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 rational number is 3/7.

To find :-

• The rational number.

Step-by-step explanation :-

Let the numerator of the rational number be "x".

• As the denominator of the rational number is 4 more than it's numerator,

Therefore,

• The denominator of the rational number will be "x + 4".

Increasing the numerator and denominator by 1,

• The numerator becomes "x + 1".
• The denominator becomes "x + 4 + 1".

Given that :-

• If the numerator and denominator of the rational number are increased by 1 each, the rational number becomes 1/2.

________________________________

Therefore,

$\longmapsto \: \bf \dfrac{x + 1}{x + 4 + 1} = \dfrac{1}{2}$

$\bf \longmapsto \: \dfrac{x + 1}{x + 5} = \dfrac{1}{2}$

$\longmapsto \: \bf 1 \: (x + 5) = 2 \: (x + 1)$

$\longmapsto \: \bf x + 5 = 2x + 2$

$\bf\longmapsto \: x - 2x = 2 - 5$

$\bf \longmapsto \: - x = - 3$

$\longmapsto \: \underline{ \boxed{\bf x = 3}}$

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Hence, the numerator and denominator of the rational number are :-

$\sf Numerator = x = 3.$

$\sf Denominator = x + 4 = 3 + 4 = 7.$

Thus :-

• The rational number is 3/7.

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Answer 2

$\large\boxed{\textsf{\textbf{\red{Question\::-}}}}$

• 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.

$\large\boxed{\textsf{\textbf{\red{Answer \::-}}}}$

• The Rational number is 3/7

$\large\boxed{\textsf{\textbf{\red{Step\:by \: step \: explanation \::-}}}}$

let the numerator of the Rational number be x

• As the denominator of the Rational number is 4 more than its numerator

Therefore

• the denominator of the Rational number will be x + 4

increasing the numerator anf denominator by 1

• the number becomes x + 1
• the denominator become x + 4 + 1

Given that

• if the numerator and denominator of the Rational number are increased by 1 each, the Rational number becomes ½

therefore

$→ \: \frac{x+ 1}{ x+ 4 + 1} = \frac{1}{2}$

$→ \: \frac{x+ 1}{ x+ 5} = \frac{1}{2}$

$→ \: 1(x+ 5) = 2(x+ 1)$

$→ \: \:x + 5 = 2x + 2$

$→ \: x - 2x = 2 - 5$

$→ \: - x = - 3$

$\large\boxed{\textsf{\textbf{\red{x=3\:}}}}$

Hence the numerator and denominator of the Rational number are :-

$\large\boxed{\textsf{\textbf{\red{Numerator \:=\:X = 3\:}}}}$

$\large\boxed{\textsf{\textbf{\red{Denominator \:=\:X +4=3+4= 7\:}}}}$

• The Rational number is 3/7