Вычислите:
1) $6\frac{4}{9} + 3\frac{5}{9}$;
2) $10\frac{11}{19} + 5\frac{14}{19}$;
3) $2\frac{3}{13} + 2\frac{11}{13}$;
4) $1\frac{5}{8} + 3\frac{7}{8}$;
5) $1 - \frac{3}{11}$;
6) $1 - \frac{13}{40}$;
7) $4 - 1\frac{4}{7}$;
8) $10 - 9\frac{3}{10}$;
9) $5\frac{2}{7} - 2\frac{5}{7}$;
10) $14\frac{6}{20} - 8\frac{12}{20}$;
11) $8\frac{3}{14} - 5\frac{9}{14}$;
12) $7\frac{10}{21} - 4\frac{16}{21}$;
13) $14\frac{8}{31} - 6\frac{8}{31}$;
14) $(12\frac{5}{22} + 7\frac{17}{22}) - (13\frac{7}{23} - 9\frac{15}{23})$.

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Решение

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Математика 5 класс Мерзляк. Номер №777

Решение 1

$6\frac{4}{9} + 3\frac{5}{9} = (6 + 3) + (\frac{4}{9} + \frac{5}{9}) = 9 + \frac{9}{9} = 9 + 1 = 10$

Решение 2

$10\frac{11}{19} + 5\frac{14}{19} = (10 + 5) + (\frac{11}{19} + \frac{14}{19}) = 15 + \frac{25}{19} = 15 + 1 + \frac{6}{19} = 16\frac{6}{19}$

Решение 3

$2\frac{3}{13} + 2\frac{11}{13} = (2 + 2) + (\frac{3}{13} + \frac{11}{13}) = 4 + \frac{14}{13} = 4 + 1 + \frac{1}{13} = 5\frac{1}{13}$

Решение 4

$1\frac{5}{8} + 3\frac{7}{8} = (1 + 3) + (\frac{5}{8} + \frac{7}{8}) = 4 + \frac{12}{8} = 4 + 1 + \frac{4}{8} = 5\frac{4}{8}$

Решение 5

$1 - \frac{3}{11} = \frac{11}{11} - \frac{3}{11} = \frac{8}{11}$

Решение 6

$1 - \frac{13}{40} = \frac{40}{40} - \frac{13}{40} = \frac{27}{40}$

Решение 7

$4 - 1\frac{4}{7} = 3\frac{7}{7} - 1\frac{4}{7} = (3 - 1) + (\frac{7}{7} - \frac{4}{7}) = 2 + \frac{3}{7} = 2\frac{3}{7}$

Решение 8

$10 - 9\frac{3}{10} = 9\frac{10}{10} - 9\frac{3}{10} = (9 - 9) + (\frac{10}{10} - \frac{3}{10}) = \frac{7}{10}$

Решение 9

$5\frac{2}{7} - 2\frac{5}{7} = 4\frac{9}{7} - 2\frac{5}{7} = (4 - 2) + (\frac{9}{7} - \frac{5}{7}) = 2\frac{4}{7}$

Решение 10

$14\frac{6}{20} - 8\frac{12}{20} = 13\frac{26}{20} - 8\frac{12}{20} = (13 - 8) + (\frac{26}{20} - \frac{12}{20}) = 5 + \frac{14}{20} = 5\frac{14}{20}$

Решение 11

$8\frac{3}{14} - 5\frac{9}{14} = 7\frac{17}{14} - 5\frac{9}{14} = (7 - 5) + (\frac{17}{14} - \frac{9}{14}) = 2 + \frac{8}{14} = 2\frac{8}{14}$

Решение 12

$7\frac{10}{21} - 4\frac{16}{21} = 6\frac{31}{21} - 4\frac{16}{21} = (6 - 4) + (\frac{31}{21} - \frac{16}{21}) = 2 + \frac{15}{21} = 2\frac{15}{21}$

Решение 13

$14\frac{8}{31} - 6\frac{8}{31} = (14 - 6) + (\frac{8}{31} - \frac{8}{31}) = 8 + 0 = 8$

Решение 14

$(12\frac{5}{22} + 7\frac{17}{22}) - (13\frac{7}{23} - 9\frac{15}{23}) = ((12 + 7) + (\frac{5}{22} + \frac{17}{22})) - ((12 - 9) + (\frac{30}{23} - \frac{15}{23})) = (19 + \frac{22}{22}) - (3 + \frac{15}{23}) = 20 - 3\frac{15}{23} = 19\frac{23}{23} - 3\frac{15}{23} = (19 - 3) + (\frac{23}{23} - \frac{15}{23}) = 16 + \frac{8}{23} = 16\frac{8}{23}$