Question

the denominator of a rational number is greater than its numerator by 4. if the numerator is increased by 1 and denominator by 3 obtained number is 1/2. find rational number??? Fast please step by step explanation

Answer 1

TO FIND RATIONAL NUMBER

EXPLANATION.

• GIVEN

Let the numerator of a rational number = x

denominator of the rational number = x + 4

it is given that that the numerator is increased by

1 and denominator is increased by 3

denominator of the rational number =

x + 4 + 3 = x + 7

new rational number = x + 1 / x + 7

new rational number equal to = 1/2

equation will be written as =

x + 1 / x + 7 = 1 / 2

2x + 2 = x + 7

x = 5

numerator of the rational number = 5

denominator of the rational number = 5 + 4 = 9

rational number = 5 / 9

Answer 2

Answer:

Rational number is 5/9

Explanation:

Given :

• Denominator of  a rational is greater than it’s numerator by 4
• Numerator is increased by 1 and denominator by 3 get the number 1/2

To Find :

• Rational Number

Solution :

$\sf{}Let\ the\ rational\ number\ be\ x$

$\sf{}Therefore,denominator\ will\ be\ x+4$

$\sf{}So,Rational\ number\ would\ be =>\dfrac{x}{x}+4$

ATQ

$\Rightarrow \sf{}\dfrac{x+1}{x+ 7}= \dfrac{1}{2}$

Cross-multiply

$\Rightarrow \sf{}x+1(2)=1(x+7)$

$\Rightarrow \sf{}x+2=x+7$

Subtract x from both sides.

$\Rightarrow \sf{}2 x + 2 - x = x + 7 - x$

$\Rightarrow\sf{}x + 2 = 7$

Subtract 2 from both sides

$\Rightarrow \sf{}x+2-2=7-2$

$\Rightarrow \sf{}x=5$

Put their values

Numerator =>5

Denominator =>5+4=9

Rational number = 5/9

$\sf{}\because\ Rational\ number\ is\ \dfrac{5}{9}$