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About this Lesson
 Type: Video Tutorial
 Length: 4:40
 Media: Video/mp4
 Use: Watch Online & Download
 Access Period: Unrestricted
 Download: MP4 (iPod compatible)
 Size: 50 MB
 Posted: 01/28/2009
This lesson is part of the following series:
PreAlgebra Review (31 lessons, $61.38)
In this lesson, Professor Burger introduces percentages. He begins by reminding us that a percent is read "5 percent of 20," and the word "of" indicates multiplication. To multiply, we will need to convert the percent into a fraction or a decimal. He does examples using both methods. To convert a percentage to a fraction, you set the percentage over 100 and continue multiplying. To convert the percentage to a decimal, you will move the decimal point over two places to the left, and then continue multiplying. You can check your work by doing the problem both ways. Thus, our example, "5 percent of 20," can be written as 5/100*20 or .05*20.
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 http://www.thinkwell.com/student/product/prealgebra. 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 UTAustin 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, padic 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
 Thinkwell
 2174 lessons
 Joined:
11/13/2008
Founded in 1997, Thinkwell has succeeded in creating "nextgeneration" 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 technologybased textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.
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FINDING A PERCENT OF A NUMBER
Well, it’s another day, so let’s do some more. Here we go. Let’s find thirty percent of one hundred eighty. How do we do that? Well, what we say is thirty percent of one hundred eighty. The “of” is a cue to my mathematical ear that tells me when I hear “of” that means multiplication. So I’m going to take thirty percent, and I have to multiply that by one hundred eighty. But first I have to convert the percent to either a fraction or a decimal. So that’s why it was great that we spent some time seeing how to translate from percentages to decimals and fractions. If we convert this to a fraction, what we see is thirty divided by one hundred. Now I take that, and I’m going to multiply that by one hundred eighty. So what do we get? If we do that, what we see here is that we can simplify this a little bit, because I can take thirty times 180 over one hundred, and so I can divide the numerator by 100 and the denominator by 100. What do I see? In the denominator I’m just left with one hundred divided by one hundred, that’s just one. And in the numerator what do I see? I see that one hundred eighty divided by one hundred is going to give me the zero here and the zero here to simplify and then this zero here and that zero are going to simplify. This is one hundred times three times eighteen. And so I see the hundreds can be simplified, and I’m just left with three times eighteen. And that works out to be fiftyfour. So we simplify this fraction down and we see fiftyfour, so fiftyfour is thirty percent of one hundred eighty.
Let’s try another one together. Here we have seven percent of forty, so how would we find this? Well, let’s do it in two ways. One way is to write this as a decimal. If I write seven percent as a decimal, that would be zero point zero seven. And “of” means times. I’m trying to find seven percent of forty. That means times forty. If I perform the multiplication, I see the answer is two point eight. So that’s one way of thinking about it, if we think about the percentage as a decimal.
Let’s think about is as a fraction and see if we get the exact same answer. Boy I hope so; otherwise, we might be in trouble. So let’s try it now as a fraction. What do we say seven percent is? That’s seven over one hundred. I’m going to multiply that times forty. That equals seven times forty divided by one hundred. I can simplify this by dividing the top by ten and the bottom by ten. If we simplify that, what do we see? Here I just see seven times four divided by ten, and that equals twentyeight divided by ten. What does that mean? That means twentyeight divided by ten, which means I get two point eight. And check it out. We see the exact same answer, two point eight as we got up here.
So seven percent of forty is two point eight. It doesn’t matter if we correctly convert the seven percent to a decimal, zero point zero seven and then multiply by forty, or correctly convert seven percent to a fraction, seven over one hundred and then multiply by forty. All roads that are correct will lead to the exact same answer. So you can see the connection among percentages, fractions and decimals. The key thing here is when someone asks us to find seven percent of something, that means we convert, and the “of” means multiply by the something.
Have fun thinking about percents. They are all around us. They are great fun. Enjoy.
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