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: Do any calculations inside parentheses or other grouping symbols, starting with the innermost and working out.

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 don't get confused, remember PEMDAS which stands for Parentheses, Exponents, Multiplication-Division, Addition-Subtraction.

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

Example:

Simplify 3 + 2 × (5 – 7)2.

Do the operation in parenthesis first.

            = 3 + 2 × (–2)2

Then evaluate the exponent. Since the negative sign is inside the parenthesis, this means (–2) × (–2).

            = 3 + 2 × 4

Multiply, and then add.

            = 3 + 8

            = 11

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.

Also, be careful with fractions. The fraction bar acts like a grouping symbol, so simplify the numerator and denominator first.

        

You can think of it this way: if you rewrote the fraction on one line, using the division symbol, you would need parentheses.