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Pre-Algebra: Multiplying Fractions & Mixed Numbers

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About this Lesson

  • Type: Video Tutorial
  • Length: 7:03
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 75 MB
  • Posted: 01/28/2009

This lesson is part of the following series:

Pre-Algebra Review (31 lessons, $61.38)

In this lesson, Professor Burger demonstrates two ways to multiply mixed numbers (numbers that contain both a fraction less than one and a whole number that is greater than or equal to one). In the first method, you will learn to convert the mixed numbers into improper fractions (fractions that are in fraction form but equal to an amount in excess of one). Then, you will learn that there is a way to simplify these numbers by canceling in the numerator and denominator. Next, you will multiply the two fractions together and write either as an improper fraction, or convert back to a mixed number. In the event a problem involves multiplying a whole number and a mixed number, Professor Burger shows you how to use the distributive property to solve it. Begin by writing the mixed number as a sum, and then distribute the whole number to both parts of the sum. Simplify and multiply the numbers to find your answer.

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 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

Thinkwell
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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 www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.

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

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Recent Reviews

Nopic_tan
Very happy with how easy this video is to follow!
06/01/2009
~ brittanie

My review's title sums it up but I would just like to add that I am very happy to have videos like these for my own review. I wish my school teachers made it look this easy.

Nopic_tan
Very happy with how easy this video is to follow!
06/01/2009
~ brittanie

My review's title sums it up but I would just like to add that I am very happy to have videos like these for my own review. I wish my school teachers made it look this easy.

MULTIPLYING MIXED NUMBERS

Let’s take a look at how to multiply two mixed numbers together. It turns out that we already know what to do. We just have to convert each of the mixed numbers separately into a fraction, an improper fraction. Once we have that, we are all set.

Let’s take a look at an example together. 2 and one-third multiplied by 1 and one-fifth. What do we do? First step, convert everything to improper fractions, because multiplying fractions is so easy that we want to do that. So first, I'm going to take this piece right here. How do I do it? I take the 2 times the 3, that’s 6, then add 1, that’s 7. So I have 7 over 3. Now what do I do? Well, now I multiply, and what is this fraction going to be? Well, 1 times 5 is 5, plus 1 is 6, over 5. So this is the improper fraction version of this. This is the improper fraction version of this, so now I have two fractions I'm multiplying. No problem. I multiply the tops; then multiply the denominators. I could multiply all of that out, but let’s see if we can simplify it first. Well, I can write the 6 as 2 times 3. Now I see a common factor in the numerator of 3 and a common factor in the denominator of 3, so this fraction is equivalent, is equal, to the fraction I get by removing those common factors. So I see 7 times 2, which is 14, over 5. So the answer is 14 over 5. But, if you want to write this as a mixed number, we would long divide, and what would we see? We’d see that this also could be written as 2 and four-fifths. So we can convert this to a mixed number. Either answer is correct. It just depends upon the form that the questioner wants the answer to be given in, either one of these. Neat! They are both the same.

All right, are you ready? How about 1 and two-fifths multiplied by 1 and one-quarter? Well, what’s the first step? The first step is always the same; we have to convert each of these mixed numbers into an improper fraction. Once we have two fractions, even if they are improper, we know how to multiply them: multiply the tops, the numerators, multiply the bottoms, the denominators. So what is the improper fraction version of 1 and two-fifths? I take the 1 and multiply it by 5, that’s 5, add a 2 and get 7. 7 over 5. Then I multiply that by the improper fraction version of 1 and one-quarter. So 1 times 4 is 4, plus 1 is 5, over 4. Now let me show you something here. Already, because we’ve looked at so many of these questions, I'm beginning to see there is a factor of 5 in the denominator; there’s a factor of 5 in the numerator, so I could write the next step, which would have been 7 times 5, divided by 5 times 4, but right here I’m going to take an extra little secret step and notice that I have, since I am multiplying, the factors that are common already in sight. So I could just jump right to writing 7 over 4, since this is 7 times 5 over 5 times 4. That’s a common factor in the numerator and denominator, and I can get rid of that. So, that’s a perfectly fine improper fraction answer to this problem, 7 over 4. If you wanted to write it as a mixed number, you would have to peel off a 1, and we’d see 1 and three-fourths. Either of these answers is correct. It just depends on how the person who asked us the question wants us to answer it. So pretty cool.

Let me show you one last question. This is a little, teeny-bit different. Four, the number 4, the whole number 4, times 2 and one-ninth. Now we can proceed in the usual way if we want to, which is to convert this to an improper fraction and then do multiplication, but let me show you a really great, easy way of doing this. That is to remember what 2 and one-ninth means. Remember what “and” means? “And” means “plus.” That’s just one whole big thing right there; it is a number. It’s 2 and one-ninth. So if I write that out, I’d see 4 times, and this is just going to be one number here, 2 and one-ninth. Now I want us to see that this is really the exact same mathematical statement, because here is the 4 and here is the 4. Here is the times, and here is the times. And this number is 2 and one-ninth, and this number is 2 and one-ninth, but it is all one number, so I put it in this parentheses. When you look at it this way, now we can use the wonderful distributive property that we know that multiplication and addition enjoy. So take the 4 and multiply it by the 2 and then add it to taking the 4 and multiplying it by the one-ninth, so you could jump right to 4 times 2, plus 4 times one-ninth. So what does this give me? Well, I know 4 times 2 is 8. And 4 times one-ninth, well, remember that 4 is the same thing as 4 over 1, so I multiply tops and multiply bottoms, and I see 4 over 9. How can I write that? I can write that as a mixed number by just remembering the secret code, 8 and four-ninths.

So when you are taking a whole number and multiplying it by a mixed number, it’s actually sort of sneaky. If you want, you can break up that mixed number into the sum of the whole number part plus the fraction part, but make sure you put parentheses around that whole thing, because that is just one number. Then use the distributive law, and out comes your answer.

Neat stuff! Congratulations, you can now multiply mixed numbers. Pretty neat stuff. I'll see you soon.

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