Order of Operations (PEMDAS)

- - Pre-Algebra, Lesson

Order of Operations - HeaderThe order of operations in mathematics, also known as PEMDAS which stands for (Parentheses, Exponents), (Multiplication, Division), and (Addition, Subtraction), is generally use to perform indicated operations in algebra or arithmetic. The calculator itself is performing operations based on PEMDAS rules.

If a group of you were to do these following simple problems, it is not very likely that you would all agree on the answers. Try these:

  1. 8+5-2
  2. 6+9\div 3
  3. 12-2\times 5
  4. 2\cdot 3^2
  5. \sqrt{4^3}
  6. 8\div4\times 2

Well, what did you get? You probably didn't have any trouble getting 11 for the first one, or 8 for the fifth. What about the second one? Did you say 5 or 9? And for the third, did you get 50 or 2? What about number 4: 18 or 36? And the number 6: 4 or 1?

Since some problems like these have two or more possible answers, hence it is necessary to set rules to avoid confusion. For this purpose we divide our six operations into three groups, each group containing a pair of opposite operations. These are (parentheses, exponents), (multiplication, division), and (addition, subtraction). For each pair, the operations must be processed from left to right.

  1. (8+16)\div2^3-2\times 3=(24\div 8-6)=3-6=-3
  2. 5-\left \{ 2-(8-3))+4 \right \}^2-2\times 3=5-\left \{ 2-(5)+4 \right \}^2-6=5-\left \{ 1 \right \}^2-6=-2

Order of Operations (PEMDAS) Worksheets

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