Order of Operations

Order of Operations

Please Excuse My Dear Aunt Sally​

Now, what does the phrase above mean? Well, the phrase above helps us understand a math concept: the order of operations. In this lesson, you will learn about the order of operations.​

Let's start off with a simple question!​

Here is a simple question: What is an operation? An operation is a mathematical action. Addition, subtraction, multiplication, division, and calculating the root are all examples of operations. But, what are the order of operations? The order of operations is when you solve a mathematical problem with this word, P E M D A S, or PEMDAS. And, this brings us back to Aunt Sally.​

​PEMDAS: Introduction

​PEMDAS, or rather P E M D A S, is when you solve a math problem in order. To remember this abbreviation, you will know this phrase: Please Excuse My Dear Aunt Sally. Now, let's take a closer look of what PEMDAS stands for.

PEMDAS: What it means​

P: Parentheses. We solve what is in the parentheses.

E: Exponents. We figure out the exponent.

M: Multiplication. We multiply to figure out the problem.

D: Division. We divide to figure out the problem.

A: Addition. We add to figure out the problem.

S: Subtraction​. We subtract to figure out the problem.

Let's go over a problem together using PEMDAS!

Problem 1: 7x4-6=?​

How do we solve this problem?​

​Should you subtract 6 from 4 and then multiply by 7? No. According to PEMDAS, we multiply before we subtract. So, multiply 7 and 4, you get 28. Then, subtract 6 from 28. We get 22. So, 7x4-6=22. Let's go over another problem!

Problem 2: 7+7x3=?​

How do we solve this problem?​

We add 7 and 7, we get 14. Then, we multiply 14 and 3, we get 42. But, this way is wrong! Remember, you do not add first. We multiply first. So, we multiply 7 and 3, we get 21. Then, we add 7 and 21, we get 28. ​So, 7+7x3=28. Let's look at some more complex problems.

Problem 3: 6x3²=?​

How do we solve this problem?​

This problem will seem tricky.​ Here is the wrong way to solve the problem: (6x3)². Multiply 6 and 3, we get 18. Then, you now get 18², which is 324. Why is that wrong? Because you violated the order of operations. You do not multiply first. You figure out the exponent first. Here is how is should be done: 3² is equal to 9, so, multiply 6 and 9, we get 54. So, 6x3²=54. Let's look out one more problem. The next problem may seem challenging.

Problem 4: 5x10-(8x6-15)+4x20/4=?​

How do we solve this problem?​

Remember the order of operations. First, we solve what's in the parentheses. 8x​6 is 48, then subtract 15, you get 33. Next, you multiply. Multiply 5 and 10, you get 50. Then, multiply 4 and 20, you get 80. Then divide 4, you get 20. Here is the equation now: 50-33+20=? Then, there could be an impossible way to solve, but now, it should look like this: 50-13. We now get 37. So, 5x10-(8x6-15)+4x20/4=37. Now, let's take a quiz!

Multiple Choice

16 + 5 x 8

• 168

• 29

• 65

• 56

• 861

Multiple Choice

3 +(35 – 21) x 2

• 34

• 13

• 31

• 43

• 20

Multiple Choice

7 + 2 x (6 + 3) ÷ 3 – 7 

• 6

• 5

• 7

• 4

• 8

Multiple Choice

11 + 19 x 2

• 60

• 50

• 49

• 54

• 72

Multiple Choice

(14 + 2) x 2 + 3

• 21

• 35

• 80

• 43

• 68

Multiple Choice

120 ÷ (6 + 12 x 2)

• 150

• 40

• 6

• 4

• 20

Multiple Choice

12 + 2 x 44

• 100

• 616

• 110

• 600

• 660

Multiple Choice

 10 x 2 – (7 + 9)

• 21

• 16

• 4

• 13

• 24