Question

The numbers of a fraction is 2 less than the denominator if one is added to its denominator it becomes 1/2 find the fraction​

Answer 1

Answer:

The numerator of a fraction is 2 less than the denominator.

If one is added to its denominator it becomes 1/2 .

TO FIND :-

The Fraction

SOLUTION :-

Let the numerator be x.

Then the fraction is -

\frac{x}{x + 2}

x+2

x

Now according to the Question ,

\begin{gathered} \frac{x}{x + 2 + 1} = \frac{1}{2} \\ \\ \\ \implies \frac{x}{x + 3} = \frac{1}{2} \\ \\ \\ \implies 2x = x + 3 \\ \\ \\ \implies \boxed{ x = 3}\end{gathered}

x+2+1

x

=

2

1

⟹

x+3

x

=

2

1

⟹2x=x+3

⟹

x=3

Therefore the Fraction is 3/5 (Ans)

VERIFICATION :-

LHS

=3/5

=3/(5+1)

= 3/6

= 1/2

= RHS

HENCE OUR ANSWER IS CORRECT

Answer 2

❍ Let the denominator be x and according to the given question, the numerator be (x – 2).

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

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

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• If one is added to the denominator, then the fraction becomes 1/2.

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Therefore,

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$\begin{gathered}:\implies\sf{\dfrac{x-2}{x+1}=\dfrac{1}{2}}\\\\\\\\:\implies\sf{2x-4=x+1}\\\\\\\\:\implies\sf{2x-x=1+4}\\\\\\\\:\implies\underline{\boxed{\frak{\pink{x=5}}}}\;\bigstar\end{gathered}$

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Hence,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Numerator = (x – 2) = (5 – 2) = 3
• Denominator = x = 5

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$\therefore\;{\underline{\sf{Hence,\;the\;fraction\;is\;\;\frak{\dfrac{3}{5}}}.}}$⠀⠀⠀