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. ### Step 1: Convert mixed numbers to improper fractions 1. **Convert \( 8 \frac{7}{12} \)**: \[ 8 \frac{7}{12} = 8 + \frac{7}{12} = \frac{8 \cdot 12 + 7}{12} = \frac{96 + 7}{12} = \frac{103}{12} \] 2. **Convert \( 2 \frac{17}{36} \)**: \[ 2 \frac{17}{36} = 2 + \frac{17}{36} = \frac{2 \cdot 36 + 17}{36} = \frac{72 + 17}{36} = \frac{89}{36} \] 3. **Convert \( 4 \frac{1}{3} \)**: \[ 4 \frac{1}{3} = 4 + \frac{1}{3} = \frac{4 \cdot 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3} \] ### Step 2: Perform the subtraction Now we need to calculate \( \frac{103}{12} - \frac{89}{36} \). To subtract these fractions, we need a common denominator. 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 we can subtract: \[ \frac{309}{36} - \frac{89}{36} = \frac{309 - 89}{36} = \frac{220}{36} \] ### Step 3: Simplify the fraction Now simplify \( \frac{220}{36} \): \[ \frac{220 \div 4}{36 \div 4} = \frac{55}{9} \] ### Step 4: Multiply by 2.7 Now we calculate: \[ \left( \frac{55}{9} \right) \cdot 2.7 \] Convert 2.7 to a fraction: \[ 2.7 = \frac{27}{10} \] Now multiply: \[ \frac{55}{9} \cdot \frac{27}{10} = \frac{55 \cdot 27}{9 \cdot 10} = \frac{1485}{90} \] ### Step 5: Simplify the multiplication result Now simplify \( \frac{1485}{90} \): \[ \frac{1485 \div 15}{90 \div 15} = \frac{99}{6} = \frac{33}{2} = 16.5 \] ### Step 6: Divide \( 4 \frac{1}{3} \) by \( 0.65 \) Now we need to calculate \( 4 \frac{1}{3} : 0.65 \): Convert \( 0.65 \) to a fraction: \[ 0.65 = \frac{65}{100} = \frac{13}{20} \] Now we divide: \[ 4 \frac{1}{3} = \frac{13}{3} \] So, \[ \frac{13}{3} \div \frac{13}{20} = \frac{13}{3} \cdot \frac{20}{13} = \frac{20}{3} \] ### Step 7: Final calculation Now we need to calculate: \[ 16.5 - \frac{20}{3} \] Convert \( 16.5 \) to a fraction: \[ 16.5 = \frac{33}{2} \] Now we need a common denominator to subtract \( \frac{33}{2} - \frac{20}{3} \). 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 \