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2.3 Dividing Fractions

Added Oct 14, 2015 •

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hi welcome to Math Antics this video is South dividing fractions but in order to understand how dividing fractions works we first need to learn about something called reciprocals a reciprocal is just a fancy term for what you get when you switch the top and bottom numbers of a fraction for example if you have the fraction 1/2 and then switch the top and bottom numbers you'll end up what's 2 / 1 - 1 is the reciprocal of 1 over 2 and 1 / 2 is the reciprocal of 2 over 1 and an inn same thing about reciprocals is multiplying a fraction by its own reciprocal will always give you one that's because you'll have the same multiplication problem on the in bottom so you'll end up with a whole fraction which is always one 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 by the reciprocal of that 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 does fractions are really just many division problems so when you multiply something by 1/2 it's the same as dividing by two since two is below the fractions division and dividing by 2 is the same as dividing by 2/1 because you can turn any number into a fraction by just writing a one as the bottom number right but look reciprocals that's why multiplying by 1/2 is the same as dividing by 2/1 and it's true the other way around 2 so it's kind of like you never have to divide fractions you can just rewrite your division problems so that you're multiplying by the reciprocal instead then when you multiply you'll 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 / 4 divided by 2/7 okay so the first thing we want to do is rewrite our problem instead of dividing by 2/7 we can multiply by the reciprocal set the reciprocal of 2 over 7 is 7 over to sew a problem becomes 3 / 4 * 7 / 2 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 Reve in the reciprocal of fractions but you only want to take the reciprocal of the second fraction the one you're dividing by okay now that our problem has change to multiplication it's easy just multiply the tops three times 7 equals 21 and multiply the bottles for x 2 equals 8 and we had the to our fraction division problem so 3 over 4 divided by 2 over 7 is 21 / 8 so that's pretty easy but let's try one more exam let's try 1516 / 9 / 22 again the first thing we want to do is rewrite our problem will change the divided by 9 22 + 2 * 22 / 9 now all we have to do is multiply but since these numbers are kind of big I'm going to use my calculator to help so we have all right on the top we have 15 times 22 equals 330 and on the bottom we have 16 times 9 equals 144 so the answer to our division problem is 330 / 144 of course that could be simplified for your final going to test but recover simplifying fractions in another video alright that's how you divide fractions you just multiply by the reciprocal and you have your answer but 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 fraction division problems written like this shows the top fraction 2/3 being divided by the bottom fraction 4 over 5 it's really just that we have 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 fraction lines here we can make it look a lot better let's rewrite this as a multiplication problem by taking the reciprocal of the bottom number to fraction that we're dividing by and multiplying it by the turn on top there that looks easier to do and it's really the same problem we just need to multiply to get the answer to 2 times 5 equals 10 + what 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 to don't forget to practice what you've learned by doing the exercises for this section thanks for watching and I'll see you next time learn more at Math Antics

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2.3 Dividing Fractions

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