Question

if 1 is subtracted from the numerator of a fraction becomes 2 by 3 but if 5 is added to the denominator of the fraction it becomes 1 by 2 find the fraction ​

Answer 1

Answer: X is 7 and the y is 9 so the fraction is 7/9

Step-by-step explanation: solution is given below in the image

Answer 2

Given:

• When 1 is subtracted from the numerator, the fraction becomes 2/3
• When 5 is added to the denominator, the fraction becomes 1/2

Find:

• The original fraction

Define the fraction:

$\text{Numerator} = x$

$\text{Denominator} = y$

$\text{Fraction} = \dfrac{x}{y}$

When 1 is subtracted from the numerator, the fraction is 2/3:

$\dfrac{x - 1}{y} = \dfrac{2}{3}$

$3(x - 1) = 2y$

$3x - 3 = 2y$

When 5 is added to the denominator, the fraction is 1/2:

$\dfrac{x}{y + 5} = \dfrac{1}{2}$

$2x = y + 5$

$y = 2x - 5$

Solve for x and y:

$3x - 3 = 2y \text { ------------------ [ 1 ]}$

$y = 2x - 5 \text { ------------------ [ 2 ]}$

Substitute [ 2 ] in [ 1 ]:

$3x - 3 = 2( 2x - 5)$

$3x - 3 = 4x - 10$

$x = 7$

Substitute x = 7 into [ 2 ]:

$y = 2(7) - 5$

$y =9$

Find the original fraction:

$\text{Fraction } = \dfrac{x}{y}$

$\text{Fraction } = \dfrac{7}{9}$

Answer: The fraction is 7/9