If we multiply a fraction by itself and divide to product by its reciprocal, the fraction thus obtained is 18 26/27. What is the original fraction?

3.66

2.67

1.33

None of these

We know that:

x × x = x²

Reciprocal of x = 1/x

According to the problem:

(x × x) ÷ (1/x) = 18/26 × 27

Simplifying the equation:

x² ÷ (1/x) = 18/26 × 27

x³ = 18/26 × 27

Now, let's solve for x:

x³ = 486/26

x³ = 18.69 (approximately)

x = ∛(18.69) ≈ 2.67