Question

The numerator of a fraction is six less than the

denominator. If three is added to the numerator, the fraction becomes 2/3. Find the original fraction.​

Answer 1

❍ Let the denominator be x and according to the given question, the numerator be (x - 6) respectively.

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━ Therefore, the fraction will be,

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$:\implies\sf{\dfrac{x-6}{x}}\qquad\qquad\bigg\lgroup\sf{eq^n\;1}\bigg\rgroup$

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

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• When three is added to the numerator, then the fraction becomes 2/3.

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Therefore,

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$:\implies\sf{\dfrac{x-6+3}{x}=\dfrac{2}{3}}\\\\\\\\:\implies\sf{\dfrac{x-3}{x}=\dfrac{2}{3}}$

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$\qquad\qquad\underline{\footnotesize{\bf{\dag}\frak{\;Cross\;multiplying:}}}$

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$:\implies\sf{3x-9=2x}\\\\\\\\:\implies\sf{3x-2x=2x}\\\\\\\\:\implies\underline{\boxed{\pink{\frak{x=9}}}}{\;\bigstar}$

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$\qquad\qquad\underline{\footnotesize{\bf{\dag}\frak{\;Putting\;value\;of\;x\;in\;eq^n\;1:}}}$

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$:\implies\sf{\dfrac{x-6}{x}}\\\\\\\\:\implies\sf{\dfrac{9-6}{9}}\\\\\\\\:\implies\sf{\cancel{\dfrac{3}{9}}}\\\\\\\\:\implies\underline{\boxed{\purple{\frak{\dfrac{1}{3}}}}}{\;\bigstar}$

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$\therefore\;{\underline{\sf{Hence,\;the\;original\;fraction\;is\;{\frak{\dfrac{1}{3}}}}.}}$⠀⠀

Answer 2

The original fraction is 1/3

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