# A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

The fraction is a part of a whole expressed as N/D, that is numerator/denominator.

## Answer: A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction is 5/12.

Let's find out the fraction with the given conditions.

**Explanation:**

Let the fraction be x/y.

Given that, the fraction becomes 1/3 when 1 is subtracted from the numerator.

(x - 1)/y = 1/3

3(x - 1) = y

3x - 3 = y

3x - y = 3 -------------(1)

Given that, the fraction becomes 1/4 when 8 is added to its denominator.

x / (y + 8) = 1/4

4x = y + 8

4x - y = 8 ------------ (2)

By solving equations (1) & (2) by the method of elimination, we get:

3x - y = 3

__(-) 4x - y = 8__

__ -x = -5__

Therefore, x = 5

From equation (1): 3x - y = 3

3 × (5) - y = 3

15 - y = 3

-y = 3 - 15

- y = -12

y = 12

Thus, the fraction, x/y = 5/12

### Therefore, the required fraction is 5/12.

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