Question

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

Answer 1

☯ GivEn that, The numerator of a fraction is 4 less than denominator if 1 is added to both numerator and denominator becomes 1/2.

☯ We have to find, the fraction.

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★ Firstly let's the denominator be x.

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Now,

$\underline{\bigstar\:\boldsymbol{According\:to\: Question\::}}$

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The numerator of a fraction is 4 less than denominator.

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Therefore,

★ Numerator of the fraction is x - 4.

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When 1 is added to both numerator and denominator becomes $\sf \dfrac{1}{2}$

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

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

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

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

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

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$:\implies{\underline{\boxed{\sf{\pink{x = 7}}}}}\;\bigstar$

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$\therefore$ Denominator of the fraction is 7.

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And, The numerator of the fraction is = (x - 4) = (7 - 4) = 3.

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Thus, The Required fraction is $\bf \dfrac{3}{7}$.