Order of Operations: PEMDAS, BODMAS & Calculator Traps
Why viral math equations cause internet arguments and how calculators parse order of operations.
Why We Need Order of Operations
Without standardized rules, an expression as basic as 3 + 4 × 2 could yield either 14 (if done left to right) or 11 (if multiplication is performed first). The mathematical convention universally establishes multiplication as higher priority than addition, giving the answer 11.
PEMDAS vs. BODMAS: Two Names, Identical Logic
• PEMDAS (US): Parentheses, Exponents, Multiplication & Division, Addition & Subtraction.
• BODMAS (UK, Commonwealth): Brackets, Orders (powers/roots), Division & Multiplication, Addition & Subtraction.
Crucial Rule: Multiplication and Division share equal priority and are evaluated from left to right. Likewise, Addition and Subtraction share equal priority and are evaluated left to right.
The Classic Viral Trap: 8 ÷ 2(2 + 2)
Evaluating 8 ÷ 2(2 + 2):
1. Inside parentheses first: (2 + 2) = 4. The expression becomes: 8 ÷ 2 × 4.
2. Division and multiplication have equal priority, so proceed left to right: 8 ÷ 2 = 4.
3. Finally: 4 × 4 = 16.
Some people get 1 because they mistakenly treat implied multiplication 2(4) as higher priority than division. Modern calculators and programming languages follow left-to-right rules and output 16.
Calculator Trap: −3² vs. (−3)²
In standard mathematical notation, exponents take precedence over the unary minus operator:
• −3² means −(3²) = −9.
• (−3)² means (−3) × (−3) = +9.
Always wrap negative numbers in parentheses when squaring them on a scientific calculator!