Order of Operations with Fractions

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: How to Solve One-Step Equations with Fractions

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:04 Why Order Matters
  • 1:31 Some Practice
  • 2:57 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Timeline
Autoplay
Autoplay
Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Mark Boster
Have you ever tried to put your socks on after putting on your shoes? It doesn't work does it? In math, there is also a certain order in which equations have to be solved to get the correct answer. In this lesson, you will learn this important order of operations.

Why Order Matters

Matter, really, does, what in order go you it? Wait, none of that made any sense! Let's put that sentence in order! 'Does it really matter what order you go in?' Clearly, of course it does! Try to eat a banana before you peel it or a watermelon before you cut it. Well, order really does matter when adding, subtracting, multiplying, or dividing fractions.

Just like we put our socks on before our shoes, when solving equations, even ones that contain fractions, order matters. Look at Equation 1 below. You can see it does matter in what order you solve the equation.

Example 1
null

When it was solved the first time, the multiplication was done before the addition. The second time it was solved, addition was done before multiplication! So what order should you go in?

Just like when you are solving equations with whole numbers, solving equations with fractions has the same order of operations. The order of operations is the order in which you solve the problem. If numbers are in parentheses, you do them first. Second, you solve for any numbers with exponents. Then, you go from left to right and do the multiplication and division. Finally, you go back and do the addition and subtraction - again, from left to right.

Sounds like a lot, right? Well, there is a very popular mnemonic device to help you remember the order of operations: PEMDAS (Please Excuse My Dear Aunt Sally) helps us remember:

P - Parentheses

E - Exponents

M & D - Multiplication and Division (left to right)

A & S - Addition and Subtraction (left to right)

Some Practice

How about trying


OOO with fractions


There is both addition and multiplication in this equation, so what's the first step? Remember your PEMDAS.

There are no parentheses or exponents, so multiplication comes first. As we can see:


first

3/9


So now you have the first part done.


13


To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account
Support