Question

the numerator of a fraction is smaller than the denominator by 8. if 1 is added to the numerator and 3is subtracted from the denominator, the new fraction is ½. find the original fraction​

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The numerator of a fraction is smaller than the denominator by 8. If 1 is added to the numerator and 3 is subtracted from the denominator,the new fraction is 1/2.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The original fraction.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the numerator be r

Let the denominator be m

$\boxed{\bf{The\:original\:fraction=\frac{r}{m} }}}}$

A/q

$\longrightarrow\sf{r=m-8......................(1)}$

&

$\longrightarrow\sf{\dfrac{r+1}{m-3} =\dfrac{1}{2} }\\\\\\\longrightarrow\sf{2(r+1)=1(m-3)}\\\\\\\longrightarrow\sf{2r+2=m-3}\\\\\\\longrightarrow\sf{2(m-8)+2=m-3\:\:\:[from(1)]}\\\\\\\longrightarrow\sf{2m-16+2=m-3}\\\\\\\longrightarrow\sf{2m-14=m-3}\\\\\\\longrightarrow\sf{2m-m=-3+14}\\\\\\\longrightarrow\sf{\pink{m=11}}$

Putting the value of m in equation (1),we get;

$\longrightarrow\sf{r=11-8}\\\\\\\longrightarrow\sf{\pink{r=3}}$

Thus;

$\boxed{\bf{The\:original\:fraction=\frac{r}{m}=\frac{3}{11} }}}}$

Answer 2

Answer:

Step-by-step explanation:

Given :-

The numerator of a fraction is smaller than the denominator by 8.

If 1 is added to the numerator and 3 is subtracted from the denominator, the new fraction is ½.

To Find :-

The Fraction.

Solution :-

let the denominator of the required fraction be x

And the numerator of the fraction be (x - 8).

According to the Question,

⇒ (x - 8 + 1)/(x - 3) = 1/2

⇒ (x - 7)/(x - 3) = 1/2

⇒ 2(x - 7) = 1(x - 3)

⇒ 2x - 14 = x - 3

⇒ 2x - x = - 3 + 14

⇒ x = 11

Fraction = (x - 8)/x = (11 - 8)/11 = 3/11

Hence, the required fraction is 3/11.