Question

The denominator of a fraction is 4 more than the numenator. If 4 is added to the numenator and 7 is added to the denominator, the value of the fraction 1 half find the original fraction.

Answer 1

`(3)/(7)`

Step-by-step explanation:

Lets take the numerator of the fraction to be = x

So the denominator of the fraction is 4 more than the numerator = x+4

The fraction is ;
`(x)/(4+x)`

Now add 4 to the numerator and add 7 to the denominator as;

`(x+4)/(4+x+7) =(x+4)/(x+11)`

This new fraction is equal to 1 half =1/2

write the equation as;

`(x+4)/(x+11) =(1)/(2)`

perform cross-product

2(x+4 )=1( x+11 )

2x+8 = x + 11

2x-x = 11-8

x=3

The original fraction is;

`(x)/(4+x) =(3)/(3+4) =(3)/(7)`