Solving Proportions

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The most common strategy involved in solving proportions is cross multiplication, in which one denominator is multiplied with the other side's numerator. Solve proportions easily, even if variables are involved, with help from a math teacher in this free video on proportions in math.

Part of the Video Series: Fractions & Proportions
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So, how does one solve proportions? Hi. I'm Jimmy Chang. I have been teaching college mathematics for nine years. And solving proportions, when you think of proportions, you think of fractions and generally, that sounds rather unpleasant. But, when you think about it, when you see proportion problems, they all involve one common strategy and that is cross multiplication. And one you master that skill, everything actually seems not so bad after all. So, here's an example. Suppose you have x over 10 equal to five over nine. Now, when you have a proportion like this, you know how to cross multiply, especially when you see that there's one fraction on one side and a fraction on the other side. How you solve it is take one denominator and multiply it with the other side's numerator. So, you have ten times five is equal to 50. And then you repeat for the other side. Take this denominator and multiply it with the other numerators and you have 9x. Now, it's a pretty easy equation to solve after all. Divide both sides by nine and you'll have x is equal to 50 over nine. Now, at first this seems like it's a reducible fraction, but after some looking at it, you'll see that, unfortunately, they have no factors in common. Now, on the other hand, if you have x in the denominator, it's the same kind of idea. Suppose you have six over x equals three over two. Again, you can solve it by cross multiplication. So, the denominator x multiplied with the numerator three. So, you have 3x, and that's equal to 2 times the other numerator, 6, and you're going to get 12. And in solving for x, just go ahead and divide both sides by three. The threes cancel and you have x=2. And you know 12 divided by 3 is going to equal to 4. But, just wherever x is going to be, whether it be the numerator or denominator, you can still solve proportions very easily. So, I'm Jimmy Chang and those are a couple strategies on solving proportions.

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