Everyday Arithmetic & How Calculators Evaluate Expressions
Whether you are splitting a restaurant bill, calculating change, or verifying dimensions, arithmetic is part of daily life. Even a query as simple as 2 + 2 = 4 relies on mathematical conventions that computers follow strictly.
The Universal Order of Operations: PEMDAS / BODMAS
When an equation contains multiple operators, calculators don't simply evaluate from left to right. They follow the established hierarchy of mathematical precedence:
- B / P: Brackets or Parentheses first — solve inside
( )before anything else. - O / E: Orders or Exponents — powers, square roots, and exponentiation like
2^3 = 8. - D & M: Division and Multiplication — evaluated in order from left to right.
- A & S: Addition and Subtraction — evaluated in order from left to right.
Why 2 + 2 × 2 is 6 (Not 8)
A classic internet puzzle asks: What is 2 + 2 × 2?
If you compute left to right: (2 + 2) = 4, then 4 × 2 = 8 (Incorrect).
By PEMDAS rules, multiplication comes first: 2 × 2 = 4, then 2 + 4 = 6 (Correct).
5 Mental Arithmetic Tricks for Daily Speed
- Multiplying by 5: Halve the number, then multiply by 10. For example: 48 × 5 = 24 × 10 = 240.
- Multiplying by 9: Multiply by 10 and subtract the original number. For example: 37 × 9 = 370 – 37 = 333.
- Squaring numbers ending in 5: Multiply the first digit by (digit + 1), then append 25. For 35²: 3 × 4 = 12 → 1,225.
- Quick Tip Calculation (15%): Find 10% (move decimal 1 place left), then add half of that value.
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