Question

The numerator of a rational number is 3 less than the denominator. If the denominator is increased by 5 and numerator by 2, we get the rational number 1÷2 ,find the rational number

Answer 1

Answer:

let denominator =x

so,numerator =x-3

=(x-3)+2/x+5=1/2

x-1/x+5=1/2

=2x-2-x+5

x=7

answer 4/7

Answer 2

The rational number is $\frac{4}{7}$ .

Step-by-step explanation:

We are given that the numerator of a rational number is 3 less than the denominator.

If the denominator is increased by 5 and numerator by 2, we get the rational number 1÷2.

Let the numerator of a rational number be x and denominator be y.

• The first condition states that the numerator of a rational number is 3 less than the denominator, that is;

                                x  =  y - 3  

                                y = x + 3  ------------------ [equation 1]

• The second condition states that if the denominator is increased by 5 and numerator by 2, we get the rational number 1÷2, that is;

                                $\frac{x+2}{y+5} =\frac{1}{2}$

                               $2x+4 = y+5$

                               $2x-y = 1$  

                               $2x -(x+3)=1$     {from equation 1}

                               $2x-x-3=1$

                                 x  =  4

Now, putting the value of x in equation 1, we get;

                                     y = x + 3

                                      y = 4 + 3 = 7

So, the required rational number is  $\frac{4}{7}$ .