Cross-MultiplicationDate: 08/04/2002 at 01:51:27 From: Cammy Subject: How do you cross multply? Please, I know it's simple but I still have trouble. I can't figure out a way to type it out, so can you just show me the basics so I can understand? Thanks, Cammy Date: 08/04/2002 at 16:14:12 From: Doctor Ian Subject: Re: How do you cross multply? Hi Cammy, When you cross-multiply, you're really multiplying each side by n/n, where n is the denominator of the other side: a c - = - b d a d c b - * - = - * - b d d b Note that this doesn't change anything, because multiplying anything by 1 doesn't change its value. So now we have ad bc -- = -- bd bd Since you're dividing both sides by the same thing, you can ignore it, to get ad = bc Once you get used to the idea, you can skip all the middle steps and just multiply the things that are crosswise from each other: a c . . . . - = - . . . . b d which is where we get the name 'cross-multiplying'. It's always good to understand something in more than one way, so here's another way to look at it. When you have any two things that are equal, this = that then if neither of them is zero, it will be true that this ---- = 1 that right? Let's look at that for a c - = - b d a/b ----- = 1 c/d a d - * - = 1 Because to divide by a fraction, b c you invert and multiply... ad -- = 1 bc ad = bc Here, we're just noting that if this/that = 1, then this = that... If you just learn to cross-multiply without understanding _why_ it works, then it can seem like magic. But after you do a couple of dozen of these the long way, your brain will automatically start looking ahead a few steps, and you'll start taking the shortcut naturally, because you're _ready_ to. And at that point, you'll never really be able to forget how to cross-multiply, because you'll always be able to figure it out again if you need to. In addition, you might want to take a look at this: Flipping and Switching Fractions http://mathforum.org/library/drmath/view/58193.html Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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