x and ().

There are certain priorities for their use. Let’s see some maths example.
Example1: 3 + 4 x 2
Example2: (3 + 4) x 2
Example3: 6 / 2 + 3
Example4: 12 / (3 - 1)
Example5: 4 - 2 + 3 x 2

Rules of Precedence:
1st priority of use: Brackets ( )
2nd Priority of use: Multiple “x” or Divide “/”
3rd priority of use: Add “+” or Subtract “-”

Let’s analyse the maths equations of above.
Example1: 3 + 4 x 2
Base on the basic maths Rules of Precedence, we need to perform the maths operation “X” first.
Why? We need to know the actual meaning of the maths operator “x”.
If a x 3, we mean that 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!).
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 multiple operator.
This is the result for Example2.

Example3 is 6 / 2 + 3 and base on the Rules of Precedence, we need to perform the maths operation Divde “/” first before the Addition operation “+”.
6 / 2 = 3 (sub-working) which makes Example3 becomes 3 + 3 = 6.
NOTE: Example3 does not have (). Therefore 6 / 2 is done first due to “/” having higher priority.
If Example3 is changed to 6 / (2 + 3), the maths equation has result = 6 / 5 since () comes first.
This explains that Example4 is 12 / (3 - 1) = 12 / 2 = 6.

How about Example5? 4 - 2 + 3 x 2
Again the multiple maths operation “x’ has to be done first. 3 x 2 = 3 + 3
Example5 becomes 4 - 2 + 3 + 3 = 2 + 3 + 3 = 5 + 3 = 8 (answer).

Tips: Practice with the Rules of Precedence in mind. Through constant practice, the concept and meaning of the maths operators will be understood and retented.

Only when learners of maths have mastered this Rules, can they move on to complex maths computation with ease and rid themselves of unnecessary maths mistakes.

Posted by: Lim Ee Hai
Source:     http://www.limeehai.com