6 ÷ 2 × (1 + 2) sparks genuine arguments online because people apply the order of operations differently — and the "correct" answer depends on a rule that's simple once you know it, but easy to misremember.

The Rule: PEMDAS / BODMAS

Both acronyms describe the same priority order, just with regional naming differences:

  • Parentheses / Brackets — resolved first
  • Exponents / Orders (powers, roots)
  • Multiplication and Division — left to right, same priority level
  • Addition and Subtraction — left to right, same priority level

The Detail Everyone Forgets

Multiplication and division are equal priority — and so are addition and subtraction. Neither "comes first" over the other in its pair; when both appear at the same level, you work strictly left to right.

This is exactly why 6 ÷ 2 × 3 isn't ambiguous despite looking like it: division and multiplication share priority, so you work left to right — 6 ÷ 2 = 3, then 3 × 3 = 9, not 6 ÷ (2×3) = 1.

Why Order of Operations Exists at All

Without an agreed order, the same string of numbers and symbols could mean different things to different people — order of operations is a shared convention that guarantees everyone reading the same expression gets the same answer.

Why Calculators Sometimes Disagree

Basic calculators evaluate operations as you press keys, left to right, with no awareness of proper priority — typing 2 + 3 × 4 can literally compute (2+3)×4 = 20 instead of the mathematically correct 2+(3×4) = 14. A scientific calculator, by contrast, is built to correctly apply full order of operations to an entire expression.

Step-by-Step: Evaluate Expressions Correctly

  1. Enter your full expression, including parentheses
  2. Let the calculator apply proper order of operations automatically
  3. Use parentheses explicitly whenever you want a specific grouping, rather than relying on default priority

Try It Yourself

Use our free Scientific Calculator — correct order of operations, every time

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