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Problem: Evaluate the following arithmetic expression:   3 + 4 x 2
   
Solution:
Student 1       Student 2
(3 + 4) x 2 3 + (4 x 2)
= 7 x 2 = 3 + 8
=14 = 11


 

It seems that each student interpreted the problem differently, resulting in two different answers. Student 1 performed the operation of addition first, then multiplication; whereas student 2 performed multiplication first, then addition. When performing arithmetic operations there can be only one correct answer. We need a set of rules in order to avoid this kind of confusion. Mathematicians have devised a standard order of operations for calculations involving more than one arithmetic operation.

Rule 1: First perform any calculations inside parentheses.
Rule 2: Next perform all multiplications and divisions, working from left to right.
Rule 3: Lastly, perform all additions and subtractions, working from left to right


 

 

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