\(1 \frac{7}{8} \cdot \left(2,1 \cdot \frac{3}{14} + \frac{9}{16}\right) =\)

Let's solve the third expression step by step: 1. Convert the mixed number to an improper fraction: $$1 \frac{7}{8} = \frac{1 \cdot 8 + 7}{8} = \frac{15}{8}$$ 2. Convert the decimal to a fraction: $$2.1 = \frac{21}{10}$$ 3. Multiply the fractions inside the parentheses: $$\frac{21}{10} \cdot \frac{3}{14} = \frac{21 \cdot 3}{10 \cdot 14} = \frac{3 \cdot 3}{10 \cdot 2} = \frac{9}{20}$$ 4. Add the fractions inside the parentheses: $$\frac{9}{20} + \frac{9}{16} = \frac{9 \cdot 4 + 9 \cdot 5}{80} = \frac{36 + 45}{80} = \frac{81}{80}$$ 5. Multiply the result by \(\frac{15}{8}\): $$\frac{15}{8} \cdot \frac{81}{80} = \frac{15 \cdot 81}{8 \cdot 80} = \frac{3 \cdot 81}{8 \cdot 16} = \frac{243}{128}$$ So, the final answer is: Answer: \(\frac{243}{128}\)