orderofop

Order of Operations:
The order in which we SIMPLIFY problems that contain more than one math operation:
               FIRST do all Parentheses and Exponents as you come to them reading your
                problem left to right.
                    Parentheses include all grouping symbols
                          a.   ( 12 - 5 )
                          b.   [ 12 -5 ]
                          c.   { 12 - 5 }
                          d.   and the fraction bar.   If your problem contains a fraction bar do all the
                                math in the numerator (top) then do all the math in the denominator
                                (bottom) and last of all divide the numerator answer by the
                                denominator answer.
                      If you have one set of parentheses inside another work from the inside out.
                                { 12 - (2 + 3) } =
                                { 12 - (5) }         =
                                 12 - 5              =
                                     7
                   Exponents are indicated by some number (called the base) raised to a power.
                  We will use the carrot key, " ^ " , to indicate raised to the power or exponent
                   For example 3 squared or 3 raised to the power of 2 will be written as
                       3 ^ 2 = 3 x 3 = 9
          EXAMPLE
                24 / 2 - (5 - 4 ) x 2 ^ 3 =      Here we would and 5 - 4 first and then
                 24 / 2 - 9 x 8              =      raise 2 to the third power

           After we have calculated everything in parentheses and all exponents, SECONDLY
               we do all Multiplication and Division as you come to it reading your problem
                from left to right.

        EXAMPLE
               24 / 2 - (5 - 4 ) x 2 ^ 3     =     Here we would and 5 - 4 first and then
                   24 / 2 - 1 x 8               =     raise 2 to the third power
                                                            Next we will divide 24 by 2 because next we do all
                     12   - 8                   =    multiplication and division as it appears in our
                                                            problem form left to right. Then we multiply 1 by 8

                  LAST of all we do Addition and Subtraction as you come to it reading your
                   problem from left to right.

          EXAMPLE
               24 / 2 - (5 - 4 ) x 2 ^ 3     =     Here we would and 5 - 4 first and then
                   24 / 2 - 1 x 8               =     raise 2 to the third power
                                                            Next we will divide 24 by 2 because next we do all
                    12   - 8                   = multiplication and division as it appears in our
                                                            problem form left to right. Then we multiply 1 by 8
                       4                           The answer of our example is 4.