Question

The numerator of a fraction is 19 less than the denominator of the fraction. GIve that the fraction 2/9 is obtained when 1 is subtracted from the numerator and 1 is added to the denominator, fing the original fraction.

Answer 1

`(7)/(26)`

Explanation:

let x be the denominator of the fraction then x - 19 is the numerator , so

`(x-19)/(x)` ← is the original fraction

subtrating 1 from the numerator and adding 1 to the denominator , then

`(x-20)/(x+1)` =
`(2)/(9)` ( cross- multiply )

9(x - 20) = 2(x + 1) ← distribute parenthesis on both sides

9x - 180 = 2x + 2 (subtract 2x from both sides )

7x - 180 = 2 ( add 180 to both sides )

7x = 182 ( divide both sides by 7 )

x = 26

Then the original fraction is

`(26-19)/(26)` =
`(7)/(26)`