The numerator and denominator of a fraction a | vedclass

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(B) Let the original fraction be $\frac{p}{q}$.Given that the ratio of the numerator to the denominator is $2:3$,we have $\frac{p}{q} = \frac{2}{3}$,w

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(B) Let the original fraction be $\frac{p}{q}$.Given that the ratio of the numerator to the denominator is $2:3$,we have $\frac{p}{q} = \frac{2}{3}$,which implies $3p = 2q$ or $q = \frac{3p}{2}$.According to the problem,if $6$ is subtracted from the numerator,the new fraction is $\frac{p-6}{q}$.It is given that this new fraction is $\frac{2}{3}$ of the original fraction:$\frac{p-6}{q} = \frac{2}{3} 	imes \frac{p}{q}$.Since $q 
eq 0$,we can cancel $q$ from both sides:$p-6 = \frac{2}{3}p$.Multiply both sides by $3$ to clear the fraction:$3(p-6) = 2p$.$3p - 18 = 2p$.$3p - 2p = 18$.$p = 18$.Thus,the numerator of the original fraction is $18$.

The numerator and denominator of a fraction are in the ratio of $2:3$. If $6$ is subtracted from the numerator,the result is a fraction that has a value $\frac{2}{3}$ of the original fraction. The numerator of the original fraction is

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