Question

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

Answer 1

Hey

Here is your answer,

Let denominator be x
Numerator = x-4
When 1 is added:-
Denominator = x+1
Numerator= x-3
x-3/x+1=1/2
x+1=2(x-3)
x+1=2x-6
x-2x=-6-1
-x=-7
x=7
Original Numerator = x-4
= 7-4
= 3
Original Denominator = x
= 7
Original Fraction = 3/7

Hope it helps you ☺

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