Solve: $$(65\frac{3}{8} : 7\frac{9}{32}) \cdot 2\frac{1}{25}$$

Let's solve the expression step by step: 1. Convert mixed numbers to improper fractions: $$65\frac{3}{8} = \frac{65 \cdot 8 + 3}{8} = \frac{520 + 3}{8} = \frac{523}{8}$$ $$7\frac{9}{32} = \frac{7 \cdot 32 + 9}{32} = \frac{224 + 9}{32} = \frac{233}{32}$$ $$2\frac{1}{25} = \frac{2 \cdot 25 + 1}{25} = \frac{50 + 1}{25} = \frac{51}{25}$$ 2. Rewrite the expression with improper fractions: $$(\frac{523}{8} : \frac{233}{32}) \cdot \frac{51}{25}$$ 3. Divide the fractions by multiplying by the reciprocal: $$\frac{523}{8} : \frac{233}{32} = \frac{523}{8} \cdot \frac{32}{233} = \frac{523 \cdot 32}{8 \cdot 233}$$ Simplify by canceling common factors (32 and 8): $$\frac{523 \cdot 4}{1 \cdot 233} = \frac{2092}{233}$$ 4. Multiply the result by the remaining fraction: $$\frac{2092}{233} \cdot \frac{51}{25} = \frac{2092 \cdot 51}{233 \cdot 25} = \frac{106692}{5825}$$ 5. Simplify the fraction. First find greatest common divisor (GCD) for 106692 and 5825. GCD(106692, 5825) = 233 $$\frac{106692}{5825} = \frac{233 \cdot 458}{233 \cdot 25} = \frac{458}{25}$$ 6. Convert the improper fraction to a mixed number: $$\frac{458}{25} = 18\frac{8}{25}$$ Answer: $$18\frac{8}{25}$$