829. Сложите дроби, полученную дробь сократите: a) \(\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2}\); б) \(\frac{1}{3} + \frac{2}{3} + \frac{1}{3} + \frac{5}{3}\); в) \(\frac{7}{13} + \frac{4}{13} + \frac{2}{13}\); г) \(\frac{1}{96} + \frac{5}{96} + \frac{11}{96} + \frac{31}{96}\); д) \(\frac{1}{42} + \frac{15}{42} + \frac{17}{42} + \frac{9}{42}\); е) \(\frac{19}{78} + \frac{53}{78} + \frac{37}{78} + \frac{21}{78}\);

Решение:

1. a) \(\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{1+1+1+1}{2} = \frac{4}{2} = 2\)
2. б) \(\frac{1}{3} + \frac{2}{3} + \frac{1}{3} + \frac{5}{3} = \frac{1+2+1+5}{3} = \frac{9}{3} = 3\)
3. в) \(\frac{7}{13} + \frac{4}{13} + \frac{2}{13} = \frac{7+4+2}{13} = \frac{13}{13} = 1\)
4. г) \(\frac{1}{96} + \frac{5}{96} + \frac{11}{96} + \frac{31}{96} = \frac{1+5+11+31}{96} = \frac{48}{96} = \frac{1}{2}\)
5. д) \(\frac{1}{42} + \frac{15}{42} + \frac{17}{42} + \frac{9}{42} = \frac{1+15+17+9}{42} = \frac{42}{42} = 1\)
6. е) \(\frac{19}{78} + \frac{53}{78} + \frac{37}{78} + \frac{21}{78} = \frac{19+53+37+21}{78} = \frac{130}{78} = \frac{65}{39}\)

Ответ:

1. а) 2
2. б) 3
3. в) 1
4. г) \(\frac{1}{2}\)
5. д) 1
6. е) \(\frac{65}{39}\)