Lesson: Eliminating Fractions

Comment on Eliminating Fractions

How do we find the least common multiple of all 5 denominators? (which = (5^5)(7^5)) for this question:

https://gmatclub.com/forum/which-of-the-following-has-the-greatest-value-248206.html
gmat-admin's picture

Question link: https://gmatclub.com/forum/which-of-the-following-has-the-greatest-value...

I knew that the least common multiple of the five denominators will consist of powers of 5 and 7.

First, since the biggest power of 5 is 5^5, the least common multiple must have 5^5

Likewise, since the biggest power of 7 is 7^5, the least common multiple must have 7^5.

Does that help?

Cheers,
Brent

It was nice to see this different question! :)

I tried to solve the equation in 4:27 by unifying the denominators multiplying each fraction by 2 and 3, and ended up with x = 20. there must be something wrong I have done in the process. but can we solve the equation by unifying the denominators rather than eliminating the fractions?
gmat-admin's picture

Let's try it.

GIVEN: (3x + 2)/2 - (x + 1)/3 = x

Rewrite fractions with common denominators.

Take (3x + 2)/2 and multiply top and bottom by 3 to get the EQUIVALENT fraction (9x + 6)/6

Take (x + 1)/3 and multiply top and bottom by 2 to get the EQUIVALENT fraction (2x + 2)/6

Our equation becomes: (9x + 6)/6 - (2x + 2)/6 = x

Combine numerators to get: (7x + 4)/6 = x

Multiply both sides by 6 to get: 7x + 4 = 6x

Solve: x = -1

Does that help?

Cheers,
Brent

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