Question

hlo answer this and take 40 points the numerator of a fraction is 6 less than the denominator. if 3 is added to the numerator, the fraction is equal to 2\3,find the original fraction ​

Answer 1

GIVEN :–

• The numerator of a fraction is 6 less than the denominator.

• If 3 is added to the numerator, the fraction is equal to ⅔ .

TO FIND :–

• Original fraction = ?

SOLUTION :–

• Let the denominator 'x' .

• So , Numerator = x - 6

▪︎ According to the question –

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

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

$\\ \implies\sf 3(x - 3)= 2(x + 3)$

$\\ \implies\sf 3x - 9= 2x + 6$

$\\ \implies\sf 3x - 2x= 9+ 6$

$\\ \implies\sf x= 9+ 6$

$\\ \implies \large{ \boxed{\sf x=15 }}$

• Hence –

$\\ \implies \sf \: original \: \: fraction = \dfrac{15 - 6}{15}$

$\\ \implies \large{ \boxed{ \sf \: original \: \: fraction = \dfrac{9}{15}}}$

Answer 2

Answer:

Suppose denominator be = x

and numerator = x - 6

$\frac{(x \: - \: 6 \: ) \: + \: 3 \: }{(x \: + \: 3} = \frac{2}{3}$

$\frac{x \: - \: 3}{x \: + \: 3} = \frac{2}{3}$

$3(x - 3) = 2(x \: + \: 3)$

$3x \: - \: 9 \: = 2x \: + \: 6 \:$

$3x - 2x = 9 + 6$

$x \: = \: 9 \: + \: 6.$

$x = 15$

$the \: orignal \: fraction \: = \frac{15 - 6}{15}$

$the \: orignal \: fraction \: = \frac{9}{15} .$