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cross multiplying fractions with variables. Confused

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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cross multiplying fractions with variables. Confused

by tonebeeze » Thu Apr 14, 2011 9:18 am
Hello,

I am still a little confused regarding the rules of cross-multiplying fractions that contain variables. For instance:

x/2 = 3/y vs.

x/(x-4) > 5/3

I would like some hard fast rules to cling onto, especially during the DS section when these constraints are often tested. Thanks for the help.
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by VivianKerr » Thu Apr 14, 2011 12:27 pm
x/2 = 3/y

You'd multiply the numerator of one, by the denominator of the other:

(x)(y) = (2)(3)

xy = 6

When two fractions (ratios) are set equal to each other, it's called a proportion.

For x / (x - 4) > 5/3, remember that this is an inequality so it is not a proportion. We do not know what x is, so we need to be very careful when we simplify.

x / (x - 4) = x/x - x/4 = 1 - x/4

1 - x/4 > 5/3

We can continue to simplify, but remember that if we multiply or divide by a negative number, we'll need to flip the inequality.

4(1 - x/4) > 4(5/3)

4 - x > 20/3

- x > 20/3 - 4

- x > 20/3 - 12/3

- x > 8/3

x < -8/3
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