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

Question

Gabriel Agustin · Accepted Answer

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

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.

Genesis Amaya · Answer

undefined The order of operations, as governed by the PEMDAS rule (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right), determines the sequence in which mathematical operations are performed. Failing to follow this rule can result in different answers for the same expression. For example:

Expression: 5 + 3 * 2

Without PEMDAS: (5 + 3) * 2 = 8 * 2 = 16
With PEMDAS: 5 + (3 * 2) = 5 + 6 = 11

Thus, applying or neglecting the PEMDAS rule leads to different results because it dictates the order in which operations are executed.