**PEMDAS** (or what others remember as Please Excuse My Dear Aunt Sally) is simply an acronym which stands for ‘Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction’. If you have a number sentence with two or more operations, the order of the letters in PEMDAS tells you how to go about these operations. It tells you what to calculate first, second, third and so on, until everything is done.

PEMDAS serves as a guideline so all of us can obtain only one correct answer in a math expression. Without PEMDAS, we can end up having two or more different answers to a single equation.

For example, 5 + 4 x 3 = ?

**WITHOUT PEMDAS,**

- We can do the addition first and get: 9 x 3 = 27
- or we can do the multiplication first and get 5 + 12 = 17

**WITH PEMDAS, however, we know these rules:**

**P means Parenthesis –**so you need to complete calculations in grouping symbols first.**E means Exponents**– so you should raise numbers with exponents to their respective powers before doing any other operation.**MD means Multiplication AND Division –**these two operations actually have the same rank so you should complete these two operations in the order they occur from left to right.**AS means Addition AND Subtraction –**again, these two operations have the same rank so you should complete these two operations in the order they occur from left to right.

Applying the PEMDAS Rules, we know that the correct way to solve the previous example is: 5 + 4 x 3 = 5 + 12 = 17

Another example: 36 – 2 (20 + 12 / 4 * 3 – 2^2) + 10

P: Complete calculations in grouping symbols (parenthesis) first

So let’s explore those which are inside the parenthesis…

E: Raise numbers with exponents to their respective powers

36 – 2 (20 + 12 / 4 * 3 – 4) + 10 =

MD: Multiply AND Divide first – from left to right

36 – 2 (20 + 3 * 3 – 4) + 10 =

36 – 2 (20 + 9 – 4) + 10 =

AS: Add AND Subtract – from left to right

36 – 2 (29 – 4) + 10 =

36 – 2 (25) + 10 =

Now that we’re done with all the operations inside the parenthesis, we go ahead with the calculations outside of the symbols.

MD: Multiply and Divide first – from left to right

36 – 2 (25) + 10 =

36 – 50 + 10 =

AS: Add and Subtract – from left to right

36 – 50 + 10 =

– 14 + 10 = -4

**FINAL ANSWER = -4**

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