Question

4) The denominator of a fraction is 6 more than its numerator. If 2 is added to both the
numerator and the denominator, the fraction becomes Find the fraction.​

Answer 1

CORRECT QUESTION.

The denominator of a fraction is 6 more than

it's numerator. if 2 is added to both the numerator

and the denominator the fraction become 1/2.

find the friction.

EXPLANATION.

• GIVEN

y = x + 6 [ denominator of fraction is 6 more than

it's numerator ]

According to Given question

equation will be written as :-

x + 2 / x + 6 + 2 = 1/2

x + 2 / x + 8 = 1/2

2x + 4 = x + 8

x = 4

put the value of x in equation

we get,

y = 4 + 6

y = 10

hence,

fraction will be written as

x/y = 4/10 = 2/5

Hence,

fraction will be = 2/5

Answer 2

Question:

The denominator of a fraction is 6 more than its numerator. If 2 is added to both the numerator and the denominator, the fraction becomes Find the fraction.

Answer:

$\underline\bold{\frac{2}{5}} \: is \: the \: fraction$

Step-by-step explanation:

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

$\implies Numerator = x$

$\implies Denominator = x + 6$

Now, 2 is added to both the numerator and the denominator

$\implies Numerator = x + 2$

$\implies Denominator = x + 8$

Thus, the equation is

$\implies\frac{x + 2}{x + 8} = \frac{1}{2}$

$\implies 2(x + 2) = 1(x + 8)$

$\implies 2x + 4 = x + 8$

$\implies 2x - x = 8 - 4$

$\implies\boxed{x = 4}$

$Also, \: given \: \boxed{y=x+6}$

Substitute the value of x = 4

$\implies y = 4 + 6$

$\implies \boxed{y = 10}$

$Fraction = \frac{x}{y}$

$\implies \frac{4}{10}$

$\implies \boxed{\frac{2}{5} }$

$\therefore \boxed{\frac{2}{5} } \: is \: the \: fraction.$

Hint:

Hint given in the question :

★ The denominator of a fraction is 6 more than its numerator.

$★ Fraction = \frac{x}{y}$