PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given at least two operations in an equation, the order of the letters in PEMDAS tells you which operation to do first, second, third, and so forth, until the equation is solved. In the event that there parentheses in an equation, PEMDAS tells you that you should solve for the inside before moving on to the rest of the equation 

The word  PEMDAS and the words bracket, examples, duplication, division, expansion, subtraction may not be memorable for somebody learning this acronym, so there is a helpful mnemonic device to aid its memorization: Please Excuse My Dear Aunt Sally. However, it might be simpler to remember the order of operations in PEMDAS. 

Why is PEMDAS important? 

Without PEMDAS, there are no rules to acquire just one right answer. As a basic model, to figure 2 * 4 + 7, I could multiply 2 and 4 first, and add 7 afterward to get 15. I also have the choice to add 4 and 7 first, and then multiply by 2 to get 22. Which answer is right? Utilizing PEMDAS, the true correct answer is 15, in light of the fact that the order for the letters in PEMDAS tell me that the multiplication, M should be performed before the addition, A. 

Here’s a clarification of the guidelines given in PEMDAS: 

P as the first letter implies you should complete any computations in parentheses first. 

Next, search for exponents, E. Solve any numbers with exponents

Despite the fact that M for multiplication in PEMDAS precedes D for division, these two activities take the same priority. Complete just these two operations in the order that they appear from left to right. 

Despite the fact that A for addition in PEMDAS precedes  S for subtraction, these two operations also have the same priority, like M and D. You search for these last two tasks from left to right and finish them in that order.

Using PEMDAS in a Mathematical Expression

Example One:

If you are told to calculate or simplify the expression 24 + 6 / 3 * 5 * 2^3 – 9, how would you implement PEMDAS? First, you look for any parentheses (P). There are none, so then look for any exponents (E). Since there is 2^3, you do that calculation first, without performing any other calculation.

24 + 6 / 3 * 5 * 8 – 9

Now, you look for multiplication (M) and division (D) from left to right, ignoring any addition or subtraction. The next series of calculations will produce the following:

24 + 6 / 3 * 5 * 8 – 9

24 + 2 * 5 * 8 – 9

24 + 10 * 8 – 9

24 + 80 – 9

Lastly, you complete addition (A) and subtraction (S) from left to right.

24 + 80 – 9 = 95

Example Two:

Calculate 36 – 2(20 + 12 / 4 * 3 – 2^2) + 10. Since there are parentheses, I must perform all calculations inside of the parentheses first, using PEMDAS for any operations in that expression.

36 – 2(20 + 12 / 4 * 3 – 2^2) + 10

36 – 2(20 + 12 / 4 * 3 – 4) + 10

36 – 2(20 + 3 * 3 – 4) + 10

36 – 2(20 + 9 – 4) + 10

36 – 2(25) + 10