Let's denote the numerator as x and the denominator as y.

From the problem, we know that:

1) x + y = 7 (since the sum of the numerator and denominator is 7)

2) (x + 1) / (y + 1) = 1/2 (since if 1 is added to the numerator and the denominator, the fraction becomes 1/2)

We can solve these two equations to find the values of x and y.

First, let's rearrange equation 1) to get y = 7 - x.

Now, we can substitute y in equation 2) with 7 - x:

(x + 1) / (7 - x + 1) = 1/2
(x + 1) / (8 - x) = 1/2

Cross-multiplying gives us 2x + 2 = 8 - x.

Adding x to both sides gives us 3x + 2 = 8.

Subtracting 2 from both sides gives us 3x = 6.

Finally, dividing both sides by 3 gives us x = 2.

Substituting x = 2 into equation 1) gives us y = 7 - 2 = 5.

So, the original fraction is 2/5.

Question

Let's denote the numerator as x and the denominator as y.

From the problem, we know that:

1) x + y = 7 (since the sum of the numerator and denominator is 7)

2) (x + 1) / (y + 1) = 1/2 (since if 1 is added to the numerator and the denominator, the fraction becomes 1/2)

We can solve these two equations to find the values of x and y.

First, let's rearrange equation 1) to get y = 7 - x.

Now, we can substitute y in equation 2) with 7 - x:

(x + 1) / (7 - x + 1) = 1/2
(x + 1) / (8 - x) = 1/2

Cross-multiplying gives us 2x + 2 = 8 - x.

Adding x to both sides gives us 3x + 2 = 8.

Subtracting 2 from both sides gives us 3x = 6.

Finally, dividing both sides by 3 gives us x = 2.

Substituting x = 2 into equation 1) gives us y = 7 - 2 = 5.

So, the original fraction is 2/5.

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