PEMDAS (or its word format of "Please Excuse My Dear Aunt Sally") is a memory device for the order of operations in mathematics.
What Does Each Letter in PEMDAS Mean?
The P in PEMDAS is for parentheses ( ).
The E in PEMDAS is exponents.
The M in PEMDAS means multiplication.
The D in PEMDAS signifies division is the next order of operation.
The A in PEMDAS relates to addition.
The S in PEMDAS correlates with subtraction.
How do PEMDAS and the Order of Operations Work?
The order of operations begins with the "P" word, which is "parentheses". Any part of an equation that includes parentheses must be simplified first.
After all operations inside parentheses are completed, a math problem must next be simplified with regards to any exponents. Any part of the equation raised to a certain degree (e.g., squared, cubed) must be simplified next.
The "M" and "D" steps are combined in the third round of simplification. Any parts of the equation where numbers are being multiplied or divided must be simplified next. Both operations are taken in turn, not of whether they are all multiplications or divisions of terms, but rather, by their location from left to right in a given equation.
The final order of operations step combines addition and subtraction. Any parts of the equation dealing with either operation of addition or subtraction must be done next. The ordering goes from left to right and it does not matter if it is subtraction or addition procedures first; the importance is that the operations are simplified in order from left to right.
The best way to learn the order of operations is to see it being used now that one knows what PEMDAS stands for.
What is an Example of PEMDAS Being Used?
Here is an equation:
5+16/2-6^2+(5*6)=?
The first step is the parentheses. That means one must simplify (5*6) first, resulting in 30.
Now, the equation looks like this:
5+16/2-6^2+30=?
The second step in the order of operations is to simplify any expression with an exponent. There is 6 raised to the power of 2 (6^2) in this, so that must be the next part of the equation simplified.
As a result, one is now at:
5+16/2-36+30=?
The third step in PEMDAS deals with any multiplication and division from left to right. There is no multiplication since the 5*6 was dealt with in step 1 with parentheses. Therefore, the division (16/2) is next.
This leaves:
5+8-36+30=?
The final step is to simplify addition and subtraction from left to right, starting with 5+8 and ending with 36+30. The final solution leaves the question mark as equal to 7.
Summary
One easy way to remember what the order of operations in mathematics is to remember the phrase PEMDAS. Many school teachers now teach this in mathematics classes, along with the alternative expression of "Please Excuse My Dear Aunt Sally" (in which each of those words starts with the same letter P-E-M-D-A-S). This helps simplify expressions and equations in the correct order, thereby guaranteeing the correct answer on a test, since some operations like multiplication and division change the answer if done in a different sequence. After all, 2 divided by 1 is not equal to 1 divided by 2; order does matter.
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