Question

9. The numerator of a fraction is 2 less than the denominator. If one is added to its denominator, it becomes 1/2 find the fraction.​

Answer 1

Given :

• The numerator of a fraction is 2 less than the denominator.
• If 1 is added to its denominator, it becomes 1/2.

To find :

• The fraction .

Solution :

Consider,

• Numerator of the fraction = x
• Denominator of the fraction = y

According to the 1st condition :-

• The numerator of a fraction is 2 less than the denominator.

$\implies\sf{x=y-2..............(1)}$

According to the 2nd condition :-

• If 1 is added to its denominator, it becomes 1/2.

$\implies\sf{\dfrac{x}{y+1}=\dfrac{1}{2}}$

$\implies\sf{\dfrac{y-2}{y+1}=\dfrac{1}{2}\:[Put\:x=y-2\: from\:eq(1)}$

$\implies\sf{2y-4=y+1}$

$\implies\sf{2y-y=1+4}$

$\implies\sf{y=5}$

• Denominator = 5

Now , put y = 5 in eq(1) for getting the value of x.

$\implies\sf{x=y-2}$

$\implies\sf{x=5-2}$

$\implies\sf{x=3}$

Therefore,

The fraction = $\sf{\dfrac{3}{5}}$

__________________

Verification :-

• Numerator = 3
• Denominator = 5

According to the condition ,

$\implies\sf{\dfrac{3}{5+1}=\dfrac{1}{2}}$

$\implies\sf{\dfrac{3}{6}=\dfrac{1}{2}}$

$\implies\sf{\dfrac{1}{2}=\dfrac{1}{2}}$

Hence Verified !