How can you have different answers to the same expressions with or without the application of the PEMDAS rule?

1 Answer
Apr 8, 2016

Answer:

PEMDAS is a guide to attempt to help reduce ambiguity, but it can result in unintentional interpretations.

Explanation:

If the order of operations is not clearly indicated then without the guidance of PEMDAS they are ambiguous.

Consider a popular example:

#9-:3(1+2)#

If we follow the rules of PEMDAS strictly without embellishment then this expression is the same as:

#9/3xx(1+2)#

According to PEMDAS we evaluate the parentheses first, then the division and multiplication from left to right:

#9/3xx(1+2) = 9/3xx3 = 3xx3 = 9#

Note however that historically the #-:# sign was used to express dividing one complete expression by another complete expression. So with that interpretation we would have:

#9-:3(1+2) = 9/(3(1+2)) = 9/(3xx3) = 9/9 = 1#

The purpose of rules like PEMDAS is to try to reduce the ambiguity, but if you want your expressions to be unambiguous it is often helpful to add some parentheses.