Order of Operations

When performing arithmetic operations there is exactly one correct answer. To avoid confusion, mathematicians have devised a standard order of operations for calculations involving more than one arithmetic operation.

            1st: Perform any calculations inside parentheses, doing the innermost first.

            2nd: Simplify any exponential expressions.

            3rd: Work all multiplications and divisions, from left to right, as they appear.

            4th: Work all additions and subtractions, from left to right, as they appear.          

So you do not get confused remember PEMDAS which stands for Parentheses, Exponents, Multiplication-Division, Addition-Subtraction.

        In California, we say Powerful Earthquakes May Deliver After-Shocks. 

Example 1:

Simplify. 2 + 3 × 4

Multiplication must be done before addition.

            = 2 + 12

            = 14

Example 2:

Simplify. 1 + 3 × 42

Exponential expressions are simplified before multiplication or addition.

            = 1 + 3 × 16

Multiplication is done before addition.

            = 1 + 48

            = 49

Example 3:

Simplify. 3 + 2(5 – 7)

Do parentheses first.

            = 3 + 2(–2)

Multiply and then add.

            = 3 + (–4)

            = –1

Be especially careful with problems like the following.

       (3 × 4)2 = 122 = 144 because parentheses come before exponents, BUT 3 × 42 = 48 because exponents come before multiplication.

       (–4)2 = (–4)(–4) = 16 BUT –42 = – 4 × 4 = –16

       3 + 4(5 + 6) ≠ 7(5 + 6) because multiplication gets done before addition.  

       So, 3 + 4(5 + 6) = 3 + 4(11) = 3 + 44 = 47.