Question

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

Answer 1

Answer:

2/5

Step-by-step explanation:

Let the numerator be x and the denominator be x + 3

• (x - 1) / (x + 3 - 1) = 1/4

• (x - 1) / (x + 2) =  1/4

By cross multiplication,

• 4 (x - 1) = x + 2  
• 4x - 4 = x + 2
• 4x - x = 2 + 4
• 3x = 6
• x = 6/3
• x = 2

By substituting the values of x,

Numerator = x = 2

Denominator = x +  3 = 2 + 3 = 5

∴The rational no. = 2/5

Answer 2

$\huge{\sf{\blue{ANSWER}}}$

GIVEN-

• The denominator of Rational Number is 3 more than the Numerator.

• If 1 is subtracted from the numerator and denominator both then the number obtained is 1/4.

To Find-

• The Rational Number.

Atq.

$\implies{Numerator=x}$

$\implies{Denomimator=x+3}$

Now,

If 1 is subtracted,

$\huge{\frac{x-1}{x+3-1}=\frac{1}{4}}$

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

• Cross Multiplication Method.

$4(x-1)=1(x+2)$

$4x-4=x+2$

$3x=6$

$x=2$

• Now Put the value of x .

$\implies{\bf{\blue{Numerator=2}}}$

$\implies{\bf{\red{Denominator=2+3=5}}}$

Hence, The Rational Number is $\huge{\frac{2}{5}}$