lesson 4: Order of Operations




lesson 4

Order of Operations

  • When evaluating mathematical expressions we follow this order of operations:
  1. Parentheses (from the inside out)
  2. Exponents (from right to left)
  3. Multiplication and division (from left to right)
  4. Addition and subtraction (from left to right)

Example:

Evaluate the expression: $$\eqalign{
& {{2 \times {3^3} \times {4^2} – 31} \over {4\left[ {5 – \left( {3 – 7} \right) \times 6} \right] + 3}} \cr
& = {{2 \times {3^3} \times {4^2} – 31} \over {4\left[ {5 – \left( { – 4} \right) \times 6} \right] + 3}} \cr
& = {{2 \times {3^3} \times {4^2} – 31} \over {4\left[ {5 – \left( { – 24} \right)} \right] + 3}} \cr
& = {{2 \times {3^3} \times {4^2} – 31} \over {4\left[ {5 + 24} \right] + 3}} \cr
& = {{2 \times {3^3} \times {4^2} – 31} \over {4 \times 29 + 3}} \cr
& = {{2 \times 27 \times 16 – 31} \over {4 \times 29 + 3}} \cr
& = {{864 – 31} \over {116 + 3}} \cr
& = {{833} \over {119}} \cr
& = 7 \cr} $$


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