Question

if a certain number is subtracted from the numerator and added to the denominator of (9)/(19) the new fraction is equivalent to (1)/(3). find the number

Answer 1

The "certain number" is 2.

Explanation:

Let x be the "certain number." The original fraction is (9/16). The certain number, x, is subtracted from the numerator (9-x) and added to the denominator (19+x) to yield a new fraction:

(9-x)/(19+x)

This is equal to (1/3)

(9-x)/(19+x) = 1/3

3(9-x)/(19+x) = 1

3(9-x) = (19+x)

27-3x = 19+x

4x = 8

x = 2