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Order of Operations

Overview

Please Excuse My Dear Aunt Sally.

What is it?

The strict hierarchy of math steps: Parentheses, Exponents, Multiply/Divide, Add/Subtract.

History

Standardized to ensure that 2 + 3 x 4 always equals 14, not 20, anywhere in the world.

Key Idea

Multiplication and Division are tied (Left to Right). Addition and Subtraction are tied (Left to Right).

Practice This Topic

Concept Guide

Plain English: Math has grammar. You can't just read left-to-right. You must handle the powerful stuff first (Groups and Powers) before the weak stuff (Adding).

Real-world example: Coding. If a programmer types `total = cost + tax * discount` without parentheses, the computer calculates tax * discount first!

How to do it

  1. P: Solve inside Parentheses first.
  2. E: Solve Exponents (powers).
  3. MD: Multiply OR Divide, whichever comes first going Left to Right.
  4. AS: Add OR Subtract, whichever comes first going Left to Right.
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Common Pitfall

Always doing Multiply before Divide. They are equals! If you see 10 / 2 * 5, you do the division first because it's on the left.

Word Problem
"You buy 2 shirts for $10 each and use a $5 coupon. Calculate cost: 2 x 10 - 5."
Reasoning: Multiply first: 2 x 10 = 20. Then Subtract: 20 - 5 = 15. Cost is $15.

Practice Examples

The Classic Trap
2 + 3 x 4 2 + 12 14
Mult beats Add.