Order of Operations
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The Order of Operations is a mathematical and Algebraic concept. It is used to simplify expressions and equations. The Order of Operations defines the order in which different operations should be simplified. It is used for operations such as addition, subtraction, multiplication and division. It is critical to the solution of equations or expressions in the mathematics world.
Order of Operations
In many math problems, you will have to solve more than one operation in order to get the answer. Mathematicians have agreed on a correct order to perform these operations, and it is very important that you know these rules. Whenever you are solving a problem with more than one operation, you will need to know the correct order in which to solve the problem. Rules for solving problems with multiple operation signs; addition, subtraction, multiplication, division and grouping symbols; parentheses or brackets are as follows:
First, working left to right solve any math operations within parentheses and change any exponential notations to standard notations.
Next, again starting on the left and working right, across the problem, solve any multiplication and division in the problem.
Lastly, and always lastly, working again from left to right solve any addition or subtraction left in the problem.
The result is the answer to the problem.
Example: 12 – 2²(9 – 6) + 5 ÷ 5
First … Parenthesis and Exponent … what ever comes first as you work from left to right.
12 – 2²(9 – 6) + 5 ÷ 5
= 12 – 4(9 – 6) + 5 ÷ 5
= 12 – 4(3) + 5 ÷ 5
Once you have solved the operations within the parentheses they are no longer being used to define a grouping to do first, but now stand for multiplication.
Second … Multiplication and Division … what ever comes first as you work from left to right.
12 – 4(3) + 5 ÷ 5
= 12 – 12 + 5 ÷ 5
= 12 – 12 + 1
Third and lastly … Addition and Subtraction … what ever comes first as you work from left to right.
12 – 12 + 1
= 0 + 1
= 1
The answer to the problem.
12 – 2²(9 – 6) + 5 ÷ 5 = 1
A good way to remember the Order of Operations is by memorizing the phrase “Please Excuse My Dear Aunt Sarah”. The first letter of each word of this phrase is key in remembering the order.
P = Parentheses
E = Exponent
M = Multiplication
D = Division
A = Addition
S = Subtraction
Memorizing the phrase “Please Excuse My Dear Aunt Sarah” will help you remember the Order of Operations.
Another good way of memorizing the Order of Operations is the word BIMDAS. The letters of the word represent the first letters of each word in the order of operations.
B stands for Brackets
I stands for Indices (indices are the same as exponents)
M stands for Multiplication
D stands for Division
A stands for Addition
S stands for Subtraction
