Question

the numerator of a fraction 4 less than its denominator . If one is added to both the numerator and denominator ,the fraction becomes 1/2.find the fraction

Answer 1

Answer:

$\sf{The \: fraction \: is \: \: \dfrac{3}{7}}$

Step-by-step explanation:

Let,

The numerator of a fraction = x

The denominator of a fraction = x + 4

If one is added to both the numerator and denominator

So,.

The numerator of a fraction = x + 1

The denominator of a fraction = x + 4 + 1

⇒ x + 5

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

⇒ 2 (x + 1) = 1 (x + 5)

⇒ 2x + 2 = x + 5

⇒ 2x - x = 5 - 2

⇒ x = 3

The numerator of a fraction = 3

The denominator of a fraction = x + 4

⇒ 3 + 4

⇒ 7

Therefore,

$\sf{The \: fraction \: is \: \: \dfrac{3}{7}}$

Answer 2

$\huge\tt\colorbox{purple}{Answer}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• Numerator is 4 less than denominator
• If 1 is added to both then the fraction becomes 1/2

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

⠀⠀⠀⠀

• Required fraction = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

⠀⠀⠀⠀

Let the denominator be x

⠀⠀⠀⠀

Therefore numerator is x - 4

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Acc. to the question :-

⠀⠀⠀⠀

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

⠀⠀⠀⠀

$\sf :\implies\:{\dfrac{x- 3}{x+1} = \dfrac{1}{2}}$

⠀⠀⠀⠀

$\sf :\implies\:{2 ( x - 3 ) = x + 1 }$

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$\sf :\implies\:{2x - 6 = x + 1 }$

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$\sf :\implies\:{2x - x = 6 + 1 }$

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$\sf :\implies\:{x = 7 }$

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Putting value of x in the fraction

⠀⠀⠀⠀

• Numerator = x - 4 = 7 - 4 = 3

⠀⠀⠀⠀

• Denominator = x = 7

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• Required fraction = 3 / 7