What is PEMDAS? – Definition, Rules, Examples

Introduction to PEMDAS

In this topic, we will discuss the importance and order of operations in mathematics if the acronym PEMDAS. Besides, without the given guidelines of the objective nature of mathematical calculation could not exist. The full form of PEMDAS is parenthesis, exponents, multiplication, division, addition, and subtraction. Moreover, the easiest way to memorize this acronym is the phrase ‘Please Excuse My Dear Aunt Sally’.

Furthermore, the calculations have to be done in the order provided means that what we have to first, second, third, and so on until the calculation is complete. Besides, if there are grouping symbols in the expression then PEMDAS will tell you to calculate within the symbols first.

Importance of PEMDAS

For obtaining the correct answer with the guidelines we need PEMDAS. For example, calculate 3 × 4 + 9 so to know the answer we can first undertake multiplication and then add the numbers we get 12 + 9 = 21. Also, there is another way in which we add first and after that multiply the product 3 × 13 = 39.

Hence, the question here is in both the answer which one is correct? The correct answer is ordering one because it uses PEMDAS which states that first multiply ‘M’ and then add ‘A’.

PEMDAS Symbols

• P is the first letter that means you have to first solve the calculation in a grouping.
• After that, look for E that is exponents and ignore any other operation, and take the exponents to their powers.
• The PEMDAS ‘M’ appears before ‘D’ but it does not mean that you have to multiply first then divide but you have to follow the order of question here mans from left to right whichever appears first.
• A and S have also the same property means whichever will appear first will be solved first.

Use of PEMDAS

The use of PEMDAS is explained clearly with the help of the formula.

Example

Suppose you are told to simplify the following expression

1. 24 + 6 / 3 × 5 × 23 -9
2. 36 – 2 (20 + 12 / 4 × 3 – 2²) + 10

Solution 1

1^ststep 24 + 6 / 3 × 5 × 8 – 9

2^ndstep 24 + 2 × 5 × 8 – 9

3^rdstep 24 + 10 × 8 – 9

4^thstep 24 + 80 – 9 = 95

In this, We follow the PODMAS and firstly look for grouping symbols but there were none. Secondly, we look for exponents, which we find as 23 so we solved it.

Thirdly, I look or M (multiplication) and D (division) from left to right and after finding them we solve them. Finally, after solving multiplication and division we look for addition ‘A’ and subtraction ‘S’ in the left to right order of whichever appears first.

Solution 2

1^ststep 36 – 2(20 + 12 / 4 × 3 – 22) + 10

2^ndstep 36 – 2(20 + 12 / 4 × 3 – 4) + 10

3^rdstep 36 – 2(20 + 3 × 3 – 4) + 10

4^thstep 36 – 2(20 + 9 – 4) + 10

5^thstep 36 – 2(25) + 10

6^thstep 36 – 50 + 10

7^thstep 36 – 50 + 10 = – 4

In this solution, over all, we use the same method but the only difference is there is a grouping symbol.

Solved Question For You

Question. Which of the following statement/s is/are correct related to PODMAS?
1. We can memorize it as Please Excuse My Dear Aunt Sally
2. It includes addition, subtraction, multiplication, division, exponents, and parenthesis.

A. Only 1
B. Both 1 and 2
C. Only 2
D. Neither 1 nor 2

Answer. The correct answer is option B.

Download Toppr app for Android and iOS or signup for free.