Question

if 1 is added to the denominator of a fraction, the fraction becomes 1/2. if 1 is added to the numerator of the fraction, the fraction becomes 1. find the fraction.​

Answer 1

Given

if 1 is added to the denominator of a fraction, the fraction becomes 1/2. if 1 is added to the numerator of the fraction, the fraction becomes 1.

To find

The fraction

Explanation

Let the numerator of the fraction be x

Let the Denominator of the fraction be y

According to the given information,

If 1 is added to the Denominator fraction becomes 1/2

$= > \dfrac{x}{y + 1} = \dfrac{1}{2}$

cross multiplying

$= > 2x = y + 1 \\ = > 2x - y = 1.............(1)$

when 1 is added to the numerator fraction becomes 1

$= > \dfrac{x + 1}{y} = 1$

cross multiplying

$= > x + 1 = y \\ = > x - y = - 1...............(2)$

eq(1)-eq(2)

$= > 2x - y - (x - y) = 1 - ( - 1)$

$= > 2x - y + y - x = 2 \\ = > x = 2$

$\boxed{\sf numerator=2}$

Substituting x=2 in eq 2

$= > x - y = - 1 \\ = > 2 + 1 = y \\ = > y = 3$

$\boxed{ \sf \: denominator = 3}$

$\underline{\sf fraction=\dfrac{x}{y}=\dfrac{2}{3}}$

Answer 2

Answer :-

Fraction is 2/3 .

Explanation :-

Let the fraction be x/y

Given

1 added to the denominator the fraction becomes 1/2

⇒ x/(y + 1) = 1/2

⇒ (y + 1)/x = 2/1

⇒ 1(y + 1) = 2x

⇒ y + 1 = 2x

⇒ y = 2x - 1 ---eq(1)

Given

1 added to the numerator the fraction becomes 1

⇒ (x + 1)/y = 1

⇒ x + 1 = y

Substitute y = 2x - 1 in the above equation

⇒ x + 1 = 2x - 1

⇒ 1 + 1 = 2x - x

⇒ 2 = x

⇒ x = 2

Substitute x = 2 in eq(1)

⇒ y = 2x - 1

⇒ y = 2(2) - 1

⇒ y = 4 - 1

⇒ y = 3

So fraction = x/y = 2/3

∴ the fraction is 2/3 .

Note :-

• The method used to solve the question is SUBSTITUTION METHD.