Module_02 // Logic
ORDER OF OPERATIONS
Mathematics is a language with strict grammar. You cannot simply read an equation from left to right. You must follow the hierarchy of command: PEMDAS.
[ THE_PRIORITY ]
P
Parentheses
Groupings first. ( ) { } [ ]
E
Exponents
Powers and Square Roots. x² √
MD
Mult / Div
Equal Rank! Left to Right.
AS
Add / Sub
Equal Rank! Left to Right.
The Left-To-Right Trap
Multiplication does not come before Division by default. They are equal. You must execute whichever appears first from left to right.
Conflict Resolution
10 - 2 + 5
Literal (Wrong)
10 - 7 = 3
Standard (Correct)
8 + 5 = 13
Interactive Lab
Operation Deconstructor
Click the next step
Multiply before you Add.
GEMA
A modern alternative: Grouping, Exponents, Multiplication (includes Div), Addition (includes Sub).
Implied Operators
A number touching a parenthesis denotes multiplication. 2(3) → 2 × 3 = 6
Verification Protocol
Knowledge Check: Order of Operations1 / 3
In the expression "5 + (3² × 2)", which operation must you perform absolutely first?
Rule Mastery
You have unraveled the hierarchy of math grammar.