Question

The denominator of a rational number is 4 more than the numerator. if the numerator and the denominator are increased by 1 each, the rational number becomes 1/2. find the number.​

Answer 1

Answer:

The original rational number is $\bf{\dfrac{3}{7}}$.

Step-by-step explanation:

Let,

• Numerator = x
• Denominator = (x + 4)

$\sf{Original \: \:fraction = \dfrac{x}{(x + 4)}}$

Condition given :

$\longrightarrow{\sf{\dfrac{x + 1}{(x + 4) + 1 } = \dfrac{1}{2} }}$

$\longrightarrow{\sf{\dfrac{x + 1}{x + 5} = \dfrac{1}{2}}}$

$\longrightarrow{\sf{2(x + 1) = 1(x + 5)}}$

$\longrightarrow{\sf{2x + 2 = x + 5}}$

$\longrightarrow{\sf{2x - x = 5 - 2}}$

$\longrightarrow{\sf{x = 3}}$

Put value of x in original Fraction.

$\longrightarrow{\sf{\dfrac{3}{(3 + 4)}}}$

$\longrightarrow{\sf{\dfrac{3}{7}}}$

Therefore, the original rational number is $\bf{\dfrac{3}{7}}$.

Answer 2

Given :-

The denominator of a rational number is 4 more than the numerator. if the numerator and the denominator are increased by 1 each, the rational number becomes 1/2

To Find :-

Fraction

Solution :-

Let the fraction be x/y

x = y - 4 (i)

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

x + 1/y + 1 = 1/2

2(x + 1) = y + 1

2x + 2 = y + 1

2x - y = 1 - 2

2x - y = -1

2(y - 4) - y = -1

2y - 8 - y = -1

y - 8 = -1

y = -1 + 8

y = 7

Using 1

x = y - 4

x = 7 - 4

x = 3

Fraction = x/y = 3/7