PEMDAS

The word "Operations" means to perform a task such as addition, subtraction, multiplication, division, etc. But, when you see something like ...

7 + (6 × 52 + 3)

You end up wondering about what part should you calculate first? Would it be better to start from the left and go to the right? Or start from the right and proceed to the left? It is very important to calculate them in the right order because if you do it in the wrong order, you’ll end up with a wrong answer. To solve this problem, our forefathers, the knowledge holders, agreed to follow a few rules to avoid any mistake. This is where PEMDAS rule which is more commonly known as  BODMAS or BEDMAS took its birth. Now, what does ‘PEMDAS’ stand for? Let’s break it and see.

P – Parentheses  [{()}]

E – Exponents (Powers and Roots)

MD- Multiplication & Division (left to right) (× and ÷)

AS – Addition & Subtraction (left to right) (+ and -)

Basically, there is absolutely no issue if you say that ‘PEMDAS’ is an acronym (order of operations pemdas) for words such as parenthesis, exponents, multiplication, division, addition, and subtraction. If you are given expression with two or more operations, you would definitely call for PEMDAS as your savior as it helps you to know what to calculate first, second, and thereon, until the calculation is completed. Not forgetting about the group symbols in the expression, PEMDAS rule tells you to first calculate within the grouping symbols.

To make it interesting and easy to remember pemdas meaning, there is a phrase that has been attached to it for you to remember it unforgettable. Here it is, PEMDAS: Please Excuse My Dear Aunt Sally. Now, you can either remember PEMDAS by the phrase or by the actual meaning of it, i.e.,  parenthesis, exponents, multiplication, division, addition, and subtraction. 

Why Is PEMDAS Important?

Suppose a teacher writes an expression on the blackboard and asks you to solve it. Let’s consider this:  2 * 4 + 7. It seems very easy, right? You simply multiply 4 with 2 to get 8 and then add 7 to get 15. But what if another boy did the addition first to get 11 and then multiplied to get 22. What would you do now? How would you know who has the right answer? To avoid this confusion we use PEMDAS rule. It is like a guideline to help you get only one correct answer. 

If you do the sum using PEMDAS rule, then the only true and correct answer is 15. This is because according to the order of the letters in PEMDAS, multiplication (M) appears before addition (A) Hence, it is only after you do your multiplication, you can proceed to addition. 

Explanation Of The Rules In PEMDAS:

• P: The word ‘P’ indicates parentheses. Therefore,  Priority is given to solve the calculation or equation which is present in the parentheses or brackets first. There are three types of brackets such as small brackets( ), curly brackets{ } or big brackets[ ]. 

• E: Exponentials; the second letter of the word PEMDAS. Therefore, such expressions should be attended first before proceeding to operations of multiplication, division, addition, and subtraction. Usually, exponentials are expressed in power or roots.

• MD: Multiplication followed by division is the next operations that are to be performed before reaching out to addition or subtraction. The calculation is done from left to right. 

• AS: Finally! Here comes the time for addition and subtraction. This also is done in the same manner as multiplication and division i.e., from left to right.

P as the first letter indicates that you complete any calculations that are in grouping symbols first.

Done and dusted, look for exponents, E. Ignore any other operation that comes your way and work on any number with exponents to their respective powers.

In Spite of M for multiplication in PEMDAS coming before D for division, the two operations actually hold the same priority. Thus, complete only those two operations in the order they occur from left to right. 

Again, A for addition is in PEMDAS comes before S for subtraction, but both of them hold the same priority. Look out for these two operations from left to right and complete them in that order.

Few pemdas examples with answers for you:

Here are a few pemdas examples for you to have a better grasp of the topic.

Example 1:  Solve 24 + \[\frac{6}{3}\] x 5 x \[2^{3}\] - 9.  

Solution 1: Step 1) We start with solving the exponent first.

24 + \[\frac{6}{3}\] x 5 x \[2^{3}\] - 9 → 24 + \[\frac{6}{3}\]x 5 x 8 - 9 

Step 2) Our next step is to divide.

24 + \[\frac{6}{3}\] x 5 x 8 - 9 → 24 + 2 x 5 x 8 - 9

Step 3) In this step we multiply.

24 + 2 x 5 x 8 - 9  → 24+10 x 8 - 9

 24 + 10 x 8 - 9 → 24 + 80 - 9

Step 4) in this step we first add and then subtract

 24 + 80 - 9 → 104 - 9 →95

Thus, 95 is the final answer. 

Example 2: Calculate 36 - 2(20 + 12 / 4 3 - 2^2) + 10.

Solution 2: Step 1) Our first step is to evaluate the exponent.

36 - 2(20 + \[\frac{12}{4}\] x 3 - \[2^{2}\]) + 10 → 36 - 2(20 + \[\frac{12}{4}\] x 3 - 4) + 10

Step 2) We have to divide in this step.

36 - 2(20 + \[\frac{12}{4}\] x 3 - 4) + 10 → 36 - 2(20 + 3 x 3 - 4) + 10

Step 3) The Next step is to multiply.

 36 - 2(20 + 3 x 3 - 4) + 10  → 36 - 2(20 + 9 - 4) + 10

Step 4) This step includes addition and subtraction.
36 - 2(20 + 9 - 4) + 10  → 36 - 2(25) + 10

Step 5) In this step we have to avoid the operation of addition and subtraction and first multiply.

36 - 2(25) + 10 → 36 - 50 + 10

Step 6) now, finally we end this sum by performing addition and subtraction.

36 - 50 + 10  → 24 

Thus, the final answer is 24.