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And welcome to math antics. This video is all about dividing fractions. But in order order to understand how dividing fractions works.
We first need to learn about something called a reciprocal is just a fancy math term for what you get when you switch the top and bottom numbers of a fractions for example. If you have the fraction 1 over 2 and then switch the top and bottom numbers. You’ll end up with 2 over 1 2.
Over. 1 is the reciprocal of 1 over 2 and 1 over. 2.
Is the reciprocal of 2 over 1 and an interesting thing about reciprocals is multiplying a fraction by its own reciprocal will always give you 1′. That’s because you’ll have the same multiplication problem on the top and bottom. So you’ll end up with a whole fraction.
Which is always 1′ okay. That’s nice. But what do reciprocals have to do with dividing fractions well reciprocals let us do a really cool trick.
That makes dividing fractions. Easy. Whenever you have to divide something by a fraction you can just multiply.
It by the reciprocal of that fraction instead and you’ll get the correct answer. And that’s great news. Because multiplying fractions is so simple this trick of multiplying by the reciprocal works.
Because fractions are really just mini division problems. So when you multiply something by 1 over. 2.
It’s the same as dividing by 2 since. 2. Is below the fraction’s division line and dividing by 2.
Is the same as dividing by 2 over 1. Because you can turn any number into a fraction by just writing a 1′ as the bottom number right. But look reciprocals that’s why multiplying by 1 over.
2 is the same as dividing by 2 over 1 and it’s true. The other way around too. So really.
It’s kind of like you never have to divide fractions you can just re write your division problems. So that you’re multiplying by the reciprocal instead then when you multiply you’ll get the answer for the original division problem as always let’s see a couple examples of how this works so you’ll really understand let’s try this problem. 3.
Over 4 divided by 2 over. 7. Okay so the first thing we want to do is re write our problem instead of dividing by 2 over.
7. We can multiply by the reciprocal instead the reciprocal of 2 over. 7 is 7 over 2.
So our problem becomes. 3. Over 4 times.
7. Over 2. Oh.
I should mention a mistake that a lot of students make when they first learn to divide fractions sometimes students take the reciprocal of the first fraction the one that’s being divided or even the reciprocal of both fractions. But you only want to take the reciprocal of the second fraction the one you are dividing by okay now that our problem has been changed to multiplication. It’s easy just multiply the tops 3 times.
7 equals. 21. And multiply the bottoms 4 times 2 equals.
8. And we have the answer to our fraction division problem so 3 over 4 divided by 2 over 7 is 21 over 8. So that’s pretty easy.
But let’s try one more example. Let’s try 15 over 16 divided by 9 over 22. Again.
The first thing. We want to do is re write our problem. We’ll change the divided by 9 over 22′ into times.
22 over 9′ now all we have to do is multiply. But since these numbers are kinda big. I’m going to use my calculator to help let’s see here so we have alright on the top.
We have 15 times. 22. Equals.
330. And on the bottom. We have16 times.
9. Equals. 144.
So the answer to our division problem is 330 over 144 of course that could be simplified for your final answer on a test. But we cover simplifying fractions in another video alright that’s how you divide fractions you just multiply by the reciprocal and you have your answer. But there’s one more thing i want to show you you already know that the line between the top and bottom number of a fraction is just another form of the division symbol.
Well that means you’ll sometimes. See fraction division problems written like this this shows. The top fraction 2.
Over 3 being divided by the bottom fraction 4. Over 5. .
It’s really just that we have a fraction made up from other fractions. The top number is a fraction and the bottom number is a fraction it just looks a little confusing because we have all these fractions lines here. But we can make it look a lot better let’s re write this as a multiplication problem by taking the reciprocal of the bottom number the fraction that we are dividing by and multiplying.
It by the fraction on top. There that looks easier to do and it’s really the same problem. We just need to multiply to get the answer so 2 times.
5 equals. 10 and 3 times. 4 equals.
12. Okay so there you have it what sounded really hard turns out to be as easy as flipping fractions upside down. If you can multiply fractions.
Then you can divide fractions. Too don’t forget to practice. What you’ve learned by doing the exercises for.
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