Question 1036683
let n = the numerator of the original fraction
let d = the denominator
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Write an equation for each statement
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The denominator of a fraction is four less than twice the numerator
d = 2n - 4
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if three is added to both the numerator and denominator, the new fraction is equal to two-thirds.
{{{((n+3))/((d+3))}}} = {{{2/3}}}
cross multiply
3(n+3) = 2(d+3)
3n + 9 = 2d + 6
3n = 2d + 6 - 9
3n = 2d - 3
replace d = (2n-4)
3n = 2(2n-4) - 3
3n = 4n - 8 - 3
3n - 4n = -11
-n = -11
n = 11
Find d using the 1st equation d = 2n - 4
d = 2(11) - 4
d = 18
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 What is the original fraction?  {{{11/18}}}
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You can check this for yourself, in the statement
"if three is added to both the numerator and denominator, the new fraction is equal to two-thirds. "