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Unit 1.2: Order of Operations

Order of Operations

It is important that we have a set procedure to solve larger, more complex problems with multiple different operators.

For example, if we had

Order of Operations Example

(17 – 6 ÷ 2) + 4 × 3

The answer we get varies wildly from how we tackle the problem

If we started with 17 – 6, that equals 11 and then divide that by 2, add 4 and multiply by 3, you get 28.5 which is not the correct answer.

 

The correct way to do it is to follow the Order of Operations which we abbreviate to be

PEMDAS (Please Excuse My Dear Aunt Sally)

  1. P – Parenthesis
  2. E – Exponents
  3. M – Multiplication
  4. D – Division
  5. A – Addition
  6. S – Subtraction

(Multiplication and division are interchangeable as well as addition and subtraction)

We start by going down the list and seeing what occurs in our expression

 

Looking at our example earlier:

Order of Operations Example

(17 – 6 ÷ 2) + 4 × 3

The first thing we would do is the math inside the parenthesis (17 – 6 ÷ 2) as this is number one in PEMDAS

Because division comes before subtraction, we deal with that part first

6 ÷ 2 = 3

Then we subtract

17 – 3 = 14

So we have

(14) + 4 × 3

Multiplication comes before addition so we multiply first

4 × 3 = 12

14 + 12 = 26

So 26 is what this expression equals, not 28.5

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ESET1140: Intermediate Technical Algebra Copyright © 2024 by froenico. All Rights Reserved.