Answer:
[tex]\frac{2}{5}[/tex].
Step-by-step explanation:
Let the unknown fraction be [tex]\frac{x}{y}[/tex] ,
where, x and y both are prime numbers less than 20.
Now, it is given that adding 1 to both numerator and denominator will make the fraction [tex]\frac{1}{2}[/tex].
Thus,
[tex]\frac{x+1}{y+1}[/tex] = [tex]\frac{1}{2}[/tex]
2(x + 1) = y + 1
2x + 2 = y + 1
2x + 1 = y.
Clearly if x will be any odd number , two times x will be odd and adding 1 to it will result in even number and y should be even number , which is not possible as only even prime is 2.
Thus , x should be the even prime which is 2.
And y will be 5.
Thus the required fraction is [tex]\frac{2}{5}[/tex].
