Question

the denominator of a fraction is 6 more than its numerator if 2 is added both to the numerator and denominator the fraction becomes 1/2 find the fraction​

Answer 1

Answer:

The fraction is $\sf{\dfrac{4}{10}}}$

Step-by-step explanation:

Let,

The numerator of a fraction = x

The denominator of a fraction = x + 6

If 2 is added both to the numerator and denominator the fraction

The numerator of a fraction = x + 2

The denominator of a fraction = x + 6 +2

⇒ x + 6 +2

⇒ x + 8

The denominator of a fraction = x + 8

The fraction becomes 1/2

⇒ $\sf{\dfrac{x + 2}{x + 8} \: = \: \dfrac{1}{2}}}$

⇒ 2 (x + 2) = 1 (x + 8)

⇒ 2x + 4 = 1x + 8

⇒ 2x - x = 8 - 4

⇒ x = 4

The numerator of a fraction = 4

The denominator of a fraction = x + 6

⇒ 4 + 6

⇒ 10

The denominator of a fraction = 10

Therefore,

The fraction is $\sf{\dfrac{4}{10}}}$

Answer 2

Given ,

• The denominator of a fraction is 6 more than its numerator

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

Let ,

The Numerator of fraction be " x "

Then , Denominator = x + 6

According to the question ,

(x + 2)/(x + 6 + 2) = 1/2

2x + 4 = x + 8

x = 4

$\sf \therefore \underline{The \: fraction \: is \: \frac{4}{10} }$