What Is a Reciprocal's Use in Math?

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In the world of mathematics, a reciprocal plays a very important role. Learn about a reciprocal's use in mathematics with help from an experienced mathematics educator in this free video clip.

Part of the Video Series: Elementary Math
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Video Transcript

Hi my name is Marija, I'm a mathematician and today I'm going to tell you what a reciprocal's use is in math. And a reciprocal has a few uses. Let's talk about what a reciprocal is first. A reciprocal is when you take a fraction for example two thirds, and you're going to switch the place of the numerator and the denominator. So I'm just going to put the three in the numerator and the two in the denominator. So the reciprocal of two thirds is three halves, OK that's what the definition is. Now one way that you can use a reciprocal is by knowing that if you multiply a number times its reciprocal, you're going to get one. And I'll show that to you. Two times three is six, and three times two is six, and six divided by six is one. That's always going to happen. So if I ever multiply a number by it's reciprocal, I'm going to get one. That fact is going to be useful for me if I have an equation such as two thirds of x equals four. If I want to solve this equation, then I need to get x alone. To get x alone, I'd have to get rid of the two thirds. Well because the two thirds is being multiplied by the x, what I can do is multiply both sides by its reciprocal. Why am I doing that? Because I know now that if I multiply a number by its reciprocal, I'm going to get one. And if I get one, then I've gotten x alone because one times x is just x. Now on the other side I'm going to go ahead and multiply four times three is 12, and the imaginary one under here, one times two is two, x equals six. So one way that a reciprocal was useful is if you have an equation where a variable is being multiplied by a fraction, you can multiply by the reciprocal and that will get rid of that fraction. The other way that a reciprocal was useful is you need it in order to divide fractions. So for example if I have one half divided by two thirds, what you need to do to solve this problem is actually multiply the fractions. So this becomes on half times three halves. So what you do when you divide fractions is you keep the first fraction, so one half stayed one half, the division becomes multiplication, and the second fraction becomes a reciprocal. So this is another place where reciprocals become important. And now you go ahead and multiply one times three is three, and two times two is four and the product would be three fourths. So two places that reciprocals are important are in solving an equation where the fraction is a coefficient of a variable, and when you are dividing fractions. My name is Marija and I just showed you why reciprocals are useful in math.

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