I need help with this math problem

Question

If you add 1 to the numerator and 1 to the denominator you would get 1/2, if you subtract 1 from the the numerator and 1 from the denominator you would get 1/3. what is the fraction

Answer 1

So we're given:

[Equation a] (n+1) / (d+1) = 1/2

[Equation b] (n-1) / (d-1) = 1/3

Let's look at [a]:

If (n+1) / (d+1) = 1/2, then multiply both sides by 2(d+1) to get:

2(n+1) = d+1

So 2n +2 = d + 1

And 2n = d + 1 - 2 = d-1

So 2n = d-1.

Let's use this in [b], replacing d-1 with 2n:

(n-1) / (d-1) = 1/3

So (n-1) / 2n = 1/3

Let's multiply both sides by 2n and get:

(n-1) = (2/3)n

So 1n - 1 = (2/3)n

And (1/3)n = 1

So n=3.

Going back to the fact that 2n = d - 1, we have 2(3) = d - 1, so 6 = d - 1, or d = 7.

Therefore, our numerator is 3 and our denominator is 7.

Let's double check this:

(3+1) / (7+1) = 4 / 8 = 1 / 2

(3-1) / (7-1) = 2 / 6 = 1 / 3

So the fraction is 3/7.