Question

The denominator of a fraction is 4 more than its numerator on subtracting one from each numerator and the denominator the fraction becomes 1 by 2 find the original fraction

Answer 1

Answer : $\bold{5/9}$



Explanation -

Let the numerator = x

Denominator = x + 4.


$fraction \: = \dfrac{x}{x + 4}$


Given : when subtracting 1 from each numerator and denominator the fraction becomes 1/2.


According to the given question -


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


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

$2(x - 1) = 1(x + 3)$


$2x - 2 = x + 3$

$2x - x = 3 + 2$

$x = 5$

So, Numerator = 5.


Finding the Fraction -


$\dfrac{x}{x + 4} = \dfrac{5}{5 + 4} = \dfrac{5}{9}$

Answer 2

Answer:

The original fraction is 5/9.

Step-by-step explanation:

Let the numerator be x.

Let the denominator be x+4.

∴Fraction=x/x+4

∴x-1/(x+4)-1 = 1/2

⇒x-1/x+3 = 1/2

⇒2(x-1)=1(x+3)_______________(∴Cross multiplication)

⇒2x-2=x+3

⇒2x-x=3+2

⇒x=5

∴x/x+4 = 5/5+4

           =5/9

Hence, the original fraction is 5/9.