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

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

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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

Answer 2

Answer:

Step-by-step explanation:

Let the fraction be a/b

Numerator= denominator-4

a=b−4⇒b−a=4

If 1 added to both numerator and denomator then fraction = 1/2

a+1/b+1 = 1/2

2a+2=b+1

2a−b=−1

(2a−b)+(b−a)=4−1

a=3,b=7

Fraction= 7/3

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