Question

The numerator of a fraction is 4 less than its denominator. if the numerator is decreased by 2 and the denominator is increased by 1, the denominator becomes 1/8. find the fraction​

Answer 1

Answer:

required fraction is 3/7

Step-by-step explanation:

let the denominator be x

the numerator is 4 less than denominator = x - 4

the required fraction is x-4/x

numerator is decreased by 2 = x - 4 - 2 = x - 6

denominator increased by 1 = x + 1

this fraction is equal to 1/8

$\frac{x - 6}{x + 1} = \frac{1}{8} \\ 8(x - 6) =1 (x + 1) \\ 8x - 48 = x + 1 \\ 8x - x = 1 + 48 \\ 7x = 49 \\ x = \frac{49}{7} \\ x = 7$

therefore the required fraction is

$\frac{x - 4}{x} \\ = \frac{7 - 4}{7} \\ = \frac{3}{7}$

verification

$\frac{x - 4 - 2}{x + 1} = \frac{1}{8} \\ \frac{7 - 4 - 2}{7 + 1} = \frac{1}{8} \\ \\ \frac{7 - 6}{8} = \frac{1}{8} \\ \frac{1}{8} = \frac{1}{8}$

Hope you get your answer