How to Multiply & Divide Mixed Numbers

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Just because you're working with a mixed number doesn't mean you can't multiply and divide. Learn how to multiply and divide mixed numbers with help from a mathematics educator in this free video clip.

Part of the Video Series: Mathematics Equations & More
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Video Transcript

Hi, my name is Jimmy Chang and we're here to talk about how to multiply and divide mixed numbers. Now the one strategy that you've really got to think about in both operations is taking the mixed numbers and converting them to improper fractions. Because if you don't do that then you're not going to come out with the answer that you're looking for. It'll be inaccurate unfortunately. So we're going to do a multiplying example and then we'll do a dividing example right after that. So here we go. Suppose you have 2 3/5 x 1 3/4. So the first thing that you've got to do is you've got to take both numbers and convert them to improper fractions. So I'm assuming you know how to do that but here's a good chance to review. So what you've got to do is take the denominator, multiply by the whole number and add to the numerator. So 5x2 is 10 add 3, it will be 13/5 times and then do the same thing with 1 3/4. Take the four, multiply by the 1 which is 4 add the 3 which is 7. So you have 13/5 x 7/4. And then what you want to do is, if you want to reduce to make it a little easier but if you can't then just multiply across. Now, 13 x 7 that's going to give you 91 and 5 x 4 is going to give you 20. Now at this point you can either leave it as an improper fraction or you can convert it to a mixed number. I'll leave it up to you. So leave it like this or you can convert it to 4 11/20. How you can find that out is by using long division. Now, in terms of dividing it's the same kind of idea but suppose you have 4 divided by 1 1/5. Now in this case, just like you did in the previous problem, you have to convert all mixed numbers to improper fractions. So take the 5 x the 1, add the 1 which is 6, so you're really dividing by 6 over 5 and since the 4 is a whole number to begin with you don't have to worry about that. Now, what you've got to do is look at the denominator 6/5 and then when you're dividing by a fraction you have to multiply by the reciprocal. So the reciprocal of 6/5 is 5/6 so it's 4 x 5/6. If you want, take the 4, convert it to a 4/1, cross cancel if you'd like. 4 and 6, they both reduce by 2 so you have a 2 and a 3 and then multiply. 2 x 5 is 10 and 1 x 3 is 3. And so 4 divided by 1 1/5 is going to give you 10/3 at the very end. But the important thing to remember is when you multiply and divide mixed numbers you really need to convert them to improper fractions before you can do anything else. So I'm Jimmy Chang and that's multiplying and dividing mixed numbers.


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