Answer:
The original fraction is [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
Let the denominator be x
We are given that The numerator of a fraction (which is in its simplest form) is 5 less than the denominator.
Numerator = x-5
So, Fraction =[tex]\frac{x-5}{x}[/tex]
If the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by 1\3 of it.
A.T.Q
[tex]\frac{2(x-5)}{x+16}=\frac{2(x-5)}{3x}[/tex]
[tex]\frac{2x-10}{x+16}=\frac{2x-10}{3x}[/tex]
[tex]3x=x+16[/tex]
[tex]2x=16[/tex]
x=8
Denominator = 8
Numerator = x-5=8-5=3
Fraction : [tex]\frac{3}{8}[/tex]
Hence the original fraction is [tex]\frac{3}{8}[/tex]
