Chapter 8: The Order of Operations

8.1 Why Do We Need Rules?

In English, the placement of a comma can change the meaning of a sentence. In Algebra, the order in which you calculate can change the value of an expression. To keep math consistent, we follow an agreed-upon hierarchy.

Parentheses Exponents Multiplication & Division Addition & Subtraction

Commonly remembered by the acronym PEMDAS (Please Excuse My Dear Aunt Sally).

8.2 The Hierarchy in Detail

Parentheses ( ): Always clear out the inside of grouping symbols first.
Exponents: Calculate powers like x2 before doing basic operations.
Multiplication and Division: These are equal in rank. Do them as they appear from left to right.
Addition and Subtraction: These are also equal in rank. Do them last, from left to right.

Warning: A common mistake is thinking Multiplication always comes before Division. If Division appears first on the left, do it first!

8.3 Modern Walkthrough

Problem: Evaluate 10 + 2 • (5 - 3)2

Step 1 (Parentheses): 10 + 2 • (2)2

Step 2 (Exponents): 10 + 2 • 4

Step 3 (Multiplication): 10 + 8

Final Answer: 18

8.4 Real-World Logic: Coding and Calculators

If you type 10 + 5 * 2 into a modern spreadsheet or a programming language like Python, it will return 20. This is because computers are hard-coded to follow these exact Algebraic laws. Understanding the order of operations isn't just about passing a test—it's about speaking the same language as the technology we use every day.

Chapter 8 Review

Calculate the following using the correct order:

15 - 3 • 4
(10 + 2) / 3
5 • 23
20 / 5 • 2 + 1

Disclosure: This page contains affiliate links; we may earn a commission from qualifying purchases.

Doctor's Recommendation: Respect the Order

PEMDAS is the law of the land in Chapter 8. A physical reminder like a PEMDAS Desk Sign acts as a permanent "Aunt Sally" on your shoulder, ensuring you never skip the parentheses or move to addition before multiplication is finished.

View PEMDAS Decor on Amazon

Reference: image_80c323.png