Question

the denominator of a rational number is 3 more than the numerator. If 1 is subtracted from numerator and denominator both the rational number in its simplest form is 1/4. what is the rational what is the rational number

Answer 1

Answer:

Given :-

• The denominator of a rational number is 3 more than the numerator.
• If 1 is subtracted from numerator and denominator both then the rational number in its simplest form is 1/4.

To Find :-

• What is the rational number.

Solution :-

Let,

➲ Numerator = x

➲ Denominator = x + 3

Then, the required rational number is :

$\leadsto \sf Rational\: Number =\: \dfrac{Numerator}{Denominator}$

$\leadsto \sf\bold{\green{Rational\: Number =\: \dfrac{x}{x + 3}}}$

According to the question,

$\bigstar$ 1 is subtracted from numerator and denominator both then the rational number in its simplest form is 1/4.

$\implies \sf \bigg\{\dfrac{Numerator - 1}{Denominator - 1}\bigg\} =\: \bigg\{\dfrac{1}{4}\bigg\}$

$\implies \sf \dfrac{x - 1}{x + 3 - 1} =\: \dfrac{1}{4}$

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

By doing cross multiplication we get,

$\implies \sf 4(x - 1) =\: 1(x + 2)$

$\implies \sf 4x - 4 =\: x + 2$

$\implies \sf 4x - x =\: 2 + 4$

$\implies \sf 3x =\: 6$

$\implies \sf x =\: \dfrac{\cancel{6}}{\cancel{3}}$

$\implies \sf\bold{\purple{x =\: 2}}$

Hence, the required rational number is :

$\longrightarrow \sf Rational\: Number =\: \dfrac{x}{x + 3}$

$\longrightarrow \sf Rational\: Number =\: \dfrac{2}{2 + 3}$

$\longrightarrow \sf\bold{\red{Rational\: Number =\: \dfrac{2}{5}}}$

${\small{\bold{\therefore\: The\: rational\: number\: is\: \dfrac{2}{5}\: .}}}$

Answer 2

Question:-

The denominator of a rational number is 3 more than the numerator. If 1 is subtracted from numerator and denominator both the rational number in its simplest form is 1/4. what is the rational number?

Given:-

• The denominator of a rational number is 3 more than the numerator.

To Find:-

• The rational number.

Solution:-

=> Let, the numerator = x and denominator = (x + 3).

• If 1 is subtracted from numerator then numerator becomes => (x – 1).

• If 1 is subtracted from denominator then denominator becomes => (x + 3 – 1) = (x + 2).

Required rational number is,

$\sf Rational\: Number =\: \dfrac{Numerator}{Denominator}$

$\leadsto \sf\bold{\pink{Rational\: Number =\:\dfrac{x}{x + 3}}}$

According to the question,

$\longmapsto\tt \frac{x - 1}{x + 2} = \frac{1}{4}$

$\longmapsto\tt4x - 4 = x + 2$

$\longmapsto\tt3x = 6$

$\longmapsto\tt \: x = 2$

So,

• numerator = 2.
• denominator = (2 + 3) = 5.

$\sf\therefore \: rational \: number \: = \frac{2}{5}$

Answer:-

$\sf Hence,rational \: number = \sf\huge\mathfrak\red{ \frac{2}{5} }$