Question

9. The numerator of a fraction is 3 less than its denominator. When both the numerator and the denominator are increased by 1 the fraction becomes 2/3. Find the fraction​

Answer 1

Answer:      8/11

Step-by-step explanation:

 let the  denominator of the fraction be x.

  since,   numerator or the fraction be  x-3

 then,  fraction =   x-3/x

a/q  

        (x-3)+1/ x+1 =  2/3

=        x-3/x+1 = 2/3               ( cross multiplication)

=        2(x+1)  =  3(x-3)

=        2x + 2 =  3x -9

=      2 +9  =    3x-2x

=        x=   11

    since  fraction =     x-3/x

                             =    11-3/ 11

                              =     8/11

Answer 2

❍ Let's say, that the denominator of the fraction be x.

As per Question, The numerator of a fraction is 3 less than it's denominator 'x'.

Therefore,

• Fraction is = (x – 3)/x.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\underline{\bigstar\:{\pmb{\sf{According\; to\; the\; given \;Question :}}}}$

⠀⠀

• When Both the Numerator and the Denominator of the fraction are increased by 1, then the fraction becomes ⅔.

⠀⠀

$\twoheadrightarrow\sf \bigg\{\dfrac{Numerator + 1}{Denominator + 1}\bigg\} = \bigg\{\dfrac{2}{3}\bigg\} \\\\\\\twoheadrightarrow\sf \bigg\{\dfrac{x - 3 + 1}{x + 1}\bigg\} = \bigg\{\dfrac{2}{3}\bigg\}\\\\\\\twoheadrightarrow\sf \dfrac{x - 2}{x + 1} = \dfrac{2}{3}\\\\\\\twoheadrightarrow\sf 3(x - 2) = 2(x + 1) \\\\\\\twoheadrightarrow\sf 3x - 6 = 2x + 2\\\\\\\twoheadrightarrow\sf 3x - 2x = 2 + 6\\\\\\\twoheadrightarrow\underline{\boxed{\pmb{\frak{\red{x = 8}}}}}\;\bigstar$

⠀⠀

Therefore,

• Numerator of the fraction, (x – 3) = (8 – 3) = 5.
• Denominator of the fraction, x = 8.

⠀⠀

∴ Hence, the required fraction is ⅝.