PEMDAS (Order of Operations)

(PEMDAS) is an acronym used to help students in their exponentially difficult journeys through Multiplying, Diving, Adding and Subtracting their way through general education.

P stands for Parentheses

E stands for Exponents

M stands for Multiplication

D stands for Division

A stands for Addition

S stands for Subtraction

This process is called the Order of Operations. Let's delve right into a problem from the book, Chapter 1.7 Problem 49:

32 ÷ 4 - 3

♥ First, we check to see if there are parentheses. There are none, so we skip this step.
♥ Next, are there exponents? No. Skip this step as well.
♥ Multiplication? No.
♥ Division? Eureka! There is division here so we have to do that first.

32 ÷ 4 = 8

♥ Here is an invisible (but equally as important) step: rewrite the problem with your new solution to the division portion.

8 - 3

♥ Is there any addition to be done? No. Skip this step.
♥ Lastly, is there subtraction? Yes! Let's subtract!

8 - 3 = 5

♥ There is nothing more to be done, and you're left with a 5.

The Answer Is 5

Now we're going to try a harder one that uses the entirety of PEMDAS.
**NOTE that I can't get exponents to work, so exponents will be represented in a circle like this: ➀ (Sorry!)
This problem is from the class handout "Section 1.7 Part II - Order of Operations: Problem 7).

35 ÷ [3➁ + (9 - 7) - 2➁] + 10 x 3

Yowza! It looks scary! But just as this problem is your beast to be slain, PEMDAS is your Excalibur.
♥ First, we do parentheses. See the brackets? Everything in there is going to be done first. Brackets are like parentheses and essentially work the same way, and usually contain actual parentheses within them. Let's solve the parentheses inside the brackets.

(9 - 7 = 2)

35 ÷ [3➁ + 2 - 2➁] + 10 x 3

♥ Exponents are next, and they're all inside the brackets.
♥ ** GO LEFT TO RIGHT when there are two of the same type of thing to do, like these exponents.

3➁ = 9

2➁ = 4

35 ÷ [9 + 2 - 4] + 10 x 3

♥ Now continue to solve inside of the brackets, as they serve as parentheses.
♥ We've done parentheses and exponents, and there are no multiplication or division problems in the brackets, so we do addition.

9 + 2 = 11

35 ÷ [11 - 4] + 10 x 3

♥ Finally, finish off the brackets with subtraction.

11 - 4 = 7

35 ÷ [7] + 10 x 3

♥ Now that there is no work to be done within parentheses (or brackets!) we move PEMDAS onto the rest of the problem. No more parentheses, no exponents, but there is multiplication.

10 x 3 = 30

35 ÷ [7] + 30

♥ After multiplication comes division. Let's divide 7 into 35.

35 ÷ 7 = 5

5 + 30

♥ In this case, our only, and final, step, is addition. Let's solve this bad boy.

5 + 30 = 35

ANSWER = 35

Awesome! Now, 2 last pieces of advice. Firstly, always go left to right. Like, if you have an order of operations problem with two sets of exponents, solve the left one first. And my other advice is, use a mnemonic device to help you remember the order of PEMDAS. I'll leave you with some you can choose to use choose to lose!

♥ Please Excuse My Dear Aunt Sally (classic!)
♥ Print Evan's Microsoft Document And Send
♥ Princess Emily's Mom Died...Aww, Sad ☹