Question

The numerator of a fraction is 4 less than the denominator. If 1 is added to both its
numerator and denominator, it becomes 1/2 - Find the fraction​

Answer 1

Answer:

3/7

Step-by-step explanation:

3/7_______(3+1)/(7+1)

4/8=1/2

Answer 2

$\huge\tt\colorbox{green}{Answer}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

⠀⠀

Numerator is 4 less than denominator

If 1 is added to both then the fraction becomes 1/2

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

⠀⠀⠀⠀

Required fraction = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

⠀⠀⠀⠀

Let the denominator be x

⠀⠀⠀⠀

Therefore numerator is x - 4

⠀⠀⠀⠀

Acc. to the question :-

⠀⠀⠀⠀

$\sf :\implies\:{\dfrac{x-4+1}{x+1} = \dfrac{1}{2}}$

⠀⠀⠀⠀

$\sf :\implies\:{\dfrac{x- 3}{x+1} = \dfrac{1}{2}}$

⠀⠀⠀⠀

$\sf :\implies\:{2 ( x - 3 ) = x + 1 }$

⠀⠀⠀⠀

$\sf :\implies\:{2x - 6 = x + 1 }$

⠀⠀⠀⠀

$\sf :\implies\:{2x - x = 6 + 1 }$

⠀⠀⠀⠀⠀⠀⠀

$\sf :\implies\:{x = 7 }$

⠀⠀⠀⠀

Putting value of x in the fraction

⠀⠀⠀⠀

Numerator = x - 4 = 7 - 4 = 3

⠀⠀⠀⠀

Denominator = x = 7

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

⠀⠀⠀⠀

Required fraction = 3 / 7