Question 181833
2 1/2 is a mixed number and has to be converted to a pure fraction
2 1/2 is actually {{{2 + 1/2}}}, so what you have to answer is:
"How many 1/2's are in 2? There are 4 1/2's in 2 because
{{{4*(1/2) = 2}}}
Now you have {{{4*(1/2) + (1/2) = 5*(1/2)}}}
and
{{{5*(1/2) = 5/2}}}
So, now you have
{{{(5/2)/x = 10/3}}}
Remeber that {{{5/2}}} 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 {{{2.5}}}, but it's OK the way it is
Now multiply both sides of the equation by {{{x}}}
{{{5/2 = (10/3)*x}}}
Now multiply both sides by {{{6}}}
{{{3*5 = 2*10*x}}}
{{{15 = 20x}}}
Divide both sides by {{{20}}}
{{{x = 15/20}}}
{{{x = 3/4}}} answer
To prove the answer, just put this result back into the
original equation
{{{(5/2)/x = 10/3}}}
{{{(5/2)/(3/4) = 10/3}}}
Now you've got fractions in both numerator and denominator,
but it's still OK
MUltiply the left side only by {{{(4/3)/(4/3)}}}, which is
actully just {{{1}}}
{{{((4/3)/(4/3))*((5/2)/(3/4)) = 10/3}}}
Notice that the denominator is {{{(4/3)*(3/4)}}} which is {{{1}}}
{{{(4/3)*(5/2) = 10/3}}}
{{{20/6 = 10/3}}}
{{{10/3 = 10/3}}}
OK