13. Выполните действия: a) 1 5 7 + 2 4 7 = б) 5 3 8 - 1 5 8 = в) 1 2 3 . 2 1 5 = г) 2 16 27 : 1 5 9 = д) 17 24 - ( 1 4 + 5 24 ) = e) 8,24 + 3,456 = ж) 0,235 · 1,06 = 3) 32,2 : 0,04 =

Решение:

1. а) \(1\frac{5}{7} + 2\frac{4}{7} = \frac{1 \cdot 7 + 5}{7} + \frac{2 \cdot 7 + 4}{7} = \frac{12}{7} + \frac{18}{7} = \frac{12 + 18}{7} = \frac{30}{7} = 4\frac{2}{7}\)
2. б) \(5\frac{3}{8} - 1\frac{5}{8} = \frac{5 \cdot 8 + 3}{8} - \frac{1 \cdot 8 + 5}{8} = \frac{43}{8} - \frac{13}{8} = \frac{43 - 13}{8} = \frac{30}{8} = \frac{15}{4} = 3\frac{3}{4}\)
3. в) \(1\frac{2}{3} \cdot 2\frac{1}{5} = \frac{1 \cdot 3 + 2}{3} \cdot \frac{2 \cdot 5 + 1}{5} = \frac{5}{3} \cdot \frac{11}{5} = \frac{5 \cdot 11}{3 \cdot 5} = \frac{11}{3} = 3\frac{2}{3}\)
4. г) \(\frac{16}{27} : 1\frac{5}{9} = \frac{16}{27} : \frac{1 \cdot 9 + 5}{9} = \frac{16}{27} : \frac{14}{9} = \frac{16}{27} \cdot \frac{9}{14} = \frac{16 \cdot 9}{27 \cdot 14} = \frac{8 \cdot 1}{3 \cdot 7} = \frac{8}{21}\)
5. д) \(\frac{17}{24} - (\frac{1}{4} + \frac{5}{24}) = \frac{17}{24} - (\frac{1 \cdot 6}{4 \cdot 6} + \frac{5}{24}) = \frac{17}{24} - (\frac{6}{24} + \frac{5}{24}) = \frac{17}{24} - \frac{11}{24} = \frac{17 - 11}{24} = \frac{6}{24} = \frac{1}{4}\)
6. е) \(8,24 + 3,456 = 11,696\)
7. ж) \(0,235 \cdot 1,06 = 0,2491\)
8. з) \(32,2 : 0,04 = 3220 : 4 = 805\)

Ответ: а) \(4\frac{2}{7}\), б) \(3\frac{3}{4}\), в) \(3\frac{2}{3}\), г) \(\frac{8}{21}\), д) \(\frac{1}{4}\), е) 11,696, ж) 0,2491, з) 805.