6.58 Найдите сумму: a) 13 + \frac{8}{13}; б) 60 + \frac{31}{60} + \frac{29}{60}; в) 18 + \frac{4}{19} + \frac{8}{9}; г) 23 + \frac{10}{11}; д) 2 + \frac{7}{15} + \frac{8}{11} + \frac{4}{11}; e) 15 + \frac{4}{11} + \frac{3}{11}.

Решение: a) $$13 + \frac{8}{13} = \frac{13 \cdot 13}{13} + \frac{8}{13} = \frac{169}{13} + \frac{8}{13} = \frac{177}{13} = 13\frac{8}{13}$$ б) $$60 + \frac{31}{60} + \frac{29}{60} = 60 + \frac{31+29}{60} = 60 + \frac{60}{60} = 60 + 1 = 61$$ в) $$18 + \frac{4}{19} + \frac{8}{9}$$ = $$18 + \frac{4*9}{19*9} + \frac{8*19}{9*19} = 18 + \frac{36}{171} + \frac{152}{171} = 18 + \frac{188}{171}=18 + 1 \frac{17}{171}=19\frac{17}{171}$$ г) $$23 + \frac{10}{11} = \frac{23 \cdot 11}{11} + \frac{10}{11} = \frac{253}{11} + \frac{10}{11} = \frac{263}{11} = 23 \frac{10}{11}$$ д) $$2 + \frac{7}{15} + \frac{8}{11} + \frac{4}{11}= 2+ \frac{7}{15} +\frac{8+4}{11} = 2 + \frac{7}{15} + \frac{12}{11} = 2 + \frac{7 \cdot 11}{15 \cdot 11} + \frac{12 \cdot 15}{11 \cdot 15} = 2 + \frac{77}{165} + \frac{180}{165} = 2 + \frac{257}{165} = 2 + 1\frac{92}{165} = 3\frac{92}{165}$$ e) $$15 + \frac{4}{11} + \frac{3}{11} = 15 + \frac{4+3}{11} = 15 + \frac{7}{11} = 15\frac{7}{11}$$