SOLUTION: Please help! Simplify by any method. {{{ ((1)/(3y)+(1)/(6y))/((1)/(2y)+(3)/(4y)) }}}

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Question 622931: Please help! Simplify by any method.

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!

There are different ways to simplify compound fractions like this. The way I prefer is this:
  1. There is a "big" fraction and parts of the numerator and denominator of the "big" fraction are "little" fractions. Find the lowest common denominator (LCD) of all the "little" denominators.
  2. Multiply the numerator and denominator of the "big" fraction by the LCD found in step one. If this is done correctly, all the "little" fractions will disappear.
  3. At this point you have a simple fraction. Simplify it.
Let's see how this works on your compound fraction.

1. Find the LCD.
Your "little" denominators are 3y, 6y, 2y and 4y. The LCD of these is 12y.

2. Multiply the numerator and denominator of the "big" fraction by the LCD:

To multiply correctly we must use the Distributive Property:

Every "little" denominator cancels out leaving:
%281%2A4%2B1%2A2%29%2F%281%2A6%2B3%2A3%29

3. Simplify
%284%2B2%29%2F%286%2B9%29
6%2F15
2%2F5

So simplifies down to 2/5

P.S. I suspect that you posted several other similar problems. I hope this helps you figure out how to do them, too.