Question

thhe sum of numerator and denominator of a fraction is 4 more than twice the denominator . If the numerator and denominator are decreased by 1 the numerators become half the the denominator. Determine the fraction​

Answer 1

The fraction is $\frac{-3}{-7}$.

• Let the numerator and the denominator of the fraction be x and y respectively.
• Now according to the first condition, sum of numerator and denominator is 4 more than twice the denominator.

x + y = 2y + 4

x - y = 4   .....(Equation 1)

• Now according to the second condition,

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

2x - 2 = y - 1

2x - y = 1   ....(Equation 2)

• Subtracting equation 2 from 1 we get,

-x = 3

x = -3

• Substituting the value of x in equation 1, we get

-3 - y = 4

y = - 3 - 4 = -7

• The given fraction becomes, $\frac{-3}{-7}$