Answer: [tex]\dfrac{7}{14}[/tex]
Step-by-step explanation:
Let the fraction be : [tex]\dfrac{x}{y}[/tex]
The value of the numerator of a particular fraction is one-half the value of its denominator.
[tex]x=\dfrac{1}{2}y[/tex] i.e. [tex]y= 2x[/tex] (1)
If the numerator is increased by 2 and the denominator is decreased by 2, the value of the resulting fraction is 3/4.
[tex]\dfrac{x+2}{y-2}=\dfrac{3}{4}[/tex] (2)
Put value of y from (1) in (2), we get
[tex]\dfrac{x+2}{2x-2}=\dfrac{3}{4}\\\\ 4(x+2)=3(2x-2)\\\\ 4x+8=6x-6\\\\ 6x-4x=8+6\\\\ 2x=14\\\\ x=7[/tex]
from (1), y= 2(7)=14
Thus , The original fraction becomes [tex]\dfrac{7}{14}[/tex]
