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Divide / Multiply When Simplifying Fractions in Equations

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Newbie | Next Rank: 10 Posts
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by bruin61579 » Sun Jul 17, 2011 9:46 am
This is a really basic question...how do you know whether to divide or multiply the numerator / denominator when you're simplifying an equation with fractions?

For instance, if you're solving for X:

x/3 = 6

Do you divide the 6 by 3 (x = 6/3 = 2) or multiply it by 3 (x=18)?

Is there a rule you can follow (i.e. you multiply when you're moving the number in the denominator, and divide when you're moving the number in the numerator)?

Thanks,
David
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by goalevan » Sun Jul 17, 2011 1:48 pm
You will perform the same operation on both sides of the equation or inequality.

To solve for x in x/3 = 6, we can multiply both sides of the equation by 3:

(x/3) * 3 = 6 * 3
x * (3/3) = 6 * 3
x * 1 = 6 * 3
x = 18

A quick way to visualize this is with "cross multiplication".

For example, in 2/6 = x/9, we can multiply both sides by 9*5 and rearrange as 2*9 = 6x, x = 3.

If fractions are multiplied on the same side of the equals sign, the numerators are multiplied with one another and the denominators are multiplied with one another.

For example, x/6 * 3/5 = (x*3)/(6*5) = 3x/30 = x/10.

There are a lot of good GMAT prep books that you can find through this site to refamiliarize yourself with the basics.
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