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What is the Order of Operations in Math? Understand the Rules

The order of operations in math is a list of the steps to take when doing a math problem. It is important to know the order of operations so you do not make any mistakes.
Mathematics
7 minutes
What is the Order of Operations in Math? Understand the Rules
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Math can be a pretty daunting topic for a lot of people. But don't let the complex numbers and algebra scare you! In reality, math is just a series of steps that we use to solve problems. We call these steps the order of operations.

Order of operations is the order in which you do mathematical operations - adding, subtracting, multiplying, and dividing. If you don't follow the order of operations, you could get a different answer than what you're supposed to.

So today, we're going to take a closer look at what the order of operations is and how to use it correctly!

Who can explain the Order of Operations?

If you're struggling with Order of Operations, don't worry-you're not alone! A lot of people find this topic confusing, but with the help of a tutor, you can get it all under control.

A math tutor can help you understand the order of operations and how to use it correctly. They can explain each step in detail and give you plenty of practice problems to make sure you understand the concept. So if you're looking for help with your whole math curriculum, a tutor is a great option!

In Learner, we have many tutors who can explain the order of operations, also known as operations precedence, and they can help you understand this basic concept. Order of operations is a fundamental part of math, so it's important to get help early on if you're struggling.

Some of the benefits you will get from working with a math tutor include:

  • Improved grades in math
  • A better understanding of Order of Operations
  • Stronger problem-solving skills 
  • And many more

How to Find Order of Operations in Math

You might find it easier to remember the order of operations while solving arithmetic equations if you use the abbreviation PEMDAS. The acronym PEMDAS is made up of the initial letter of each word of the sentence, which is typically expanded into the phrase 

"Please Excuse My Dear Aunt Sally." 

Working from left to right, solve math questions using the conventional mathematical procedure:

The operations are:

  • P: Parentheses first. Find and solve parenthesized expressions first, proceeding from left to right in the equation; if there are nested parentheses, work from innermost to outermost.
  • E: Exponents (ie Powers and Square Roots, etc.) Calculate all exponential and root expressions second, working from left to right in the equation.
  • MD: Multiplication and Division (left-to-right) Then, proceeding from left to right in the equation, answer the formulas for multiplication AND division as they appear. You should begin with this step for the MDAS rule.
  • AS: Addition and Subtraction (left-to-right). Next, solve addition AND subtraction expressions as they happen in the equation, proceeding from left to right.

For example, take a look at the Order of Operations in this equation:

6 + (5 - 3)2

In this equation, we have to use the Order of Operations to simplify it correctly.

If we just solve it from left hand side to the right, we would get:

6 + (5 - 3)2 

= 11 - 6

= 5

Although, this is not the correct answer! The Order of Operations tells us that we have to solve the parentheses first. So, we would solve:

6 + (5 - 3)2      Solve for parentheses

= 6 + (2)2         Solve for multiplication

= 6 + 4               Solve for addition

= 10

And that is the correct answer!

As you can see, the Order of Operations is very important when simplifying equations. It is a fundamental rule that you must always follow to get the correct answer.

Let’s try another one:

(2+3)4             Solve for parenthesis

= 54                  Solve for exponent

= 625

If you're struggling with Order of Operations, don't hesitate to reach out to a tutor for help. They can walk you through the steps and make sure you understand the concept. Order of Operations is a tricky topic, but with the help of a tutor, you can master it in no time!

When choosing a tutor there are a few key qualities to look for:

1. Expertise

Of course, you want to make sure your tutor is an expert in Order of Operations. They should be able to explain the concept clearly and help you with any problems you're having.

A great way to gauge a tutor's expertise is by reading their reviews. All tutors on Learner typically have many positive reviews from students they've helped in the past.

2. Patience and clarity

It's important to find a tutor who is patient and can explain things clearly. Order of Operations can be confusing, so you want to make sure your tutor is able to break it down for you in a way that makes sense.

3. Practice problems

A good tutor will give you plenty of practice problems to work on. This is important because the best way to learn is by doing. The more practice problems you do, the better you'll understand the concept.

If you're looking for a math tutor, Learner has many great tutors to choose from.

4. Tutoring Experience

It's also beneficial to find a tutor with plenty of experience. Order of Operations is a tricky concept, so you want to make sure your tutor knows what they're doing.

You can check a tutor's experience by reading their profile. Math tutors on Learner typically have years of experience helping students just like you.

5. Organizational skills

Organizational skills are important for math tutors because they have to be able to keep track of many different concepts. A good math tutor will be able to explain the concept in a clear and organized way.

Order of Operations can look like a difficult concept, but with the help of a tutor, you can master it!

Red Flags to Look Out For in When Considering a Math Tutor

When you're looking for a math tutor, there are a few red flags to look out for. Some are:

1. Lack of Expertise 

If a tutor lacks expertise in math they may not be able to help the student as effectively as they could with another subject. This could lead to frustration on the part of the student and a waste of time and money.

2. Impatience

If a tutor is impatient, they may not be able to take the time to explain math concepts like order precedence in a way that the student can understand. This could lead to confusion and further frustration on the part of the student.

3. Limited Practice Problems

As stated before, math is best learned by doing. If a tutor only provides a limited number of practice problems, the student may not get enough exposure to the concept to fully understand it.

4. Inexperience

If a tutor is inexperienced with math, they may not be able to help the student as effectively as someone with more experience. This could lead to frustration on the part of the student and a waste of time and money.

5. Poor Organizational Skills

For math tutors, organizational skills are key. If a tutor is disorganized, they may not be able to keep track of all the fundamental concepts that need to be explained to the student. This could lead to further confusion on the part of the student.

Questions to Ask a Potential Order of Operations tutor

  • What is your experience with basic math operations? 
  • What are some fundamental math concepts that you find difficult to explain? 
  • How do you usually explain Order Precedence to students? 
  • Do you have any Order of Operations practice problems that I can try?  
  • What are the cautions when dealing with order precedence?
  • How does PEMDAS differ from BODMAS, MDAS, GEMDAS, and BEDMAS?
  • Order precedence can be tricky- how do you make sure students understand the concepts? 
  • What math resources do you recommend for students learning order precedence? 
  • Fundamental math concepts can be confusing- how do you help students who are struggling? 
  • What general math tips do you have for students? 
  • Are there any fundamental math concepts that you think are particularly important for students to understand? Why?

If you're looking for a math tutor, make sure to ask these questions to get a better idea of the tutor's expertise and whether they would be a good fit for you.

What to Expect When Working With an Online Math Tutor at Learner

When working with a math tutor at Learner, you can expect: 

  • A tutor who is experienced with fundamental math concepts and can help you understand them, even making them fun
  • A tutor who is patient and can take the time to explain Order of Operations in a way that you can understand
  • A tutor who is organized and can keep track of all the fundamental math concepts that need to be explained to you. 
  • A tutor who is flexible and can adapt their teaching style to your needs. 
  • A tutor who is supportive and can help you overcome any struggles you may have with fundamental math concepts

At Learner, we only work with the best tutors who are experts in their field and can provide you with the high-quality instruction that you need to succeed.

Frequently Asked Questions

What are the 4 order of operations?

The four Order of Operations are (parentheses exponents multiplication division)

Which operation comes first in math?

In math, the Order of Operations that comes first is parentheses. This means that any operations inside of parentheses should be done first.

About the author:

Mike developed his passion for education as a math instructor at Penn State University. He expanded his educational experience launching and running an Executive Education business - training over 100,000 students per year. As the CEO of Learner, Mike focuses on accelerating learning and unleashing the potential of students. 

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