Order of operations

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There are quite a few mnemonics for the order of operations. A common one in the UK is BODMAS:

  • Brackets
  • Orders
  • Division
  • Multiplication
  • Addition
  • Subtraction

Elsewhere, PEMDAS is popular.

But division and multiplication have equal precedence, and so do addition and subtraction. A common convention is that operations with equal precedence are evaluated from left to right.

This leads to all sorts of misunderstandings.

\( 8 \div 2(1+3) = 16 \text{ or } 1 \)