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Order of Operations

The Hook

Please Excuse My Dear Aunt Sally.

What is it?

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

Time Travel (History)

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

Cheat Code

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

Practice This Now!

The Field Guide

In 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).

In The Real World: 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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Booby Trap!

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.

Real World Challenge
"You buy 2 shirts for $10 each and use a $5 coupon. Calculate cost: 2 x 10 - 5."
The Logic: Multiply first: 2 x 10 = 20. Then Subtract: 20 - 5 = 15. Cost is $15.

Training Drills

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