1. Выполни указанные действия: 1) 5 \frac{10}{19} : \frac{15}{19} 2) 1 \frac{1}{4} + \frac{9}{10} 3) 3 \frac{1}{5} \cdot 1 \frac{1}{4} 4) 5 \frac{2}{3} - 3 \frac{5}{6} 5) 4 \frac{2}{5} : 1 \frac{3}{5} 6) 5 \frac{5}{6} - 2 \frac{1}{21} 7) 2 \frac{2}{11} + \frac{2}{11} 8) 5 \frac{1}{3} \cdot 5

Решение:

• 1) \( 5 \frac{10}{19} : \frac{15}{19} = \frac{19 \cdot 5 + 10}{19} : \frac{15}{19} = \frac{105}{19} : \frac{15}{19} = \frac{105}{19} \cdot \frac{19}{15} = \frac{105}{15} = 7 \)
• 2) \( 1 \frac{1}{4} + \frac{9}{10} = \frac{5}{4} + \frac{9}{10} = \frac{5 \cdot 5}{20} + \frac{9 \cdot 2}{20} = \frac{25+18}{20} = \frac{43}{20} = 2 \frac{3}{20} \)
• 3) \( 3 \frac{1}{5} \cdot 1 \frac{1}{4} = \frac{16}{5} \cdot \frac{5}{4} = \frac{16}{4} = 4 \)
• 4) \( 5 \frac{2}{3} - 3 \frac{5}{6} = \frac{17}{3} - \frac{23}{6} = \frac{17 \cdot 2}{6} - \frac{23}{6} = \frac{34-23}{6} = \frac{11}{6} = 1 \frac{5}{6} \)
• 5) \( 4 \frac{2}{5} : 1 \frac{3}{5} = \frac{22}{5} : \frac{8}{5} = \frac{22}{5} \cdot \frac{5}{8} = \frac{22}{8} = \frac{11}{4} = 2 \frac{3}{4} \)
• 6) \( 5 \frac{5}{6} - 2 \frac{1}{21} = \frac{35}{6} - \frac{43}{21} = \frac{35 \cdot 7}{42} - \frac{43 \cdot 2}{42} = \frac{245 - 86}{42} = \frac{159}{42} = \frac{53}{14} = 3 \frac{11}{14} \)
• 7) \( 2 \frac{2}{11} + \frac{2}{11} = \frac{24}{11} + \frac{2}{11} = \frac{26}{11} = 2 \frac{4}{11} \)
• 8) \( 5 \frac{1}{3} \cdot 5 = \frac{16}{3} \cdot 5 = \frac{80}{3} = 26 \frac{2}{3} \)