SOLUTION: 2{{{1/2}}} OVER x = {{{10/3}}} 2{{{1/2}}} is the numerator and x is the denomanator, I need to figure out what x is. I dont know how to slove a problem with a fraction like this

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Question 181833: 2 OVER x =
2 is the numerator and x is the denomanator, I need to figure out what x is. I dont know how to slove a problem with a fraction like this. I have submited this problem before but couldnt understand the answer. So please show your work and please explain how you got the answer. And if you can could you please explain to me why the fraction is like that and what they are used for so I can better understand it in the future?
Thank You
Found 2 solutions by edjones, josmiceli:
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
2.5/x=10/3
7.5=10x multiply each side by 3x (LCM) to eliminate fractions.
x=.75
.
Another way:
2 1/2 = 5/2
5/2 / x = 5/2 * 1/x = 5/2x
5/2x = 10/3
15=20x multiply each side by 6x (LCM) to eliminate fractions.
x=.75
Ed

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
2 1/2 is a mixed number and has to be converted to a pure fraction
2 1/2 is actually , so what you have to answer is:
"How many 1/2's are in 2? There are 4 1/2's in 2 because

Now you have
and

So, now you have

Remeber that is just a number and it's OK for it to be
the numerator of a fraction. If you wanted to, you could
represent it as , but it's OK the way it is
Now multiply both sides of the equation by

Now multiply both sides by

Divide both sides by

answer
To prove the answer, just put this result back into the
original equation

Now you've got fractions in both numerator and denominator,
but it's still OK
MUltiply the left side only by , which is
actully just

Notice that the denominator is which is

OK