Question

8. The denominator of a rational number is greater than its numerator by 7. If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1\5 find the rational number.​

Answer 1

Step-by-step explanation:

Let the numerator of the fraction be x and the denominator of the fraction be ( x + 7 ) as it is 7 more than the numerator.

∴ Fraction =

Given that if 3 is subtracted from the numerator and 2 is added to its denominator , the new number becomes 1/5

As numerator was x, 3 subtracted from numerator = ( x - 3 )

As denominator was x + 7 , 2 added to denominator = ( x + 7 + 2 )

= x + 9

New fraction =

According to the question, new fraction is equal to 1 / 5.

1 / 5 = ( x - 3 ) / ( x + 9 )

x + 9 = 5( x - 3 )

x + 9 = 5x - 15

9 + 15 = 5x - x

24 = 4x

24 / 4 = x

6 = x

Therefore the required fraction is

Rational number = 6 / 13