In each and every discipline there is a way to do things and a way not to do things.
Order of operations fall under the same category and must be performed also in a certain way. The order of operations is:
3) Multiplication or Division, left to right
4) Addition or Subtraction, left to right.
P: Parentheses/Grouping Symbols.
All operations located inside the parenthesis must done First. In case there is more than one set of parentheses, the operation should begin from the most interior set , and work your way toward outside.
E: Exponents. Determine the value of the exponents.
M/D: Multiply/Divide. In order to obtain the right result, one must work from left to right.
A/S: Add/Subtract. Again this is the same principle, work from left to right.
For example, this is how we work out this expression:
9 + 3 X 2 – 4 X 3 + 9
Let us rewrite the expression
9 + (3 X 2) – (4 X 3) + 9
Let's work with the first parentheses:
9 + 6 – (4 X 3) + 9
Let us work with the second parentheses:
9 + 6 – 12 + 9
We can solve the expression this way
9 + 6 = 15 - (12 + 9) = -3
We now have:
15 – 3 = 12.
As you can see 15 is bigger than – 3. The result must carry the sign of the bigger number. In order to familiarize with these rules, think of the letters PEMDAS ( parentheses
– exponents – multiplications – divisions – additions – subtractions). Sometimes they refer to it as : P lease E xcuse M y D ear A unt S ally.