5.445 Вычислите: a) 2 +; б) 1 +; в) 5 +; e) 4 -; г) +; д) --; ж) 6 +; з) 9 -; и) 2 -; к) 15 -; л) 8 +; м) 9 -; о) 17 -; п) 35 -;

Решение:

Давай решим эти примеры по порядку:

а)

2 \(\frac{1}{3}\) + \(\frac{1}{3}\) = \(\frac{2 \cdot 3 + 1}{3}\) + \(\frac{1}{3}\) = \(\frac{7}{3}\) + \(\frac{1}{3}\) = \(\frac{7 + 1}{3}\) = \(\frac{8}{3}\) = 2 \(\frac{2}{3}\)

б)

1 \(\frac{1}{3}\) + \(\frac{2}{7}\) = \(\frac{1 \cdot 3 + 1}{3}\) + \(\frac{2}{7}\) = \(\frac{4}{3}\) + \(\frac{2}{7}\) = \(\frac{4 \cdot 7}{3 \cdot 7}\) + \(\frac{2 \cdot 3}{7 \cdot 3}\) = \(\frac{28}{21}\) + \(\frac{6}{21}\) = \(\frac{28 + 6}{21}\) = \(\frac{34}{21}\) = 1 \(\frac{13}{21}\)

в)

5 \(\frac{2}{3}\) + \(\frac{1}{3}\) = \(\frac{5 \cdot 3 + 2}{3}\) + \(\frac{1}{3}\) = \(\frac{17}{3}\) + \(\frac{1}{3}\) = \(\frac{17 + 1}{3}\) = \(\frac{18}{3}\) = 6

e)

4 \(\frac{3}{4}\) - 1 \(\frac{1}{3}\) = \(\frac{4 \cdot 4 + 3}{4}\) - \(\frac{1 \cdot 3 + 1}{3}\) = \(\frac{19}{4}\) - \(\frac{4}{3}\) = \(\frac{19 \cdot 3}{4 \cdot 3}\) - \(\frac{4 \cdot 4}{3 \cdot 4}\) = \(\frac{57}{12}\) - \(\frac{16}{12}\) = \(\frac{57 - 16}{12}\) = \(\frac{41}{12}\) = 3 \(\frac{5}{12}\)

г)

\(\frac{3}{7}\) + \(\frac{4}{9}\) = \(\frac{3 \cdot 9}{7 \cdot 9}\) + \(\frac{4 \cdot 7}{9 \cdot 7}\) = \(\frac{27}{63}\) + \(\frac{28}{63}\) = \(\frac{27 + 28}{63}\) = \(\frac{55}{63}\)

д)

\(\frac{5}{9}\) - \(\frac{1}{6}\) = \(\frac{5 \cdot 2}{9 \cdot 2}\) - \(\frac{1 \cdot 3}{6 \cdot 3}\) = \(\frac{10}{18}\) - \(\frac{3}{18}\) = \(\frac{10 - 3}{18}\) = \(\frac{7}{18}\)

ж)

6 \(\frac{1}{3}\) + 1 \(\frac{1}{3}\) = \(\frac{6 \cdot 3 + 1}{3}\) + \(\frac{1 \cdot 3 + 1}{3}\) = \(\frac{19}{3}\) + \(\frac{4}{3}\) = \(\frac{19 + 4}{3}\) = \(\frac{23}{3}\) = 7 \(\frac{2}{3}\)

з)

9 \(\frac{5}{10}\) - \(\frac{7}{10}\) = \(\frac{9 \cdot 10 + 5}{10}\) - \(\frac{7}{10}\) = \(\frac{95}{10}\) - \(\frac{7}{10}\) = \(\frac{95 - 7}{10}\) = \(\frac{88}{10}\) = 8 \(\frac{8}{10}\) = 8 \(\frac{4}{5}\)

и)

2 \(\frac{1}{2}\) - \(\frac{3}{8}\) = \(\frac{2 \cdot 2 + 1}{2}\) - \(\frac{3}{8}\) = \(\frac{5}{2}\) - \(\frac{3}{8}\) = \(\frac{5 \cdot 4}{2 \cdot 4}\) - \(\frac{3}{8}\) = \(\frac{20}{8}\) - \(\frac{3}{8}\) = \(\frac{20 - 3}{8}\) = \(\frac{17}{8}\) = 2 \(\frac{1}{8}\)

к)

15 \(\frac{7}{15}\) - \(\frac{3}{10}\) = \(\frac{15 \cdot 15 + 7}{15}\) - \(\frac{3}{10}\) = \(\frac{232}{15}\) - \(\frac{3}{10}\) = \(\frac{232 \cdot 2}{15 \cdot 2}\) - \(\frac{3 \cdot 3}{10 \cdot 3}\) = \(\frac{464}{30}\) - \(\frac{9}{30}\) = \(\frac{464 - 9}{30}\) = \(\frac{455}{30}\) = 15 \(\frac{5}{30}\) = 15 \(\frac{1}{6}\)

л)

\(\frac{3}{8}\) + \(\frac{5}{12}\) = \(\frac{3 \cdot 3}{8 \cdot 3}\) + \(\frac{5 \cdot 2}{12 \cdot 2}\) = \(\frac{9}{24}\) + \(\frac{10}{24}\) = \(\frac{9 + 10}{24}\) = \(\frac{19}{24}\)

м)

\(\frac{5}{9}\) - \(\frac{1}{6}\) = \(\frac{5 \cdot 2}{9 \cdot 2}\) - \(\frac{1 \cdot 3}{6 \cdot 3}\) = \(\frac{10}{18}\) - \(\frac{3}{18}\) = \(\frac{10 - 3}{18}\) = \(\frac{7}{18}\)

о)

\(\frac{17}{30}\) - \(\frac{3}{6}\) = \(\frac{17}{30}\) - \(\frac{3 \cdot 5}{6 \cdot 5}\) = \(\frac{17}{30}\) - \(\frac{15}{30}\) = \(\frac{17 - 15}{30}\) = \(\frac{2}{30}\) = \(\frac{1}{15}\)

п)

\(\frac{17}{35}\) - \(\frac{4}{15}\) = \(\frac{17 \cdot 3}{35 \cdot 3}\) - \(\frac{4 \cdot 7}{15 \cdot 7}\) = \(\frac{51}{105}\) - \(\frac{28}{105}\) = \(\frac{51 - 28}{105}\) = \(\frac{23}{105}\)

Ответ: а) 2 \(\frac{2}{3}\); б) 1 \(\frac{13}{21}\); в) 6; e) 3 \(\frac{5}{12}\); г) \(\frac{55}{63}\); д) \(\frac{7}{18}\); ж) 7 \(\frac{2}{3}\); з) 8 \(\frac{4}{5}\); и) 2 \(\frac{1}{8}\); к) 15 \(\frac{1}{6}\); л) \(\frac{19}{24}\); м) \(\frac{7}{18}\); о) \(\frac{1}{15}\); п) \(\frac{23}{105}\)

Ты молодец! У тебя всё получится!