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What is PEMDAS Rule?

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What is PEMDAS? Is it the name of a mathematician? When you see this name you get this kind of confusion. But the answer is no. It’s not the name of a mathematician, it is just an acronym used to remember the order of operations.

It is quite essential to remember this acronym to solve mathematical expressions involving multiple operations and brackets. Let us discuss this PEMDAS rule in detail now.

PEMDAS Full Form | PEMDAS Meaning

PEMDAS

An operation’s order is recalled by the first letter of the word it represents. Thus PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

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The name PEMDAS is used in the USA and France. Different countries use different mnemonics. Mnemonics are an effective means of memorizing and remembering information. 

PEMDAS uses letters to indicate what to calculate first, second, third, etc., until the calculation is complete. It can also be remembered as “Please Excuse My Dear Aunt Sally”.

Why is the PEMDAS Rule Required?

In the absence of PEMDAS, there is no guideline to obtain the only correct answer. For example, I could multiply 2 + 6 5  and then add to get 32. I can also solve this by adding first and then multiplying to get 40. Which is correct? You can find the correct answer by using PEMDAS. In PEMDAS multiplication comes first before addition. Hence the correct answer is 32. Thus PEMDAS rule helps us in finding the correct answer for the problems involving multiple operations.

Order of Operations:

As you know PEMDAS expands as Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Hence for a given problem following steps are involved to get a correct solution.

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  1. Parentheses: If parentheses or brackets are involved in a problem then, Start solving the operations within the common brackets first, next solve flower brackets, lastly solve square brackets. 

Eg: Solve: [{(4 2) + 5} – 4]

Solution: (4 2) = 2, {(4 2) + 5} = {2 + 5} = 7 then [{(4 2) + 5} – 4] = [7 – 4] = 3

  1. Exponents: After solving the parentheses one must look for exponents present. Solve the exponents.

Eg: Solve: (36÷4) 

Solution: 36 4 = 9 then (36÷4) = 9 = 3

  1. Multiplication or division: Multiplication or division is performed after exponents. Remember in PEMDAS, M comes before D does not mean that the multiplication must be performed first. You have to solve from left to right always, if division comes first from the left side, then you have to perform division only and then multiplication.

Eg: Solve: 25 5 + (9 – 22)

Solution: (4 – 22) = (9 – 4) = 5

25 5 + (4 – 22) = 25 5 + 5 

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Next perform division

25 5 = 5

Now 25 5 + 5 = 5 + 5 = 10

  1. Addition or Subtraction: Like multiplication and division, addition or subtraction can be performed in any order. Given a problem is solved from left to right, the operation that comes first from left is performed first. 

Eg: Solve: 25 – 5 + (15 3)

Solution: (15 3) = 5

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25 – 5 + (15 3) Here subtraction comes first from left so perform subtraction.

25 – 5 = 20, 25 – 5 + (15 3)  = 20 + 5 = 25

With this ends the order of operations.

Hope you understood the PEMDAS rule well. If you still want more examples to be solved to understand the concept better, I recommend Cuemath classes. There you get ample examples to solve. The concepts are better understood if you attend the live classes. You can log on to the Cuemath website for more details of the classes.

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