We are independent & ad-supported. We may earn a commission for purchases made through our links.
Advertiser Disclosure
Our website is an independent, advertising-supported platform. We provide our content free of charge to our readers, and to keep it that way, we rely on revenue generated through advertisements and affiliate partnerships. This means that when you click on certain links on our site and make a purchase, we may earn a commission. Learn more.
How We Make Money
We sustain our operations through affiliate commissions and advertising. If you click on an affiliate link and make a purchase, we may receive a commission from the merchant at no additional cost to you. We also display advertisements on our website, which help generate revenue to support our work and keep our content free for readers. Our editorial team operates independently of our advertising and affiliate partnerships to ensure that our content remains unbiased and focused on providing you with the best information and recommendations based on thorough research and honest evaluations. To remain transparent, we’ve provided a list of our current affiliate partners here.

What is the Order of Operations?

Mary McMahon
Updated May 21, 2024
Our promise to you
All The Science is dedicated to creating trustworthy, high-quality content that always prioritizes transparency, integrity, and inclusivity above all else. Our ensure that our content creation and review process includes rigorous fact-checking, evidence-based, and continual updates to ensure accuracy and reliability.

Our Promise to you

Founded in 2002, our company has been a trusted resource for readers seeking informative and engaging content. Our dedication to quality remains unwavering—and will never change. We follow a strict editorial policy, ensuring that our content is authored by highly qualified professionals and edited by subject matter experts. This guarantees that everything we publish is objective, accurate, and trustworthy.

Over the years, we've refined our approach to cover a wide range of topics, providing readers with reliable and practical advice to enhance their knowledge and skills. That's why millions of readers turn to us each year. Join us in celebrating the joy of learning, guided by standards you can trust.

Editorial Standards

At All The Science, we are committed to creating content that you can trust. Our editorial process is designed to ensure that every piece of content we publish is accurate, reliable, and informative.

Our team of experienced writers and editors follows a strict set of guidelines to ensure the highest quality content. We conduct thorough research, fact-check all information, and rely on credible sources to back up our claims. Our content is reviewed by subject-matter experts to ensure accuracy and clarity.

We believe in transparency and maintain editorial independence from our advertisers. Our team does not receive direct compensation from advertisers, allowing us to create unbiased content that prioritizes your interests.

The order of operations is a set of rules which must be kept in mind when doing math problems. These rules tell people when to perform various operations in a math problem with mixed operations, such as (7 + 2) x 4 - 3. There are a number of possible answers to this problem, depending on the order in which the multiplication, subtraction, and addition are performed, but only one right answer, because the order of operations tells people how to do the problem.

According to the order of operations, when one is faced with a math problem which has mixed operations, anything in parentheses should be done first, followed by exponents and roots, and then, working from left to right, multiplication and division. Finally, also working from left to right, addition and subtraction. People sometimes use the acronym PEMDAS, for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction, to remember the order of operations. The mnemonic "please excuse my dear Aunt Sally" to help people learn this acronym is used in a number of beginning math classes.

Taking the problem in the example above, the first thing to do would be the addition inside the parenthesis, 7+2, which equals 9. Next, the multiplication should be done, to reach 36. Finally, the 3 must be subtracted, for a total of 33. The order of operations applies to any math problem, from simple to complex. If there weren't a particular order established, people could come up with equally correct results. For example, someone could read the above problem and come up with an answer of 9, by adding 7+2 to get 9, subtracting 3 from 4 to get 1, and multiplying 9 by 1 to arrive at 9.

The left to right rule for addition and subtraction and multiplication and division in the order of operations is also important. In a problem like 9 - 7 + (4 x 5) ÷ 10, for example, one would do the parenthesis first, ending up with 9 - 7 + 20 ÷ 10. Division comes next, so 20 ÷ 10 = 2. Addition doesn't take precedence over subtraction, so these are done left to right. The answer to the problem is therefore 4, because 9 - 7 = 2, and 2 + 2 = 4. Prioritizing addition over subtraction and not following the left to right rule would result in 9 - 9 = 0, a very different answer!

In a way, the order of operations tells people how to read math problems, just like the rules of grammar tell people how to read written languages. The rules of grammar and mathematics are both designed to make sure that everyone can write and read in a universal way which ensures that people can communicate freely with people they may never personally interact with. The standardization created by the order of operations is especially important in mathematics because there are so many ways to work complex problems without it, and this would result in a multitude of conflicting answers.

All The Science is dedicated to providing accurate and trustworthy information. We carefully select reputable sources and employ a rigorous fact-checking process to maintain the highest standards. To learn more about our commitment to accuracy, read our editorial process.
Mary McMahon
By Mary McMahon

Ever since she began contributing to the site several years ago, Mary has embraced the exciting challenge of being a All The Science researcher and writer. Mary has a liberal arts degree from Goddard College and spends her free time reading, cooking, and exploring the great outdoors.

Discussion Comments
By anon52891 — On Nov 17, 2009

The calculation in the second to last paragraph is wrong, I think. The numerator is to be figured out before the denominator. And THEN you do the division.

Mary McMahon
Mary McMahon

Ever since she began contributing to the site several years ago, Mary has embraced the exciting challenge of being a...

Learn more
All The Science, in your inbox

Our latest articles, guides, and more, delivered daily.

All The Science, in your inbox

Our latest articles, guides, and more, delivered daily.