Math, asked by binkalmandal, 3 months ago

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​

Answers

Answered by ruchikakapri
1

Step-by-step explanation:

The denominator of a rational number is greater then its numerator by 4. If the numerator is increased by 11 and the denominator is decreased by 1, the new number becomes 7/3.

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Answered by llTheUnkownStarll
3

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

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