Question

If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from denominator, it reduces to 1/3. Find the fraction.

Answer 1

The fraction where adding 2 to the numerator results in ½ and subtracting 1 from the denominator results in ⅓ is 5/14.

Step-by-step explanation:

We need to find a fraction where adding 2 to the numerator gives us ½, and subtracting 1 from the denominator gives us ⅓. Let's represent the unknown fraction as ⅗, where x is the numerator, and y is the denominator.

According to the problem:

• When 2 is added to the numerator: ⅗ + 2 = ½
• When 1 is subtracted from the denominator: ⅗ - ⅐ = ⅓

We can then set up two equations based on the above information:

1. ⅗ + 2/y = 1/2
2. ⅗/(y - 1) = 1/3

To solve for x and y, we can cross-multiply and get two separate equations:

1. 2x + 4 = y
2. 3x = y - 1

After simplifying, we can set the two equations equal to each other since both equal y:

2x + 4 = 3x - 1

Solving for x, we get x = 5. Plugging x = 5 into either equation, we find y = 14. Therefore, our original fraction is 5/14.