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Hi and welcome to Math Antics. This video is all about dividing fractions,

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But in order to understand how dividing fractions works,

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we first need to learn about something called reciprocals.

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A reciprocal is just a fancy math term for what you get

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when you switch the top and bottom numbers of a fraction.

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For example, if you have the fraction 1/2

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and then switch the top and bottom numbers, you'll end up with 2/1.

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2/1 is the reciprocal of 1/2 and 1/2 is the reciprocal of 2/1.

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And an interesting thing about reciprocals is multiplying a fraction

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by its own reciprocal will always give you one.

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That's because you'll have the same multiplication problem on the top and bottom.

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So you'll end up with a whole fraction, which is always one.

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OK, that's nice.

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But what do reciprocals have to do with dividing fractions?

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Well, reciprocals let us do a really cool trick that makes dividing fractions easy.

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Whenever you have to divide something by a fraction,

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you can just multiply it by the reciprocal of that fraction instead

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and you'll get the correct answer.

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And that's great news because multiplying fractions is so simple.

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This trick of multiplying by the reciprocal works

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because fractions are really just mini-division problems.

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So when you multiply something by 1/2,

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it's the same as dividing by two, since two is below the fraction's division line.

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And dividing by two is the same as dividing by 2/1 because you can turn

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any number into a fraction by just writing a one as the bottom number,

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right?

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But look, reciprocals. That's why multiplying by 1/2 is the same as dividing by 2/1.

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And it's true the other way around too.

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So really,

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it's kind of like you never have to divide fractions.

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You can just rewrite your division problems so

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that you're multiplying by the reciprocal instead.

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Then when you multiply, you'll get the answer for the original division problem.

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As always, let's see a couple examples of how this works

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so you'll really understand.

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Let's try this problem: 3/4 divided by 2/7.

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OK,

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so the first thing we want to do is rewrite our problem.

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Instead of dividing by 2/7, we can multiply by the reciprocal instead.

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The reciprocal of 2/7 is 7/2.

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So our problem becomes 3/4 times 7/2.

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Oh, I should mention a mistake that a lot of

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students make when they first learn to divide fractions.

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Sometimes students take the reciprocal of the first fraction,

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the one that's being divided or even the reciprocal of both fractions.

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But you only want to take the reciprocal of the second fraction,

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the one you're dividing by.

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OK, now that our problem has been changed to multiplication, it's easy.

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Just multiply the tops, three times seven equals 21,

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and multiply the bottoms, four times two equals eight.

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And we have the answer to our fraction division problem.

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So 3/4 divided by 2/7 is 21/8.

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So that's pretty easy,

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but let's try one more example. Let's try 15/16 divided by 9/22.

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Again, the first thing we want to do is rewrite our problem.

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We'll change the divided by 9/22 into times 22/9.

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Now, all we have to do is multiply,

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but since these numbers are kind of big, I'm going to use my calculator to help.

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Let's see here.

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So we have, all right,

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on the top, we have 15 times 22 equals 330.

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And on the bottom, we have 16 times nine equals 144.

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So the answer to our division problem is 330/144.

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Of course, that could be simplified for your final answer on a test,

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but we cover simplifying fractions in another video.

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All right,

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that's how you divide fractions.

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You just multiply by the reciprocal and you have your answer.

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But there's one more thing I want to show you.

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You already know that the line between the top and bottom number

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of a fraction is just another form of the division symbol.

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Well,

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that means you'll sometimes see fraction division problems written like this.

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This shows the top fraction, 2/3, being divided by the bottom fraction, 4/5.

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It's really just that we have a fraction made up from other fractions.

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The top number is a fraction and the bottom number is a fraction.

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It just looks a little confusing because we have all these fraction lines here.

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But we can make it look a lot better.

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Let's rewrite this as a multiplication problem by

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taking the reciprocal of the bottom number,

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the fraction that we're dividing by,

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and multiplying it by the fraction on top.

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Tthere, that looks easier to do. And it's really the same problem.

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We just need to multiply to get the answer.

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So two times five equals 10

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and three times four equals 12.

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Ok. So there you have it.

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What sounded really hard turns out to be as easy as flipping fractions upside down.

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If you can multiply fractions, then you can divide fractions too.

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Don't forget to practice what you've learned

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by doing the exercises for this section.

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Thanks for watching and I'll see you next time.

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