What fraction becomes 13 when 1 is subtracted from the numerator and becomes 14 when 8 is added to its denominator?

To find the fraction, let’s denote the fraction as x/y, where x is the numerator and y is the denominator.

According to the problem:

1. When 1 is subtracted from the numerator, the fraction equals 13:

x - 1 / y = 13

This can be rewritten as:

x - 1 = 13y

x = 13y + 1

2. When 8 is added to the denominator, the fraction equals 14:

x / (y + 8) = 14

This can be rewritten as:

x = 14(y + 8)

x = 14y + 112

Now we have two equations:

• 1: x = 13y + 1
• 2: x = 14y + 112

We can set these two expressions for x equal to each other:

13y + 1 = 14y + 112

Solving for y gives:

1 - 112 = 14y - 13y

-111 = y

Now that we have y = -111, we can substitute this value back into one of the equations to find x. Using the first equation:

x = 13(-111) + 1

x = -1443 + 1

x = -1442

So we have:

• x = -1442
• y = -111

The fraction can be expressed as:

Fraction = x/y = -1442 / -111

Thus, the fraction simplifies to:

Fraction = 1442 / 111

Therefore, the fraction we are looking for is:

1442 / 111