How to Simplify Complex Fractions

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A complex fraction implies that there's a fraction on the top or on the bottom. Use cross multiplying and reciprocals to simplify complex fractions with help from a tutor in this free video on math lessons and study tips.

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Lets take a look at simplifying a complex fraction. So the word itself complex fraction kind of intimidates people. But really it's not that bad. Complex fraction just means it doesn't mean it's that complex. It just implies that there's a fraction on the top and a fraction on the bottom. So actually I don't think that there needs to be a fraction on top and on the bottom, it just means you have a fraction in one of the parts. A normal fraction would look like this. Two thirds, but if you take out the two or the three and you put a fraction in that part, so take out this two and make it one half over three. That's called a complex fraction it's just a technical term. So if we want to simplify this complex fraction, nobody likes to have fractions in the numerator, the top, or the denominator, the bottom of a fraction. To simplify it out, all we do is very simple. All we do is we take the inverse, the reciprocal that is of this number. So that would be four thirds, reciprocal is the technical term, it means just flip it. You multiply by the reciprocal of the bottom number and you have to do it on the top as well. In a fraction, to keep a fraction equivalent or equal all you need to do, you need to multiply whatever you do to the bottom, you have to do to the top as well. So to eliminate this we are going to multiply by the reciprocal. The reason we do that is because three fourths times four thirds, the three's cross cancel, the fours cross cancel eliminating that just making it one on the bottom. On the top, we get one times four, we could actually cross cancel here but we won't in this case. One times four is four, two times three is six so I get four over six over one. Now in a fraction when you have over one, you really don't need it. So we can actually eliminate that part. So the answer is this complex fraction actually just simplifies to four sixth. And of course any time you can reduce you should. So four sixth, you can divide the top and bottom by two and that's why we get two thirds. If I cross canceled way back here, that would have saved me an extra step.

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