Question

The numerator of a fraction is 6 lessbthan the denominator. If 3 is added to the numerator, the fraction becomes equal to 2/3, find the original fraction​

Answer 1

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The numerator of a fraction is $6$ less than the denominator. If $3$ is added to the numerator, the fraction becomes equal to $\frac{2}{3}$, find the original fraction.

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• The numerator of a fraction is $6$ less than the denominator.
• When $3$ is added to the numerator, the fraction becomes equal to $\frac{2}{3}$.

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The original fraction.

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Let the denominator be $x$.

So, numerator = $(x-6)$

According to condition,

➳ $\frac{(x-6)+3}{x}= \frac{2}{3}$

➳ $\frac{(x-6+3)}{x} = \frac{2}{3}$

➳ $\frac{(x-3)}{x} =\frac{2}{3}$

➳ $3(x-3)=2x$

➳ $3x-9=2x$

➳$3x-2x=9$

➳ $x = 9$

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$x =9$

Denominator $=x=9$

Numerator $=(x-6)=(9-6)=3$

The original fraction $=\frac{3}{9}$

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The original fraction is $\frac{3}{9}$.

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$\frac{(3+3)}{9} =\frac{2}{3}$

➳ $\frac{6}{9} =\frac{2}{3}$

➳ $\frac{(6÷3)}{(9÷3)} =\frac{2}{3}$

➳ $\frac{2}{3} =\frac{2}{3}$

So, L.H.S $=$ R.H.S.

Hence, verified.

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