Question

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

Answer 1

may be numerator is 3 and denominator is 7 as we add 1 then numerator will be 4 and denominator will be 8 and then the no is 1/2

Answer 2

Given:

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

To find:

• Original Fraction

Solution:

$\mapsto\sf{Let\:Numerator\:be=x}$

As Given that Denominator of a rational number is greater than its numerator by 4 . So ,

$\mapsto\sf{Denominator=x+4}$

Now ,

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

$\mapsto\sf{Numerator=x+1}$

$\mapsto\sf{Denominator=x+4+1} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= \: x + 5$

According to the question:

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

$\mapsto \: \sf{2(x+1)=1(x+5)}$

$\mapsto\sf{2x+2=1x+5}$

$\mapsto\sf{2x-1x=5-2}$

$\mapsto \underline {\boxed{\frak{x=3}}} \blue \bigstar$

• Value of x is 3.

Therefore,

$\mapsto\sf{Numerator=x = \bold3}$

$\mapsto\sf{Denominator=4+3}$

$\mapsto \sf {7}$

$\mapsto \underline {\boxed{\frak {Fraction = \frac{3}{7} }}} \pink \bigstar$

• Hence, the rational number is 3/7.

Thank you!

@itzshivani