PEMDAS and the Common Errors in the Order of Operations

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.


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.

This is also similar with addition and subtraction. If the two operations are adjacent, it should be performed from left to right.  The answer to

5 - (-3) + 7 = 15

and not

5 - (-3) + 7 = 5 - 4 = 1

With that said, what is the answer to 6 \div 2(1 + 2)? Is it equal to 9 or is it equal to 1?

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3 thoughts on “PEMDAS and the Common Errors in the Order of Operations

  1. In India, we use BODMAS rule which is similar or in fact the same as the PEMDAS rule.

    Bodmas stands for Bracket Open Division Multiplication Addition Subtraction.
    Sometimes it also stands for Bracket Of Division Multiplication Addition Subtraction. Where division and multiplication are sisters and addition and subtraction are sisters and either of them can be used first.

    I find E for exponential quite useful in PEMDAS.

    By the way, how should I submit my guest article to you. Will MS Word format do?

    • Thank you for sharing Sohael. Yes, MS Word will do. Please include a 2-3 sentences by line about you and a link to your blog/website if you have one. 🙂

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