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Pre-Algebra: Using the Order of Operations


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About this Lesson

  • Type: Video Tutorial
  • Length: 2:12
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 23 MB
  • Posted: 01/28/2009

This lesson is part of the following series:

Pre-Algebra Review (31 lessons, $61.38)

When evaluating numerical expressions, the set of rules that must be followed to ensure that everyone get the same answer is called the Order of Operations. The Order of Operations is as follows:
1) Parentheses
2) Exponents
3) Multiply/Divide
4) Add/Subtract

What this means is that operations involving parentheses should be done first. Next, you should perform any calculations or operations that involve exponents. After that, you'll want to perform any multiplication or division that is called for. Finally, you can finish up by performing any addition and subtraction operations. If you encounter multiple operations within a set of parentheses, you will follow the order of operations to simplify the expression within the parentheses.

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

About this Author

2174 lessons

Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit or visit Thinkwell's Video Lesson Store at

Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...


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Let’s take a look at these examples. Here there are parentheses. That tells me this is the first thing I’ve got to do. The parentheses trump everything else. What does this equal? 12 minus 20 divided by 5 times 2, which is 10. What’s the next thing I do? The next thing I do is the division. So,I do the division. I see 12 minus--, well 20 divided by 10, which is 2. Now I have 12 minus 2. That’s 10. So the answer is 10. Neat.

How about this one? I’m going to really see if I can make it complicated. I don’t even know where to start on this one, because there’s so much stuff here. We have to notice there are lots of parentheses. There’s an outer parentheses and an inner parentheses. The first thing we do is we start with the inner parentheses. We’re going to focus on this. Inside of that, what’s the rule? The rule is to first do any multiplication or division. So I start way deep inside of here, focusing on that. What does this equal? I am going to write it all out. 3 plus parentheses 10 minus 18 divided by 6, which is 3. That’s where we are right now. We do the stuff inside the parentheses now. I compute 10 minus 3, and I get 7. I still have these parentheses. They might not look like curly parentheses, but those brackets count as parentheses. Any grouping kind of thing counts as parentheses. Believe it or not, we deal with the stuff inside those brackets. What do we see? 3 plus 7 is 10. The only thing left is to square 10 and get 100. You can even parse things as complicated as this, if you do it with a little bit of care.

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