PEMDAS and the Common Errors in the Order of Operations

August 26, 2012 GB High School Mathematics

PEMDAS is the acronym for the order of operations. P stands for parentheses, E for exponent, and MDAS for Mulitplication, Division, Addition, and Subtraction respectively.

PEMDAS

This means we want to evaluate a numerical expression such as

$5(6 + 3)^2 - 8$

we have to ‘operate’ to the order of PEMDAS. The operation is as follows.

Parentheses: $5(6 + 3)^2 - 8 = 5(9)^2 - 8$ .

Exponent: $5(9)^2 - 8 = 5(81) - 8$

Multiplication: $5(81) - 8 = 405 - 8$

Subtraction: $405 - 8 = 397$

Now, the common misconception in PEMDAS is when the order of operations MD are adjacent. Since M comes before D, it is thought that M should always be performed first. This is not the case.When multiplication and division are adjacent operations, the operation should be performed from left to right. For example, $8 \div 4 \times 3 = 6$ and not $\frac{8}{12}$ since we have to divide first before we multiply.