Question 707485
 "a fraction is equal to 1/2."
{{{n/d}}} = {{{1/2}}}
Cross multiply
d = 2n
:
 "if its numerator is increased by 1 and its denominator is increased by 5 the value of the resulting fraction is 4/9"
{{{(n+1)/(d+5)}}} = {{{4/9}}}
Cross multiply
9(n+1) = 4(d+5)
9n + 9 = 4d + 20
9n = 4d + 20 - 9
9n = 4d + 11
replace d with 2n
9n = 4(2n) + 11
9n = 8n + 11
9n - 8n = 11
n = 11
then
d = 22
hence
{{{11/22}}} is the original fraction (which = 1/2)
:
:
Check this
{{{(11+1)/(22+5)}}} = 
{{{12/27}}} reduces to {{{4/9}}}