Question

The numerator of a fraction is 2 less than the denominaton
If one is added to its denominator it becomes 1/2 Find the
fraction.​

Answer 1

Correct Question :-

• The numerator of a fraction is 2 less than the denominator. If one is added to its denominator it becomes ½. Find the fraction.

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Answer :-

• Fraction = $\dfrac{3}{5}$

Explanation :-

Let the numerator of the fraction be x and Denominator of the fraction be (x + 2) respectively.

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$\underline{\bigstar{ \bf According\:to\:the\:question\::}}$⠀⠀

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If one is added to the denominator of the fraction. Than, the fraction becomes ½.

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Therefore,

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$:\implies\sf \dfrac{x}{x + 2 + 1} = \dfrac{1}{2} \\\\\\:\implies\sf \dfrac{x}{x +3} = \dfrac{1}{2} \\\\\\:\implies\sf 2(x) = 1(x + 3)\\\\\\:\implies\sf 2x = x + 3\\\\\\:\implies\sf 2x - x = 3\\\\\\:\implies{\underline{\boxed{\bf{\pink{x = 3}}}}}\;\bigstar$

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Hence,

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Numerator of the fraction, x = 3.

Denominator of the fraction (x + 2) = (3 + 2) = 5.

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$\therefore\:{\underline{\sf{The\: required\; fraction\;is\: \bf{ \dfrac{3}{5}}.}}}$

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$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: Verification\: :}}}}}\mid}$⠀

We're given that, If one is added to the denominator of the fraction. Than, the fraction becomes ½. Now, Let's verify the answer.

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$:\implies\sf \dfrac{x}{5} = \dfrac{1}{2} \\\\\\:\implies\sf \dfrac{3}{5 + 1} = \dfrac{1}{2}\\\\\\:\implies\sf \cancel\dfrac{3}{6}^{\;\;\dfrac{1}{2}} = \dfrac{1}{2}\\\\\\:\implies{\underline{\boxed{\sf {\dfrac{1}{2} = \dfrac{1}{2}}}}}$

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$\qquad\quad\therefore\:{\underline{\textsf{\textbf{Hence Verified!}}}}$