Question

If 1 is added to the denominator of a fraction, the
fraction becomes 1/2.
If 1 is added to the
numerator of the fraction, the fraction becomes 1.
Find the fraction.
(ICSE)​

Answer 1

Answer:

$\frac{2}{3}$

Step-by-step explanation:

let the fraction is  $\frac{x}{y}$

1st case : $\frac{x}{y+1} =\frac{1}{2}$

then: 2X = Y+1

so : 2X-1 = Y           ( eq.1)

2nd case : $\frac{x+1}{y} =1$

then : X+1 = Y      (eq.2)

So , If we equalize (eq.1) to (eq.2)

2X-1 = X+1

So 2X = X+2

So X= 2

By Substituting By the Value of X in eq.2, we will find that :

Y = 3

Check :

$\frac{2}{3+1} =\frac{2}{4} =\frac{1}{2}$

$\frac{2+1}{3} =\frac{3}{3} =1$