Question

The denominator of a rational number is 4 more than the numerator. if the numerator and the denominator are increased by 1 each, the rational number becomes 1/2. find the number.​

Answer 1

Given :

• The denominator of a rational number is greater than its numerator by 4.
• If the numerator and the denominator are increased by 1 each, the rational number becomes 1/2.

To Find :

• Original Fraction .

Solution :

$\longmapsto\tt{Let\:Numerator\:be=x}$

As Given that Denominator of a rational number is greater than its numerator by 4 . So ,

$\longmapsto\tt{Denominator=x+4}$

Now ,

• If the numerator and the denominator are increased by 1 each, the rational number becomes 1/2.

$\longmapsto\tt{Numerator=x+1}$

$\longmapsto\tt{Denominator=x+4+1=x+5}$

A.T.Q :

$\longmapsto\tt{\dfrac{x+1}{x+5}=\dfrac{1}{2}}$

$\longmapsto\tt{2(x+1)=1(x+5)}$

$\longmapsto\tt{2x+2=1x+5}$

$\longmapsto\tt{2x-1x=5-2}$

$\longmapsto\tt\bf{x=3}$

Value of x is 3 .

Therefore :

$\longmapsto\tt{Numerator=x}$

$\longmapsto\tt\bf{3}$

$\longmapsto\tt{Denominator=4+3}$

$\longmapsto\tt\bf{7}$

So , The Fraction is 3/7 .

Answer 2

Given denominator is 4 more than numerator

x/x+4 is the given fraction

x+1/x+5 = ½

2(x+1)=x+5

2x+2=x+5

x=3

Therefore, the given number is x/x+4=3/7

Hope the answer helps you thank you