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Order of operations

Order of operations

This order of operations convention is as follows.

  1. Evaluate any expressions in brackets first.
  2. THEN evaluate any functions (e.g. powers, roots, trigonometric functions, logarithms).
  3. THEN evaluate any multiplications or divisions.
  4. THEN evaluate additions or subtractions.
  5. OTHERWISE operations of equal priority are evaluated left to right.

For example:

\( \newcommand{\eqncomment}[2]{\small{\text{ #2}} } \newcommand{\ceqns}{\begin{array}{rcll}} \newcommand{\ceqne}{\end{array}} \) \[ \ceqns && 8-12\div(7-4\times2) &\eqncomment{0.5}{evaluate the brackets first,}\\ &&&\eqncomment{0.5}{multiplication first,} \\ &=& 8-12\div(7-8) & \eqncomment{0.5}{evaluate the brackets,} \\ &=& 8-12\div -1 &\eqncomment{0.5}{complete the division,} \\ &=& 8-(-12) \\ &=& 8+12 &\eqncomment{0.5}{finally, complete the addition,} \\ &=& 20 \ceqne \]


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