Question

the numerator of a fraction is four less than its denominator if 1 is added to both its numerator and denominator the fraction beacome 1/2 find the fraction​

Answer 1

Given :

• The numerator of a fraction is four less than its denominator.
• 1 is added to both its numerator and denominator the fraction beacome 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 four less than its denominator.

$\implies\sf{x=y-4............(1)}$

According to the 2nd condition :-

• 1 is added to both its numerator and denominator the fraction beacome 1/2.

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

$\implies\sf{\dfrac{y-4+1}{y+1}=\dfrac{1}{2}\:[put\:x=y-4\: from\:eq(1)]}$

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

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

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

$\implies\sf{y=7}$

• Denominator = 7

Now put y = 7 in eq(1) for getting value of x.

$\implies\sf{x=y-4}$

$\implies\sf{x=7-4}$

$\implies\sf{x=3}$

• Numerator = 3

Therefore ,

$\sf{Original\: fraction=\dfrac{3}{7}}$