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

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 ​

in progress 0
Anna 2 months 2021-11-10T20:16:36+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-10T20:17:45+00:00

    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} .

    0
    2021-11-10T20:18:07+00:00

    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}}} \\

Leave an answer

Browse

14:4+1-6*5-7*14:3+5 = ? ( )