743. Выполни действия:
1) $\frac{7}{18} + \frac{5}{18} = \frac{7+5}{18} = \frac{12}{18} = \frac{2}{3}$
2) $\frac{11}{24} + \frac{8}{24} = \frac{11+8}{24} = \frac{19}{24}$
3) $\frac{23}{47} - \frac{14}{47} = \frac{23-14}{47} = \frac{9}{47}$
4) **Допущение:** В условии ошибка, и должно быть $\frac{31}{58} - \frac{16}{58}$. Тогда $\frac{31}{58} - \frac{16}{58} = \frac{31-16}{58} = \frac{15}{58}$
5) $\frac{3}{29} + \frac{6}{29} + \frac{8}{29} = \frac{3+6+8}{29} = \frac{17}{29}$
6) $\frac{29}{64} - \frac{14}{64} - \frac{9}{64} = \frac{29-14-9}{64} = \frac{6}{64} = \frac{3}{32}$
744. Выполни действия:
1) $\frac{5}{19} + \frac{6}{19} = \frac{5+6}{19} = \frac{11}{19}$
2) $\frac{7}{13} - \frac{4}{13} = \frac{7-4}{13} = \frac{3}{13}$
3) $\frac{19}{25} + \frac{4}{25} + \frac{22}{25} = \frac{19+4+22}{25} = \frac{45}{25} = \frac{9}{5} = 1\frac{4}{5}$
4) $\frac{34}{39} - \frac{15}{39} - \frac{8}{39} = \frac{34-15-8}{39} = \frac{11}{39}$
777. Вычисли:
1) $6\frac{4}{9} + 3\frac{5}{9} = (6+3) + (\frac{4}{9} + \frac{5}{9}) = 9 + \frac{9}{9} = 9 + 1 = 10$
2) $10\frac{11}{19} + 5\frac{14}{19} = (10+5) + (\frac{11}{19} + \frac{14}{19}) = 15 + \frac{25}{19} = 15 + 1\frac{6}{19} = 16\frac{6}{19}$
3) $2\frac{3}{13} + 2\frac{11}{13} = (2+2) + (\frac{3}{13} + \frac{11}{13}) = 4 + \frac{14}{13} = 4 + 1\frac{1}{13} = 5\frac{1}{13}$
4) $1\frac{5}{8} + 3\frac{7}{8} = (1+3) + (\frac{5}{8} + \frac{7}{8}) = 4 + \frac{12}{8} = 4 + 1\frac{4}{8} = 5\frac{1}{2}$
5) $1 - \frac{3}{11} = \frac{11}{11} - \frac{3}{11} = \frac{11-3}{11} = \frac{8}{11}$
6) $1 - \frac{13}{40} = \frac{40}{40} - \frac{13}{40} = \frac{40-13}{40} = \frac{27}{40}$
7) $4 - 1\frac{4}{7} = 4 - \frac{11}{7} = \frac{28}{7} - \frac{11}{7} = \frac{28-11}{7} = \frac{17}{7} = 2\frac{3}{7}$
8) $10 - 9\frac{3}{10} = 10 - \frac{93}{10} = \frac{100}{10} - \frac{93}{10} = \frac{100-93}{10} = \frac{7}{10}$
9) $5\frac{2}{7} - 2\frac{5}{7} = 5\frac{2}{7} - 2\frac{5}{7} = \frac{37}{7} - \frac{19}{7} = \frac{37-19}{7} = \frac{18}{7} = 2\frac{4}{7}$
10) $14\frac{6}{20} - 8\frac{12}{20} = 14\frac{6}{20} - 8\frac{12}{20} = \frac{286}{20} - \frac{172}{20} = \frac{286-172}{20} = \frac{114}{20} = \frac{57}{10} = 5\frac{7}{10}$
11) $8\frac{3}{14} - 5\frac{9}{14} = 8\frac{3}{14} - 5\frac{9}{14} = \frac{115}{14} - \frac{79}{14} = \frac{115-79}{14} = \frac{36}{14} = \frac{18}{7} = 2\frac{4}{7}$
12) $7\frac{10}{21} - 4\frac{16}{21} = 7\frac{10}{21} - 4\frac{16}{21} = \frac{157}{21} - \frac{100}{21} = \frac{157-100}{21} = \frac{57}{21} = \frac{19}{7} = 2\frac{5}{7}$
13) $14\frac{8}{31} - 6\frac{8}{31} = (14-6) + (\frac{8}{31} - \frac{8}{31}) = 8 + 0 = 8$
14) $(12\frac{5}{22} + 7\frac{17}{22}) - (13\frac{7}{23} - 9\frac{15}{23}) = (12+7) + (\frac{5}{22} + \frac{17}{22}) - ((13-9) + (\frac{7}{23} - \frac{15}{23})) = 19 + \frac{22}{22} - (4 - \frac{8}{23}) = 19 + 1 - 4 + \frac{8}{23} = 16\frac{8}{23}$
778. Вычислите:
1) $7\frac{14}{15} + 2\frac{1}{15} = (7+2) + (\frac{14}{15} + \frac{1}{15}) = 9 + \frac{15}{15} = 9 + 1 = 10$
2) $9\frac{24}{27} + 12\frac{13}{27} = (9+12) + (\frac{24}{27} + \frac{13}{27}) = 21 + \frac{37}{27} = 21 + 1\frac{10}{27} = 22\frac{10}{27}$
3) $1 - \frac{12}{19} = \frac{19}{19} - \frac{12}{19} = \frac{19-12}{19} = \frac{7}{19}$
4) $8 - 3\frac{6}{15} = 8 - \frac{51}{15} = \frac{120}{15} - \frac{51}{15} = \frac{120-51}{15} = \frac{69}{15} = \frac{23}{5} = 4\frac{3}{5}$
5) $12 - 11\frac{6}{11} = 12 - \frac{127}{11} = \frac{132}{11} - \frac{127}{11} = \frac{132-127}{11} = \frac{5}{11}$
6) $16\frac{3}{13} - 6\frac{8}{13} = 16\frac{3}{13} - 6\frac{8}{13} = \frac{211}{13} - \frac{86}{13} = \frac{211-86}{13} = \frac{125}{13} = 9\frac{8}{13}$
7) $13\frac{4}{9} - 2\frac{8}{9} = 13\frac{4}{9} - 2\frac{8}{9} = \frac{121}{9} - \frac{26}{9} = \frac{121-26}{9} = \frac{95}{9} = 10\frac{5}{9}$
8) $10\frac{7}{16} - 4\frac{12}{16} = 10\frac{7}{16} - 4\frac{12}{16} = \frac{167}{16} - \frac{76}{16} = \frac{167-76}{16} = \frac{91}{16} = 5\frac{11}{16}$
9) $29\frac{49}{53} - 8\frac{49}{53} = (29-8) + (\frac{49}{53} - \frac{49}{53}) = 21 + 0 = 21$
10) $(20\frac{16}{25} + 13\frac{9}{25}) - (23\frac{4}{14} + 7\frac{13}{14}) = (20+13) + (\frac{16}{25} + \frac{9}{25}) - ((23+7) + (\frac{4}{14} + \frac{13}{14})) = 33 + \frac{25}{25} - (30 + \frac{17}{14}) = 33 + 1 - 30 - 1\frac{3}{14} = 34 - 30 - 1\frac{3}{14} = 4 - 1\frac{3}{14} = 2\frac{11}{14}$
