Решим данные примеры:
1) 1 - 8/19
$$1 - \frac{8}{19} = \frac{19}{19} - \frac{8}{19} = \frac{19-8}{19} = \frac{11}{19}$$
2) 6 - 9/14
$$6 - \frac{9}{14} = \frac{6 \cdot 14}{14} - \frac{9}{14} = \frac{84}{14} - \frac{9}{14} = \frac{84-9}{14} = \frac{75}{14} = 5\frac{5}{14}$$
3) 7 - 1 8/9
$$7 - 1\frac{8}{9} = 7 - \frac{1 \cdot 9 + 8}{9} = 7 - \frac{17}{9} = \frac{7 \cdot 9}{9} - \frac{17}{9} = \frac{63}{9} - \frac{17}{9} = \frac{63-17}{9} = \frac{46}{9} = 5\frac{1}{9}$$
Найдите разность:
1) 8 7/8 - 5 3/4
$$8\frac{7}{8} - 5\frac{3}{4} = \frac{8 \cdot 8 + 7}{8} - \frac{5 \cdot 4 + 3}{4} = \frac{71}{8} - \frac{23}{4} = \frac{71}{8} - \frac{23 \cdot 2}{4 \cdot 2} = \frac{71}{8} - \frac{46}{8} = \frac{71-46}{8} = \frac{25}{8} = 3\frac{1}{8}$$
2) 7 7/15 - 4 5/18
$$7\frac{7}{15} - 4\frac{5}{18} = \frac{7 \cdot 15 + 7}{15} - \frac{4 \cdot 18 + 5}{18} = \frac{112}{15} - \frac{77}{18} = \frac{112 \cdot 6}{15 \cdot 6} - \frac{77 \cdot 5}{18 \cdot 5} = \frac{672}{90} - \frac{385}{90} = \frac{672-385}{90} = \frac{287}{90} = 3\frac{17}{90}$$
3) 16 11/18 - 8 8/27
$$16\frac{11}{18} - 8\frac{8}{27} = \frac{16 \cdot 18 + 11}{18} - \frac{8 \cdot 27 + 8}{27} = \frac{299}{18} - \frac{224}{27} = \frac{299 \cdot 3}{18 \cdot 3} - \frac{224 \cdot 2}{27 \cdot 2} = \frac{897}{54} - \frac{448}{54} = \frac{897-448}{54} = \frac{449}{54} = 8\frac{17}{54}$$
4) 8 17/28 - 7 23/42
$$8\frac{17}{28} - 7\frac{23}{42} = \frac{8 \cdot 28 + 17}{28} - \frac{7 \cdot 42 + 23}{42} = \frac{241}{28} - \frac{317}{42} = \frac{241 \cdot 3}{28 \cdot 3} - \frac{317 \cdot 2}{42 \cdot 2} = \frac{723}{84} - \frac{634}{84} = \frac{723-634}{84} = \frac{89}{84} = 1\frac{5}{84}$$
Выполните вычитание:
1) 6 1/14 - 1/7
$$6\frac{1}{14} - \frac{1}{7} = \frac{6 \cdot 14 + 1}{14} - \frac{1}{7} = \frac{85}{14} - \frac{1 \cdot 2}{7 \cdot 2} = \frac{85}{14} - \frac{2}{14} = \frac{85-2}{14} = \frac{83}{14} = 5\frac{13}{14}$$
2) 8 9/40 - 6 13/50
$$8\frac{9}{40} - 6\frac{13}{50} = \frac{8 \cdot 40 + 9}{40} - \frac{6 \cdot 50 + 13}{50} = \frac{329}{40} - \frac{313}{50} = \frac{329 \cdot 5}{40 \cdot 5} - \frac{313 \cdot 4}{50 \cdot 4} = \frac{1645}{200} - \frac{1252}{200} = \frac{1645-1252}{200} = \frac{393}{200} = 1\frac{193}{200}$$
3) 5 5/6 - 2 6/7
$$5\frac{5}{6} - 2\frac{6}{7} = \frac{5 \cdot 6 + 5}{6} - \frac{2 \cdot 7 + 6}{7} = \frac{35}{6} - \frac{20}{7} = \frac{35 \cdot 7}{6 \cdot 7} - \frac{20 \cdot 6}{7 \cdot 6} = \frac{245}{42} - \frac{120}{42} = \frac{245-120}{42} = \frac{125}{42} = 2\frac{41}{42}$$
4) 9 7/34 - 1 29/102
$$9\frac{7}{34} - 1\frac{29}{102} = \frac{9 \cdot 34 + 7}{34} - \frac{1 \cdot 102 + 29}{102} = \frac{313}{34} - \frac{131}{102} = \frac{313 \cdot 3}{34 \cdot 3} - \frac{131}{102} = \frac{939}{102} - \frac{131}{102} = \frac{939-131}{102} = \frac{808}{102} = \frac{404}{51} = 7\frac{47}{51}$$
Итоговые ответы:
1) $$\frac{\mathbf{11}}{\mathbf{19}}$$
2) $$\mathbf{5\frac{5}{14}}$$
3) $$\mathbf{5\frac{1}{9}}$$
Найдите разность:
1) $$\mathbf{3\frac{1}{8}}$$
2) $$\mathbf{3\frac{17}{90}}$$
3) $$\mathbf{8\frac{17}{54}}$$
4) $$\mathbf{1\frac{5}{84}}$$
Выполните вычитание:
1) $$\mathbf{5\frac{13}{14}}$$
2) $$\mathbf{1\frac{193}{200}}$$
3) $$\mathbf{2\frac{41}{42}}$$
4) $$\mathbf{7\frac{47}{51}}$$