Question

a numerator of a fraction is 6 less than the denominator if 3 is added to the numerator the fraction become equal to 2÷3 find the original fraction.

Answer 1

let the denominator be x
then, numerator = x-6

according to question ,

=> (x-6)+3/x = 2/3
=> (x-6+3)/x = 2/3
=> (x-3)/x = 2/3

=> 3(x-3) = 2x
=> 3x-9 = 2x
=> 3x-2x = 9
=> x = 9. (denominator)

numerator = x-6 => 9-6 = 3

then , fraction = 3/9

hope this helps

Answer 2

Hi ,

Let the denominator = x

Numerator = x - 6

Original fraction = ( x - 6 ) / x ---( 1 )

According to the problem given,

( x - 6 + 3 ) / x = 2/3

( x - 3 ) / x = 2 / 3

3( x - 3 ) = 2x

3x - 9 = 2x

3x - 2x = 9

x = 9

Put x = 9 in equation ( 1 ),

Original fraction = ( x - 6 ) / x

= ( 9 - 6 ) / 9

= 3 / 9

I hope this helps you.

:)