Fractions and Cross MultiplicationDate: 07/14/98 at 02:12:54 From: Lauri Novotny Subject: Multiplying fractions Hello Dr. Math, A friend recently asked for my help in refreshing her basic math skills (she is an older student who will soon be going back to school). I agreed to help her, and we were quickly into fractions (+,-,x,/). When we started to do multiplication, my first response was to tell her that (a/b)(c/d) = ac/bd, but then there was something in my brain that said to cross multiply. I looked it up in a book and I know now that my first response was correct, but it has left me wondering when do you "cross multiply." I have tried to find the answer but without much success. Can you help me? Laura Date: 07/15/98 at 12:17:50 From: Doctor Peterson Subject: Re: Multiplying fractions Hi, Laura. I always like to help someone who's helping someone else! There are a couple of ways I have seen the idea of cross multiplication used. Only the first of them is really something I recommend. 1. To show that two fractions are equal If I have an equation like: 5 30 - = -- 6 36 and want to check whether it is true, one way is to cross multiply: 5 * 36 = 180 30 * 6 = 180 Since these are equal, the fractions are equal. This is most useful in algebra, where you can quickly transform an equation like: x-2 x+3 --- = --- x+4 x-2 to: (x-2)(x-2) = (x+3)(x+4) It's a better habit to think of this instead as multiplying both sides by the product of the denominators, but thinking of it as cross- multiplying can be a convenient trick. 2. To add two fractions Some people think of the numerator of a sum as cross-multiplying, since you add two crossed products: a c ad + bc --- + --- = ------- b d bd I don't like expressing it this way, because it leaves out the step of finding the least common denominator (since bd is only a common denominator, not necessarily the smallest), making the work often more complicated than it has to be. It sounds as if you have what it takes to help your friend. If you haven't looked at our Dr. Math archives, you might want to check them out, since we have some good explanations of things like multiplying and adding fractions: http://mathforum.org/dr.math/tocs/fractions.elem.html - Doctor Peterson, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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