Find the numerator of the fraction in the given question

Question

When 1 is added to the numerator of a fraction the value of the fraction becomes 1/2 . And when 1 is subtracted from the numerator for the same fraction the value of the fraction becomes 1/3 . Find the numerator of the fraction

Answer 1

Let the fraction be a/b

(a + 1)/b = 1/2 or 2(a + 1) = b and 2a + 2 = b

(a - 1)/b = 1/3 or 3(a - 1) = b and 3a - 3 = b

Since both equations = b, use substitution and

2a + 2 = 3a - 3 subtract 2a from each side

2 = a - 3 and add 3 to both sides

5 = a, then pick one of the equations and substitute for a

2(5) + 2 = b, 12 = b

the original fraction (a/b) is 5/12 ( to check this, 6/12 = 1/2, and 4/12 = 1/3)