Order of Operations 05:03 minutes

Video Transcript

Transcript Order of Operations

The Order of Operations. The ORDER of OPERATIONS! Yesterday, my dear Aunt Sally did everything in the wrong order. Look, she put her underpants above her skirt! She sent us to school. Then, she made our breakfast after we left. Later she baked cookies, but added the eggs in after the cookies came out.
My dear Aunt Sally did everything in the wrong order! As you can see, order is very important in everyday life. It is also important in math. Solving math problems is like following a recipe. You must follow the recipe for the Order of Operations, or PEMDAS to simplify expressions.

Steps in PEMDAS

  • The first step in the Order of Operations is P for Parentheses. All expressions inside the parentheses should be evaluated first.
  • E stands for Exponents. Exponents should be evaluated second.
  • The next step is M and D, which stands for Multiplication and Division. After parentheses and exponents have been evaluated you should multiply and divide.
  • Finally A and S means Addition and Subtraction. They represent the last step in the Order of Operations. The rule about solving left to right also applies to Addition and Subtraction.

Ok let’s evaluate some expressions. We’ll start with an easy one. You will see that following PEMDAS will always lead us to the right answer!

Calculation Example 1 & 2 using PEMDAS

First let’s look at two similar expressions: 8 - 2 + 5 and 8 – (2 + 5). The only difference between them is the use of parentheses. The first expression only has addition and subtraction so you should perform the operation in order from left to right: 8 − 2 = 6 and 6 + 5 = 11.
The second expression has parentheses. In PEMDAS the P for parentheses comes first. So, the Order of Operations tells you to evaluate the inside of the parentheses first: 2 + 5 = 7 and 8 − 7 = 1. Although these problems seem similar. They have two different answers.

Calculation Example 3 using PEMDAS

Okay, let's try a harder problem. This one has parentheses, exponents, addition, and subtraction! Parentheses come first. 8 − 2 gives you 6 and 5 + 2 gives you 7. Next comes Exponents: 6² = 36. Finally, you add 36 + 7 = 43.

Calculation Example 4 using PEMDAS

Now it's time to get even more tricky! Look at how many operations we are using! This expression has Parentheses, Exponents, Multiplication, Division, Addition, AND subtraction!
First you should be looking at the Parentheses. Inside you have 8 ÷ 2 − 2. Once inside the parentheses you have to use PEMDAS again. Division comes before subtraction so you must divide 8 by 2 before subtracting 2. Now you have 4 − 2. Resulting in 2. In the other parentheses you must evaluate the exponent before adding. You will need to square 5 before adding 2: 5² = 25, 25 + 2 will leave us with 27.
This problem is already looking better since we have taken care of the parentheses. The next step is E for exponents. 2 cubed gives you 8. Now we do multiplcation and division moving from left to right: 4 · 8 = 32 and 27 ÷ 9 = 3. The last step is Addition! 32 + 3 = 35. See? We started with this big expression, but by following the rules of PEMDAS we are able to simplify the expression to get 35!

PEMDAS Mnemonic

No matter how difficult the expression looks: Simply follow PEMDAS to get things done! You can remember PEMDAS with this sentence: Please excuse my dear Aunt Sally! So, please excuse my dear Aunt Sally. She was a little bit confused yesterday.