Question

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

Answer 1

let the denominator=A,

then numerator=A-4,

then
fraction will be (A-4)/A,

now according to question, we have

[(A-4)+1]/(A+1) = 1/2,

(A-3)/(A+1) = 1/2,

2A-6=A+1,

then

2A-A=1+6,

A=7,

therefore

fraction =(7-4)/7 =3/7

Answer 2

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

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

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

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

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• Required fraction = ??

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

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Let the denominator be x

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Therefore numerator is x - 4

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Acc. to the question :-

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

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

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

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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

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Numerator = x - 4 = 7 - 4 = 3

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Denominator = x = 7

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

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• Required fraction = 3 / 7