Question

The numerator of a rational number is is 3 less than its denominator. If 4 is added to the numerator and 12 is added to the denominator, then the rational number becomes 1/2. Find the numbers​

Answer 1

Answer:

Step-by-step explanation:

Le the denominator be x and the numerator be (x – 3)

By using the formula

Fraction = numerator/denominator

= (x – 3)/x

So, when numerator is increased by 2 and Denominator is increased by 5, then fraction is 1/2

(x – 3 + 2)/(x + 5) = 1/2

(x – 1)/(x + 5) = 1/2

By using cross-multiplication, we get

2(x – 1) = x + 5

2x – 2 = x + 5

2x – x = 2 + 5

x = 7

∴ Denominator is x = 7, numerator is (x – 3) = 7 – 3 = 4

And the fraction = numerator/denominator = 4/7

Answer 2

Step-by-step explanation:

Let the denominator of rational number be x

Then as given numerator = (x - 3)

Now as 4 added to numerator and 12 added to denominator,

We will form an equation and solve for x

=> (x + 4)/(x - 3 + 12) = 1/2

=> (x + 4)/(x + 9) = 1/2

By cross multiplication we have

=> 2(x + 4) = (x + 9)

=> 2x + 8 = x + 9

=> 2x- x = 9 - 8

=> x = 1

Now denominator = x = 1

And numerator = (1 - 3) = - 2

Hence rational number = - 2/1