1. **State the problem:** Calculate the product of 22 and the fraction \(\frac{3}{5.5}\). 2. **Formula used:** Multiplication of a whole number by a fraction is given by \(a \times \frac{b}{c} = \frac{a \times b}{c}\). 3. **Convert the decimal denominator:** \(5.5 = \frac{11}{2}\), so \(\frac{3}{5.5} = \frac{3}{\frac{11}{2}} = 3 \times \frac{2}{11} = \frac{6}{11}\). 4. **Multiply:** \(22 \times \frac{6}{11} = \frac{22 \times 6}{11}\). 5. **Simplify the fraction:** \(\frac{22 \times 6}{11} = \frac{\cancel{22}^2 \times 6}{\cancel{11}^1} = 2 \times 6 = 12\). 6. **Final answer:** \(12\).