Question

The numerator of a fraction is 4 less than the denominator. If 1 is added to both its
numerator and denominator, it becomes 1/2. Find the fraction.​

Answer 1

Answer :-

Required fraction is 3/7.

Explanation :-

Let the denominator of the fraction be x

Numerator of the fraction = 4 less than the denominator = (x - 4)

If 1 is added to both numerator and denominator

Numerator = (x - 4) + 1 = x - 4 + 1 = (x - 3)

Denominator = (x + 1)

Given

If 1 is added to both numerator and denominator fraction becomes 1/2

⇒ (x - 3)/(x + 1) = 1/2

By cross multiplication

⇒ 2(x - 3) = 1(x + 1)

⇒ 2x - 6 = x + 1

⇒ 2x - x = 1 + 6

⇒ x = 7

Denominator of the fraction = x = 7

Numerator f the fraction = (x - 4) = (7 - 4) = 3

Fraction = Numerator/Denominator = 3/7

∴ the required fraction is 3/7.

Answer 2

Answer:

3/7

Step-by-step explanation:

let numerator be a

then the denominator will be [ a + 4 ]

and fraction ( a/b )

According to question 1 is added

both numerator and denomirator it

becomes 1/2

i,e [ a + 1]/[ a + 4 + 1 ] = 1/2

[ a + 1 ]/[ a + 5 ] = 1/2

cross multiply above

2[ a + 1 ] = [ a + 5 ]

2a + 2 = a + 5

2a - a = 5 - 2

a = 3

numerator a = 3

and denominator a + 4 = 3 + 4 = 7

Hence

Required fraction a/b = 3/7.