Arithmetic » Basic rules/calculation order
The calculation order in arithmetic is:
1. What is between
Brackets
2.
Powers and
Roots from left to right
3.
Multiplications and
Divisions from left to right
4.
Additions and
Subtractions from left to right
Note: In some countries they use
parentheses instead of brackets and/or
indices or
exponents instead of powers.
In operators/signs:   In letters:   Mnemonic: 
 
 
Big 
Puffy  Rats 
Make  Dora 
Always  Scared 

To reduce the risk of a mistake, you solve these exercises with intermediate steps.
Note: Writing intermediate steps is different from making calculations.
Take a look at the examples below. In the first exercise the calculation '3 × 5 = 15' is not written down! Because you changed 3 × 5 in your intermediate step to 15 you show that that is what you calculated.
Examples
12 +  3 × 5  = 
12 +  15  = 27 

12 ÷ 2  –  2 × 2  = 
6  –  4  = 2 





24 –  (7 +  3 × 2  ) =  
24 –  (7 +  6  ) =  
24 –  13  =  11 

9 +  –4^{3}  ×  –  = 
9 +  –64  ×  –4  = 
9 +  256  = 265 

No more possible confusion?
With such clear 'rules of way' there will not be any mistakes with the calculation order anymore, right? ... Wrong. Look at the exercise 8/2(4).
Perhaps you knew already, but you are allowed to leave out the multiplication sign, so this exercise means 8 ÷ 2 × 4 = 4 × 4 = 16. However, there are people who say that because the multiplication is left out, that means the 2 × 4 has to be done first, as those 'clearly' belong to each other.
In that case, we will get 8 ÷ 8 = 1.
Unfortunately the calculator also does not help in giving one clear answer.
It is not for nothing mathematicians like to write divisions as a fraction.
That way we will get 82(4) = 16 and 82(4) = 1. No confusion possible.