Привет! Давай разберем эти примеры вместе. Я помогу тебе понять, как их решать.
Первая группа примеров:
1) \( 5 - \frac{2}{3} \)
\( = \frac{5 \times 3}{3} - \frac{2}{3} \)
\( = \frac{15}{3} - \frac{2}{3} \)
\( = \frac{15 - 2}{3} \)
\( = \frac{13}{3} \)
\( = 4\frac{1}{3} \)
2) \( 8 - \frac{3}{11} \)
\( = \frac{8 \times 11}{11} - \frac{3}{11} \)
\( = \frac{88}{11} - \frac{3}{11} \)
\( = \frac{88 - 3}{11} \)
\( = \frac{85}{11} \)
\( = 7\frac{8}{11} \)
3) \( 10 - 5\frac{1}{5} \)
\( = 10 - \frac{5 \times 5 + 1}{5} \)
\( = 10 - \frac{26}{5} \)
\( = \frac{10 \times 5}{5} - \frac{26}{5} \)
\( = \frac{50}{5} - \frac{26}{5} \)
\( = \frac{50 - 26}{5} \)
\( = \frac{24}{5} \)
\( = 4\frac{4}{5} \)
4) \( 7 - 3\frac{7}{9} \)
\( = 7 - \frac{3 \times 9 + 7}{9} \)
\( = 7 - \frac{27 + 7}{9} \)
\( = 7 - \frac{34}{9} \)
\( = \frac{7 \times 9}{9} - \frac{34}{9} \)
\( = \frac{63}{9} - \frac{34}{9} \)
\( = \frac{63 - 34}{9} \)
\( = \frac{29}{9} \)
\( = 3\frac{2}{9} \)
5) \( 11 - 5\frac{4}{15} \)
\( = 11 - \frac{5 \times 15 + 4}{15} \)
\( = 11 - \frac{75 + 4}{15} \)
\( = 11 - \frac{79}{15} \)
\( = \frac{11 \times 15}{15} - \frac{79}{15} \)
\( = \frac{165}{15} - \frac{79}{15} \)
\( = \frac{165 - 79}{15} \)
\( = \frac{86}{15} \)
\( = 5\frac{11}{15} \)
6) \( 18 - 10\frac{19}{20} \)
\( = 18 - \frac{10 \times 20 + 19}{20} \)
\( = 18 - \frac{200 + 19}{20} \)
\( = 18 - \frac{219}{20} \)
\( = \frac{18 \times 20}{20} - \frac{219}{20} \)
\( = \frac{360}{20} - \frac{219}{20} \)
\( = \frac{360 - 219}{20} \)
\( = \frac{141}{20} \)
\( = 7\frac{1}{20} \)
Вторая группа примеров:
1) \( 7\frac{2}{13} - 1\frac{7}{13} \)
\( = \frac{7 \times 13 + 2}{13} - \frac{1 \times 13 + 7}{13} \)
\( = \frac{91 + 2}{13} - \frac{13 + 7}{13} \)
\( = \frac{93}{13} - \frac{20}{13} \)
\( = \frac{93 - 20}{13} \)
\( = \frac{73}{13} \)
\( = 5\frac{8}{13} \)
2) \( 4\frac{3}{7} - 2\frac{5}{7} \)
\( = \frac{4 \times 7 + 3}{7} - \frac{2 \times 7 + 5}{7} \)
\( = \frac{28 + 3}{7} - \frac{14 + 5}{7} \)
\( = \frac{31}{7} - \frac{19}{7} \)
\( = \frac{31 - 19}{7} \)
\( = \frac{12}{7} \)
\( = 1\frac{5}{7} \)
3) \( 21\frac{5}{8} - 15\frac{7}{8} \)
\( = \frac{21 \times 8 + 5}{8} - \frac{15 \times 8 + 7}{8} \)
\( = \frac{168 + 5}{8} - \frac{120 + 7}{8} \)
\( = \frac{173}{8} - \frac{127}{8} \)
\( = \frac{173 - 127}{8} \)
\( = \frac{46}{8} \)
\( = \frac{23}{4} \)
\( = 5\frac{3}{4} \)
4) \( 16\frac{3}{14} - 6\frac{5}{14} \)
\( = \frac{16 \times 14 + 3}{14} - \frac{6 \times 14 + 5}{14} \)
\( = \frac{224 + 3}{14} - \frac{84 + 5}{14} \)
\( = \frac{227}{14} - \frac{89}{14} \)
\( = \frac{227 - 89}{14} \)
\( = \frac{138}{14} \)
\( = \frac{69}{7} \)
\( = 9\frac{6}{7} \)
5) \( 10\frac{21}{40} - 9\frac{33}{40} \)
\( = \frac{10 \times 40 + 21}{40} - \frac{9 \times 40 + 33}{40} \)
\( = \frac{400 + 21}{40} - \frac{360 + 33}{40} \)
\( = \frac{421}{40} - \frac{393}{40} \)
\( = \frac{421 - 393}{40} \)
\( = \frac{28}{40} \)
\( = \frac{7}{10} \)
6) \( 5\frac{8}{17} - 1\frac{10}{17} \)
\( = \frac{5 \times 17 + 8}{17} - \frac{1 \times 17 + 10}{17} \)
\( = \frac{85 + 8}{17} - \frac{17 + 10}{17} \)
\( = \frac{93}{17} - \frac{27}{17} \)
\( = \frac{93 - 27}{17} \)
\( = \frac{66}{17} \)
\( = 3\frac{15}{17} \)
Ответ: Все решено выше!
Прекрасно! Ты отлично справляешься с этими примерами. Продолжай в том же духе, и у тебя всё получится!