Question

the sum of denominator and numerator of a fraction is 3 less than twice the denominator if the each of the numerator and denominator is decreased by 1 the fraction becomes 1/2 find the fraction​

Answer 1

The rational number is $\frac{-2}{7}$ .

• Let the numerator of the fraction be x and denominator be y.
• The sum of denominator and numerator is given as 3 less than twice the denominator.

x+ y = 2y - 3

x - y = -3       ........(Equation 1)

• Now when 1 is decreased from the numerator and from the denominator then the fraction becomes $\frac{1}{2}$

$\frac{x-1}{y-1} = \frac{1}{2}$

2x - 2 = y - 1

2x - y = 1     .........(Equation 2)

• Adding 1 and 2 , we get

3x = -2

x = -2/3

• Now substituting the value of x in equation 1 we get,

y = -2/3 + 3

y = 7/3

• Therefore the fraction becomes $\frac{x}{y}$
• That is $\frac{-2/3}{7/3}$ .