1. Найдите: 1) 8\frac{16}{23}-2\frac{12}{23}+2\frac{3}{23}; 2) 6\frac{5}{11}-2\frac{7}{11}; 3) 7-4\frac{4}{5}; 4) 25\frac{2}{9}+76\frac{8}{9}; 5) 17\frac{2}{5}-5\frac{2}{5}

1) 8\frac{16}{23}-2\frac{12}{23}+2\frac{3}{23} = (8 - 2 + 2) + (\frac{16}{23} - \frac{12}{23} + \frac{3}{23}) = 8 + \frac{16 - 12 + 3}{23} = 8 + \frac{7}{23} = 8\frac{7}{23}

2) 6\frac{5}{11}-2\frac{7}{11} = 6\frac{5}{11}-2\frac{7}{11} = (5 + 1)\frac{5}{11}-2\frac{7}{11} = 5\frac{16}{11}-2\frac{7}{11} = (5 - 2) + (\frac{16}{11} - \frac{7}{11}) = 3 + \frac{16-7}{11} = 3 + \frac{9}{11} = 3\frac{9}{11}

3) 7-4\frac{4}{5} = 7 - 4\frac{4}{5} = (6 + 1)-4\frac{4}{5} = 6\frac{5}{5}-4\frac{4}{5} = (6 - 4) + (\frac{5}{5} - \frac{4}{5}) = 2 + \frac{5-4}{5} = 2 + \frac{1}{5} = 2\frac{1}{5}

4) 25\frac{2}{9}+76\frac{8}{9} = 25\frac{2}{9}+76\frac{8}{9} = (25 + 76) + (\frac{2}{9} + \frac{8}{9}) = 101 + \frac{2+8}{9} = 101 + \frac{10}{9} = 101 + 1\frac{1}{9} = 102\frac{1}{9}

5) 17\frac{2}{5}-5\frac{2}{5} = (17 - 5) + (\frac{2}{5} - \frac{2}{5}) = 12 + 0 = 12

Ответ: 1) 8\frac{7}{23}; 2) 3\frac{9}{11}; 3) 2\frac{1}{5}; 4) 102\frac{1}{9}; 5) 12