2. Вычислите: a) \(\frac{3}{5}+\frac{1}{6}\); б) \(\frac{7}{15}+\frac{1}{3}\); в) \(\frac{1}{20}+\frac{2}{15}\); г) \(\frac{5}{9}-\frac{1}{2}\); д) \(\frac{3}{4}-\frac{5}{16}\); e) \(\frac{7}{22}-\frac{2}{33}\).

Решение:

а) \(\frac{3}{5}+\frac{1}{6} = \frac{3 \cdot 6}{5 \cdot 6} + \frac{1 \cdot 5}{6 \cdot 5} = \frac{18}{30} + \frac{5}{30} = \frac{18+5}{30} = \frac{23}{30}\)

Ответ: \(\frac{23}{30}\)

б) \(\frac{7}{15}+\frac{1}{3} = \frac{7}{15} + \frac{1 \cdot 5}{3 \cdot 5} = \frac{7}{15} + \frac{5}{15} = \frac{7+5}{15} = \frac{12}{15} = \frac{4}{5}\)

Ответ: \(\frac{4}{5}\)

в) \(\frac{1}{20}+\frac{2}{15} = \frac{1 \cdot 3}{20 \cdot 3} + \frac{2 \cdot 4}{15 \cdot 4} = \frac{3}{60} + \frac{8}{60} = \frac{3+8}{60} = \frac{11}{60}\)

Ответ: \(\frac{11}{60}\)

г) \(\frac{5}{9}-\frac{1}{2} = \frac{5 \cdot 2}{9 \cdot 2} - \frac{1 \cdot 9}{2 \cdot 9} = \frac{10}{18} - \frac{9}{18} = \frac{10-9}{18} = \frac{1}{18}\)

Ответ: \(\frac{1}{18}\)

д) \(\frac{3}{4}-\frac{5}{16} = \frac{3 \cdot 4}{4 \cdot 4} - \frac{5}{16} = \frac{12}{16} - \frac{5}{16} = \frac{12-5}{16} = \frac{7}{16}\)

Ответ: \(\frac{7}{16}\)

e) \(\frac{7}{22}-\frac{2}{33} = \frac{7 \cdot 3}{22 \cdot 3} - \frac{2 \cdot 2}{33 \cdot 2} = \frac{21}{66} - \frac{4}{66} = \frac{21-4}{66} = \frac{17}{66}\)

Ответ: \(\frac{17}{66}\)