NP Chapter 3 Problem Set Question #2 (page 43)

[acrum]

Simply 66 ÷ (-33) x |-9|

The answer key shows -18 as the answer. And the reasoning is "Therefore, 66 ÷ (-33) yields a negative number (-2)".

Why wouldn't PEMDAS apply here? Shouldn't -33 x |-9| be done first? In which case the answer I have is -2/9.

Is this an error in the book?

[john.cappuccitti]

With respect to PEMDAS, the order of operations is as follows:

1. Parentheses
2. Exponents
3. Multiplication/ Division
4. Addition/ Subtraction

Multiplication and Division can be done interchangeably (granted, as long as you have already dealt with all operations in parentheses and exponents, and BEFORE you do any addition or subtraction.

With respect to your specific question, your problem arises due to how you are reading the question. The question should be read in the following way:

[66/(-33)] x l-9l

which is equivalent to:

[66/(-33)] x l-9l/1

Your error is that you are reading the question as follows:

66/[-33 x l-9l]

which is equivalent to:

[66/(-33)] x [1/l-9l]

You are incorrectly multiplying by the reciprocal of l-9l

[Ben Ku]

The acronym PEMDAS can be misleading if applied incorrectly.
(1) Parentheses must be simplified first, from INSIDE to OUTSIDE.
(2) Exponents are taken care of next
(3) Multiplication and Division are done together, from the LEFT to the RIGHT
(4) Addition and Subtraction are done together, from the LEFT to the RIGHT

So you do have to do 66 div (-33) before multiplying by | -9 |