Reciprocating the Denominator

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At some point during your mathematical studies you may have to work with reciprocating the denominator of a problem. Learn about reciprocating the denominator 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. I'm Jimmy Chang and we're here to talk about reciprocating the denominator. Now, when it comes to reciprocating the denominator, we're really looking at the reciprocal of the denominator because oftentimes when you have to divide by the denominator, you would need to think about the reciprocal because dividing fractions really involves multiplication which involves flipping the denominator. So, we'll just go through a couple of examples and you'll see how this works. Now, suppose you have a situation where you have four fifths divided by seven thirds. Now, like we talked about before, dividing fractions really involves multiplication. You just have to think about what the denominator is. The denominator is seven thirds. So, when we're talking about reciprocating the denominator, we're really talking about taking this and then finding the reciprocal of it. Now, the reciprocal of course is flipping the fraction. So, the reciprocal of seven thirds is really three sevenths. So instead of dividing four fifths, by seven thirds, you're actually multiplying four fifths by the reciprocal, three sevenths. Now, in this case you can just multiply across. Four times three is twelve, five times seven is going to give you thirty five. Now, if you were to go in to algebra, let's just say you have six fifths divided by three over x, hypothetically. It works the same way. You take your denominator, and think about the reciprocal, three over x. The reciprocal of that is x over three. So, you;re really taking six fifths and multiplying by x over three. And then you just multiply across and you'll have six times x is six x, five times three is fifteen and then you can reduce that. It looks like both of them reduces by two. So you have two x, or excuse me, divide both sides by three, so you have 2 x divide by five. Now, I want to stress though, you can only do this is you're denominator only has one term term. Because if you have more than one term that are added, if you have two terms added or subtracted by each other, you reciprocal thing. So, I'm Jimmy Chang and that's a brief introduction to reciprocating the denominator.


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