1. **State the problem:** Calculate the product of the numbers $\left(49,\frac{6}{100}\right)$ and $\frac{4464}{9000}$. 2. **Convert the mixed number to an improper fraction:** $49,\frac{6}{100} = 49 + \frac{6}{100} = \frac{49 \times 100}{100} + \frac{6}{100} = \frac{4900}{100} + \frac{6}{100} = \frac{4906}{100}$ 3. **Write the multiplication:** $$\frac{4906}{100} \times \frac{4464}{9000}$$ 4. **Multiply the numerators and denominators:** $$\frac{4906 \times 4464}{100 \times 9000} = \frac{21899584}{900000}$$ 5. **Simplify the fraction by dividing numerator and denominator by 16:** $$\frac{\cancel{16}1368724}{\cancel{16}56250}$$ 6. **Simplify further by dividing numerator and denominator by 2:** $$\frac{\cancel{2}684362}{\cancel{2}28125}$$ 7. **Final simplified fraction:** $$\frac{684362}{28125}$$ 8. **Convert to decimal for easier interpretation:** $$684362 \div 28125 \approx 24.32$$ **Final answer:** $24.32$