Задание 5. Выполни действия со смешанными числами. 1. 2\frac{5}{13}+5\frac{8}{13} 2. 9\frac{15}{21}-3\frac{10}{21} 3. 10\frac{16}{34}-1\frac{14}{34} 4. 6\frac{7}{15}+9\frac{13}{15} 5. 15\frac{1}{10}-6\frac{4}{10} 6. 3\frac{6}{17}-2\frac{7}{17} 7. 23\frac{6}{19}-15\frac{16}{19} 8. 17\frac{2}{5}-15\frac{5}{17} 9. 5\frac{9}{23}-4\frac{15}{23} 10. 10\frac{1}{9}-3\frac{5}{9} 11. 12\frac{8}{10}-10\frac{9}{10} 12. 5\frac{2}{7}-4\frac{5}{7} 13. 2\frac{3}{5}+3\frac{4}{5} 14. 11\frac{6}{7}+13\frac{5}{7} 15. 8\frac{9}{16}-5\frac{7}{16} 16. 10\frac{5}{9}-4\frac{5}{9}

Задание 5. Выполним действия со смешанными числами.

1. $$2\frac{5}{13}+5\frac{8}{13} = (2+5) + (\frac{5}{13} + \frac{8}{13}) = 7 + \frac{13}{13} = 7 + 1 = 8$$
2. $$9\frac{15}{21}-3\frac{10}{21} = (9-3) + (\frac{15}{21} - \frac{10}{21}) = 6 + \frac{5}{21} = 6\frac{5}{21}$$
3. $$10\frac{16}{34}-1\frac{14}{34} = (10-1) + (\frac{16}{34} - \frac{14}{34}) = 9 + \frac{2}{34} = 9 + \frac{1}{17} = 9\frac{1}{17}$$
4. $$6\frac{7}{15}+9\frac{13}{15} = (6+9) + (\frac{7}{15} + \frac{13}{15}) = 15 + \frac{20}{15} = 15 + 1\frac{5}{15} = 16\frac{1}{3}$$
5. $$15\frac{1}{10}-6\frac{4}{10} = (15-6) + (\frac{1}{10} - \frac{4}{10}) = 9 - \frac{3}{10} = 8\frac{10}{10} - \frac{3}{10} = 8\frac{7}{10}$$
6. $$3\frac{6}{17}-2\frac{7}{17} = (3-2) + (\frac{6}{17} - \frac{7}{17}) = 1 - \frac{1}{17} = \frac{17}{17} - \frac{1}{17} = \frac{16}{17}$$
7. $$23\frac{6}{19}-15\frac{16}{19} = (23-15) + (\frac{6}{19} - \frac{16}{19}) = 8 - \frac{10}{19} = 7\frac{19}{19} - \frac{10}{19} = 7\frac{9}{19}$$
8. $$17\frac{2}{5}-15\frac{5}{17} = (17-15) + (\frac{2}{5} - \frac{5}{17}) = 2 + (\frac{2 \cdot 17}{5 \cdot 17} - \frac{5 \cdot 5}{17 \cdot 5}) = 2 + (\frac{34}{85} - \frac{25}{85}) = 2 + \frac{9}{85} = 2\frac{9}{85}$$
9. $$5\frac{9}{23}-4\frac{15}{23} = (5-4) + (\frac{9}{23} - \frac{15}{23}) = 1 - \frac{6}{23} = \frac{23}{23} - \frac{6}{23} = \frac{17}{23}$$
10. $$10\frac{1}{9}-3\frac{5}{9} = (10-3) + (\frac{1}{9} - \frac{5}{9}) = 7 - \frac{4}{9} = 6\frac{9}{9} - \frac{4}{9} = 6\frac{5}{9}$$
11. $$12\frac{8}{10}-10\frac{9}{10} = (12-10) + (\frac{8}{10} - \frac{9}{10}) = 2 - \frac{1}{10} = 1\frac{10}{10} - \frac{1}{10} = 1\frac{9}{10}$$
12. $$5\frac{2}{7}-4\frac{5}{7} = (5-4) + (\frac{2}{7} - \frac{5}{7}) = 1 - \frac{3}{7} = \frac{7}{7} - \frac{3}{7} = \frac{4}{7}$$
13. $$2\frac{3}{5}+3\frac{4}{5} = (2+3) + (\frac{3}{5} + \frac{4}{5}) = 5 + \frac{7}{5} = 5 + 1\frac{2}{5} = 6\frac{2}{5}$$
14. $$11\frac{6}{7}+13\frac{5}{7} = (11+13) + (\frac{6}{7} + \frac{5}{7}) = 24 + \frac{11}{7} = 24 + 1\frac{4}{7} = 25\frac{4}{7}$$
15. $$8\frac{9}{16}-5\frac{7}{16} = (8-5) + (\frac{9}{16} - \frac{7}{16}) = 3 + \frac{2}{16} = 3 + \frac{1}{8} = 3\frac{1}{8}$$
16. $$10\frac{5}{9}-4\frac{5}{9} = (10-4) + (\frac{5}{9} - \frac{5}{9}) = 6 + 0 = 6$$

Ответ: 1) $$8$$, 2) $$6\frac{5}{21}$$, 3) $$9\frac{1}{17}$$, 4) $$16\frac{1}{3}$$, 5) $$8\frac{7}{10}$$, 6) $$\frac{16}{17}$$, 7) $$7\frac{9}{19}$$, 8) $$2\frac{9}{85}$$, 9) $$\frac{17}{23}$$, 10) $$6\frac{5}{9}$$, 11) $$1\frac{9}{10}$$, 12) $$\frac{4}{7}$$, 13) $$6\frac{2}{5}$$, 14) $$25\frac{4}{7}$$, 15) $$3\frac{1}{8}$$, 16) $$6$$