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

EXPLANATION.

Denominator of a rational number is 4 more than the numerator.

If numerator and denominator are increased by 1 each the rational becomes = 1/2.

As we know that,

Le, we assume that.

Numerator of a number = x.

Denominator of a number = x + 4.

Rational number = (x)/(x + 4).

If numerator and denominator are increased by 1 each the rational becomes = 1/2

Numerator of a number = (x + 1).

Denominator of a number = (x + 4 + 1) = (x + 5).

Rational number = 1/2.

⇒ (x + 1)/(x + 5) = 1/2.

⇒ 2(x + 1) = 1(x + 5).

⇒ 2x + 2 = x + 5.

⇒ 2x - x = 5 - 2.

⇒ x = 3.

Rational number = (x)/(x + 4).

⇒ (3)/(3+ 4).

⇒ (3)/(7)

⇒ The number = 3/7.

Answer 2

Answer:

Given :-

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

To Find :-

• What is the original fraction.

Solution :-

Let,

$\mapsto \bf{Numerator =\: x}$

$\mapsto \bf{Denominator =\: x + 4}$

Hence, the required original fraction will be :

$\implies \sf \dfrac{Numerator}{Denominator}$

$\implies \sf\bold{\green{ \dfrac{x}{x + 4}}}$

According to the question,

$\implies \sf \dfrac{Numerator + 1}{Denominator + 1} =\: New\: Number$

$\implies \sf \dfrac{x + 1}{x + 4 + 1} =\: \dfrac{1}{2}$

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

By doing cross multiplication we get,

$\implies \sf 2(x + 1) =\: 1(x + 5)$

$\implies \sf 2x + 2 =\: x + 5$

$\implies \sf 2x - x =\: 5 - 2$

$\implies \sf\bold{\purple{x =\: 3}}$

Hence, the required original fraction will be :

$\longrightarrow \sf Original\: Fraction =\: \dfrac{x}{x + 4}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{3}{3 + 4}$

$\longrightarrow \sf\bold{\red{Original\: Fraction =\: \dfrac{3}{7}}}$

${\small{\bold{\underline{\therefore\: The\: orginal\: fraction\: is\: \dfrac{3}{7}\: .}}}}$