Question

The denominator of a fraction is 3 more than the numerator. If both the numerator and the denominator are decreased by 2, the resulting fraction is equivalent to 8/11. Find the fraction

Answer 1

The problem is solved by setting up an equation based on the given conditions and then solving for the unknown numerator. The original fraction is found to be 10/13.

Step-by-step explanation:

The problem involves finding an unknown fraction given a relationship between its numerator and denominator, as well as the behavior of the fraction after modification.

Let's assume the numerator of the fraction is x, then the denominator would be x + 3.

According to the problem, reducing both the numerator and the denominator by 2 gives a fraction equivalent to 8/11.

Mathematically, this can be written as:

(x - 2) / (x + 3 - 2) = 8/11

To solve for x, we cross-multiply and get:

11(x - 2) = 8(x + 1)

Expanding both sides gives us:

11x - 22 = 8x + 8

Combining like terms, we find that:

3x = 30

Therefore:

x = 10

The original fraction is 10/13, since 10 + 3 = 13.

Answer 2

(-6) / (-9)

Step-by-step explanation:

D = 3+N

(D - 2) / (N - 2) = (N + 3 - 2) / (N - 2) = 8 / 11

8 (N - 2) = 11 ( N + 1)

8N - 16 = 11N + 11

3N = -27

N = -9

D = -6

D / N = -6/-9 = 2/3