a) \( \left(8 \frac{7}{12}-2 \frac{17}{36}\right) \cdot 2.7-4 \frac{1}{3}: 0.65 \)

To solve the expression \( \left(8 \frac{7}{12}-2 \frac{17}{36}\right) \cdot 2.7-4 \frac{1}{3}: 0.65 \), we will break it down step by step. 1. **Convert mixed numbers to improper fractions:** - \( 8 \frac{7}{12} = 8 \cdot 12 + 7 = 96 + 7 = 103 \) so \( 8 \frac{7}{12} = \frac{103}{12} \) - \( 2 \frac{17}{36} = 2 \cdot 36 + 17 = 72 + 17 = 89 \) so \( 2 \frac{17}{36} = \frac{89}{36} \) - \( 4 \frac{1}{3} = 4 \cdot 3 + 1 = 12 + 1 = 13 \) so \( 4 \frac{1}{3} = \frac{13}{3} \) 2. **Calculate \( 8 \frac{7}{12} - 2 \frac{17}{36} \):** - Find a common denominator for \( \frac{103}{12} \) and \( \frac{89}{36} \). The least common multiple of 12 and 36 is 36. - Convert \( \frac{103}{12} \) to have a denominator of 36: \[ \frac{103}{12} = \frac{103 \cdot 3}{12 \cdot 3} = \frac{309}{36} \] - Now subtract: \[ \frac{309}{36} - \frac{89}{36} = \frac{309 - 89}{36} = \frac{220}{36} \] - Simplify \( \frac{220}{36} \): \[ \frac{220 \div 4}{36 \div 4} = \frac{55}{9} \] 3. **Multiply by 2.7:** - Convert 2.7 to a fraction: \( 2.7 = \frac{27}{10} \) - Now multiply: \[ \frac{55}{9} \cdot \frac{27}{10} = \frac{55 \cdot 27}{9 \cdot 10} = \frac{1485}{90} \] - Simplify \( \frac{1485}{90} \): \[ \frac{1485 \div 15}{90 \div 15} = \frac{99}{6} = \frac{33}{2} = 16.5 \] 4. **Calculate \( 4 \frac{1}{3} : 0.65 \):** - Convert \( 0.65 \) to a fraction: \( 0.65 = \frac{65}{100} = \frac{13}{20} \) - Now divide \( \frac{13}{3} \) by \( \frac{13}{20} \): \[ \frac{13}{3} \div \frac{13}{20} = \frac{13}{3} \cdot \frac{20}{13} = \frac{20}{3} \] 5. **Final calculation:** - Now we need to subtract \( \frac{20}{3} \) from \( 16.5 \): - Convert \( 16.5 \) to a fraction: \( 16.5 = \frac{33}{2} \) - Find a common denominator for \( \frac{33}{2} \) and \( \frac{20}{3} \). The least common multiple of 2 and 3 is 6. - Convert both fractions: \[ \frac{33}{2} = \frac{33 \cdot 3}{2 \cdot 3} = \frac{99}{6} \] \[ \frac{20}{3} = \frac{20 \cdot 2}{3 \cdot 2} = \frac{40}{6} \] - Now subtract: \[ \frac{99}{6} - \frac{40}{6} = \frac{99 - 40}{6} = \frac{59}{6} \] Thus, the final result is: \[ \frac{59}{6} \text{ or } 9 \frac{