1) 15\frac{17}{26}+22\frac{3}{26}= 2) 209\frac{1}{29}+105 = 3) 136\frac{15}{31}+107\frac{7}{31}= 4) 64\frac{6}{10}+12\frac{9}{10} = 5) 141\frac{11}{40}-41\frac{21}{40}= 6) 419\frac{8}{23}-105 = 7) 25\frac{18}{23}-24\frac{18}{23} = 8) 55\frac{113}{144}-8 = 9) 8\frac{2}{74}-1\frac{7}{74}= 10) 6\frac{3}{11}-2= 11) 51\frac{1}{8}-1\frac{7}{8}= 12) 5\frac{5}{4}-2\frac{1}{4}= 13) 36\frac{9}{20}-3 = 14) 81\frac{2}{14}-63\frac{7}{14}= 15) 85\frac{4}{4}-71\frac{3}{4}=

Давай разберем по порядку эти примеры на сложение и вычитание смешанных чисел. 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) \(209\frac{1}{29}+105 = 209 + 105 + \frac{1}{29} = 314 + \frac{1}{29} = 314\frac{1}{29}\) 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) \(141\frac{11}{40}-41\frac{21}{40} = (141 - 41) + (\frac{11}{40} - \frac{21}{40}) = 100 - \frac{10}{40} = 100 - \frac{1}{4} = 99\frac{3}{4}\) 6) \(419\frac{8}{23}-105 = 419 - 105 + \frac{8}{23} = 314 + \frac{8}{23} = 314\frac{8}{23}\) 7) \(25\frac{18}{23}-24\frac{18}{23} = (25 - 24) + (\frac{18}{23} - \frac{18}{23}) = 1 + 0 = 1\) 8) \(55\frac{113}{144}-8 = 55 - 8 + \frac{113}{144} = 47 + \frac{113}{144} = 47\frac{113}{144}\) 9) \(8\frac{2}{74}-1\frac{7}{74} = (8 - 1) + (\frac{2}{74} - \frac{7}{74}) = 7 - \frac{5}{74} = 6\frac{69}{74}\) 10) \(6\frac{3}{11}-2 = 6 - 2 + \frac{3}{11} = 4 + \frac{3}{11} = 4\frac{3}{11}\) 11) \(51\frac{1}{8}-1\frac{7}{8} = (51 - 1) + (\frac{1}{8} - \frac{7}{8}) = 50 - \frac{6}{8} = 50 - \frac{3}{4} = 49\frac{1}{4}\) 12) \(5\frac{5}{4}-2\frac{1}{4} = (5 - 2) + (\frac{5}{4} - \frac{1}{4}) = 3 + \frac{4}{4} = 3 + 1 = 4\) 13) \(36\frac{9}{20}-3 = 36 - 3 + \frac{9}{20} = 33 + \frac{9}{20} = 33\frac{9}{20}\) 14) \(81\frac{2}{14}-63\frac{7}{14} = (81 - 63) + (\frac{2}{14} - \frac{7}{14}) = 18 - \frac{5}{14} = 17\frac{9}{14}\) 15) \(85\frac{4}{4}-71\frac{3}{4} = (85 - 71) + (\frac{4}{4} - \frac{3}{4}) = 14 + \frac{1}{4} = 14\frac{1}{4}\)

Ответ: 1) \(37\frac{10}{13}\); 2) \(314\frac{1}{29}\); 3) \(243\frac{22}{31}\); 4) \(77\frac{1}{2}\); 5) \(99\frac{3}{4}\); 6) \(314\frac{8}{23}\); 7) 1; 8) \(47\frac{113}{144}\); 9) \(6\frac{69}{74}\); 10) \(4\frac{3}{11}\); 11) \(49\frac{1}{4}\); 12) 4; 13) \(33\frac{9}{20}\); 14) \(17\frac{9}{14}\); 15) \(14\frac{1}{4}\)

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