5. Найдите значение выражения: 1) (5/26 - 3/25) * 13/2 2) (1/5 + 8/15) * 6 3) (2 3/4 + 2 1/5) * 16 4) 1/12 : (1/18 - 2/9) 5) 1/72 - 1/99 6) 18 * (1/9)^2 - 20 * 1/9

Краткое пояснение:

Пошаговое решение:

1. 1) \[ \left( \frac{5}{26} - \frac{3}{25} \right) \cdot \frac{13}{2} = \left( \frac{5 \cdot 25 - 3 \cdot 26}{26 \cdot 25} \right) \cdot \frac{13}{2} = \left( \frac{125 - 78}{650} \right) \cdot \frac{13}{2} = \frac{47}{650} \cdot \frac{13}{2} = \frac{47 \cdot 13}{650 \cdot 2} = \frac{47 \cdot 13}{(50 \cdot 13) \cdot 2} = \frac{47}{100} \]
2. 2) \[ \left( \frac{1}{5} + \frac{8}{15} \right) \cdot 6 = \left( \frac{1 \cdot 3}{5 \cdot 3} + \frac{8}{15} \right) \cdot 6 = \left( \frac{3}{15} + \frac{8}{15} \right) \cdot 6 = \frac{11}{15} \cdot 6 = \frac{11 \cdot 6}{15} = \frac{11 \cdot (2 \cdot 3)}{5 \cdot (3 \cdot 1)} = \frac{22}{5} \]
3. 3) \[ \left( 2 \frac{3}{4} + 2 \frac{1}{5} \right) \cdot 16 = \left( \frac{2 \cdot 4 + 3}{4} + \frac{2 \cdot 5 + 1}{5} \right) \cdot 16 = \left( \frac{11}{4} + \frac{11}{5} \right) \cdot 16 = \left( \frac{11 \cdot 5 + 11 \cdot 4}{4 \cdot 5} \right) \cdot 16 = \left( \frac{55 + 44}{20} \right) \cdot 16 = \frac{99}{20} \cdot 16 = \frac{99 \cdot 16}{20} = \frac{99 \cdot (4 \cdot 4)}{5 \cdot 4} = \frac{99 \cdot 4}{5} = \frac{396}{5} \]
4. 4) \[ \frac{1}{12} : \left( \frac{1}{18} - \frac{2}{9} \right) = \frac{1}{12} : \left( \frac{1}{18} - \frac{2 \cdot 2}{9 \cdot 2} \right) = \frac{1}{12} : \left( \frac{1}{18} - \frac{4}{18} \right) = \frac{1}{12} : \left( \frac{1 - 4}{18} \right) = \frac{1}{12} : \left( \frac{-3}{18} \right) = \frac{1}{12} : \left( \frac{-1}{6} \right) = \frac{1}{12} \cdot \left( \frac{6}{-1} \right) = \frac{6}{-12} = \frac{-1}{2} \]
5. 5) \[ \frac{1}{72} - \frac{1}{99} \]
• Найдем общий знаменатель для 72 и 99.
• \[ 72 = 8 \cdot 9 = 2^3 \cdot 3^2 \]
• \[ 99 = 9 \cdot 11 = 3^2 \cdot 11 \]
• НОК(72, 99) = \[ 2^3 \cdot 3^2 \cdot 11 = 8 \cdot 9 \cdot 11 = 72 \cdot 11 = 792 \]
• \[ \frac{1}{72} - \frac{1}{99} = \frac{1 \cdot 11}{72 \cdot 11} - \frac{1 \cdot 8}{99 \cdot 8} = \frac{11}{792} - \frac{8}{792} = \frac{11 - 8}{792} = \frac{3}{792} = \frac{1}{264} \]
6. 6) \[ 18 \cdot \left( \frac{1}{9} \right)^2 - 20 \cdot \frac{1}{9} = 18 \cdot \frac{1}{81} - \frac{20}{9} = \frac{18}{81} - \frac{20}{9} = \frac{2 \cdot 9}{9 \cdot 9} - \frac{20}{9} = \frac{2}{9} - \frac{20}{9} = \frac{2 - 20}{9} = \frac{-18}{9} = -2 \]

Ответ: 1) 47/100, 2) 22/5, 3) 396/5, 4) -1/2, 5) 1/264, 6) -2