Вычислите (833-836). 833. a) \frac{1}{10} + \frac{7}{100}; б) \frac{21}{100} + \frac{1}{10}; в) \frac{3}{5} + \frac{9}{10}; г) \frac{2}{3} + \frac{5}{6}; д) \frac{15}{24} + \frac{3}{8}; е) \frac{7}{6} + \frac{16}{18}; ж) \frac{1}{12} + \frac{1}{6}; з) \frac{1}{3} + \frac{1}{6}.

a) \(\frac{1}{10} + \frac{7}{100} = \frac{1 \cdot 10}{10 \cdot 10} + \frac{7}{100} = \frac{10}{100} + \frac{7}{100} = \frac{10+7}{100} = \frac{17}{100}\)

б) \(\frac{21}{100} + \frac{1}{10} = \frac{21}{100} + \frac{1 \cdot 10}{10 \cdot 10} = \frac{21}{100} + \frac{10}{100} = \frac{21+10}{100} = \frac{31}{100}\)

в) \(\frac{3}{5} + \frac{9}{10} = \frac{3 \cdot 2}{5 \cdot 2} + \frac{9}{10} = \frac{6}{10} + \frac{9}{10} = \frac{6+9}{10} = \frac{15}{10} = \frac{3}{2} = 1\frac{1}{2}\)

г) \(\frac{2}{3} + \frac{5}{6} = \frac{2 \cdot 2}{3 \cdot 2} + \frac{5}{6} = \frac{4}{6} + \frac{5}{6} = \frac{4+5}{6} = \frac{9}{6} = \frac{3}{2} = 1\frac{1}{2}\)

д) \(\frac{15}{24} + \frac{3}{8} = \frac{15}{24} + \frac{3 \cdot 3}{8 \cdot 3} = \frac{15}{24} + \frac{9}{24} = \frac{15+9}{24} = \frac{24}{24} = 1\)

е) \(\frac{7}{6} + \frac{16}{18} = \frac{7 \cdot 3}{6 \cdot 3} + \frac{16}{18} = \frac{21}{18} + \frac{16}{18} = \frac{21+16}{18} = \frac{37}{18} = 2\frac{1}{18}\)

ж) \(\frac{1}{12} + \frac{1}{6} = \frac{1}{12} + \frac{1 \cdot 2}{6 \cdot 2} = \frac{1}{12} + \frac{2}{12} = \frac{1+2}{12} = \frac{3}{12} = \frac{1}{4}\)

з) \(\frac{1}{3} + \frac{1}{6} = \frac{1 \cdot 2}{3 \cdot 2} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{2+1}{6} = \frac{3}{6} = \frac{1}{2}\)

Ответ: a) \(\frac{17}{100}\); б) \(\frac{31}{100}\); в) \(1\frac{1}{2}\); г) \(1\frac{1}{2}\); д) 1; е) \(2\frac{1}{18}\); ж) \(\frac{1}{4}\); з) \(\frac{1}{2}\)