Question

The numerator of a fraction is 5 less than its denominator. If 2 is subtracted from the numerator and 2 is

added to the denominator, the fraction becomes 2/5. find the original fraction.​

Answer 1

X= 13

N= x-5 = 8

D= 13

Fraction will be = 8/13

The answer is in the Attachment

Answer 2

Answer:

The fraction is $\sf{\dfrac{8}{13}}$

Step-by-step explanation:

Numerator of the fraction = 5 less than its denominator

When 2 is subtracted from the numerator and 2 is added to denominator is = 2/5

Original Fraction = ??

Let the original rational number be,

• Numerator as x
• Denominator as (x + 5)

According to the Question,

When 2 is subtracted from the numerator and 2 is added to denominator is = 2/5

$\sf{\longrightarrow \: \dfrac{x - 2}{(x + 5) + 2} = \dfrac{2}{5} }$

$\sf{\longrightarrow \: \dfrac{x - 2}{x + 7} = \dfrac{2}{5} }$

$\sf{\longrightarrow \: 5(x - 2)} = 2(x + 7)$

$\sf{\longrightarrow \: 5x - 10= 2x +14}$

$\sf{\longrightarrow \: - 10 - 14= 2x - 5x}$

$\sf{\longrightarrow \: - 24= - 3x}$

$\sf{\longrightarrow \: x = \dfrac{24}{3}}$

$\sf{\longrightarrow \: x = 8}$

____________________________

Denominator =

$\sf{\longrightarrow \: 8 + 5}$

$\sf{\longrightarrow \: 13}$

____________________________

Original fraction =

• Numerator = 8
• Denominator = 13

Therefore, the fraction is $\sf{\dfrac{8}{13}}$