Вариант №1 1) 15\frac{17}{26}+22\frac{3}{26}= 2) 209\frac{1}{29}+105\frac{15}{29}= 3) 136\frac{15}{31}+107\frac{7}{31}= 4) 64\frac{6}{10}+12\frac{9}{10}= 5) 141\frac{10}{11}-41\frac{10}{11}= 6) 419\frac{23}{40}-105\frac{8}{40}= 7) 25\frac{18}{23}-24\frac{40}{23}= 8) 55\frac{2}{144}-8\frac{113}{144}= 9) 8\frac{3}{74}-1\frac{7}{74}= 10) 6\frac{6}{11}-2\frac{2}{11}= 11) 51-1\frac{7}{8}= 12) 5\frac{5}{4}-2\frac{1}{4}= 13) 36\frac{9}{20}-3\frac{7}{20}= 14) 81\frac{2}{14}-63\frac{7}{14}= 15) 85\frac{3}{4}-71\frac{1}{4}=

Решим данные примеры.

1. $$15\frac{17}{26}+22\frac{3}{26} = (15+22) + (\frac{17}{26} + \frac{3}{26}) = 37 + \frac{20}{26} = 37 + \frac{10}{13} = 37\frac{10}{13}$$
2. $$209\frac{1}{29}+105\frac{15}{29} = (209+105) + (\frac{1}{29} + \frac{15}{29}) = 314 + \frac{16}{29} = 314\frac{16}{29}$$
3. $$136\frac{15}{31}+107\frac{7}{31} = (136+107) + (\frac{15}{31} + \frac{7}{31}) = 243 + \frac{22}{31} = 243\frac{22}{31}$$
4. $$64\frac{6}{10}+12\frac{9}{10} = (64+12) + (\frac{6}{10} + \frac{9}{10}) = 76 + \frac{15}{10} = 76 + 1\frac{5}{10} = 77\frac{1}{2}$$
5. $$141\frac{10}{11}-41\frac{10}{11} = (141-41) + (\frac{10}{11} - \frac{10}{11}) = 100 + 0 = 100$$
6. $$419\frac{23}{40}-105\frac{8}{40} = (419-105) + (\frac{23}{40} - \frac{8}{40}) = 314 + \frac{15}{40} = 314 + \frac{3}{8} = 314\frac{3}{8}$$
7. $$25\frac{18}{23}-24\frac{40}{23} = (25-24) + (\frac{18}{23} - \frac{40}{23}) = 1 - \frac{22}{23} = \frac{23}{23} - \frac{22}{23} = \frac{1}{23}$$
8. $$55\frac{2}{144}-8\frac{113}{144} = (55-8) + (\frac{2}{144} - \frac{113}{144}) = 47 - \frac{111}{144} = 46 + \frac{144}{144} - \frac{111}{144} = 46\frac{33}{144} = 46\frac{11}{48}$$
9. $$8\frac{3}{74}-1\frac{7}{74} = (8-1) + (\frac{3}{74} - \frac{7}{74}) = 7 - \frac{4}{74} = 6 + \frac{74}{74} - \frac{4}{74} = 6\frac{70}{74} = 6\frac{35}{37}$$
10. $$6\frac{6}{11}-2\frac{2}{11} = (6-2) + (\frac{6}{11} - \frac{2}{11}) = 4 + \frac{4}{11} = 4\frac{4}{11}$$
11. $$51-1\frac{7}{8} = 50 + 1 - 1\frac{7}{8} = 50 + \frac{8}{8} - \frac{7}{8} = 50\frac{1}{8}$$
12. $$5\frac{5}{4}-2\frac{1}{4} = 5 + \frac{5}{4} - 2 - \frac{1}{4} = 5 + 1\frac{1}{4} - 2 - \frac{1}{4} = 6\frac{1}{4} - 2\frac{1}{4} = (6-2) + (\frac{1}{4} - \frac{1}{4}) = 4$$
13. $$36\frac{9}{20}-3\frac{7}{20} = (36-3) + (\frac{9}{20} - \frac{7}{20}) = 33 + \frac{2}{20} = 33\frac{1}{10}$$
14. $$81\frac{2}{14}-63\frac{7}{14} = (81-63) + (\frac{2}{14} - \frac{7}{14}) = 18 - \frac{5}{14} = 17 + \frac{14}{14} - \frac{5}{14} = 17\frac{9}{14}$$
15. $$85\frac{3}{4}-71\frac{1}{4} = (85-71) + (\frac{3}{4} - \frac{1}{4}) = 14 + \frac{2}{4} = 14 + \frac{1}{2} = 14\frac{1}{2}$$

Ответ: 1) $$37\frac{10}{13}$$; 2) $$314\frac{16}{29}$$; 3) $$243\frac{22}{31}$$; 4) $$77\frac{1}{2}$$; 5) $$100$$; 6) $$314\frac{3}{8}$$; 7) $$\frac{1}{23}$$; 8) $$46\frac{11}{48}$$; 9) $$6\frac{35}{37}$$; 10) $$4\frac{4}{11}$$; 11) $$50\frac{1}{8}$$; 12) $$4$$; 13) $$33\frac{1}{10}$$; 14) $$17\frac{9}{14}$$; 15) $$14\frac{1}{2}$$