415. Вычислите: a) $$rac{1}{2} + \frac{3}{4} + \frac{5}{8}$$; б) $$rac{23}{24} - \frac{5}{12} - \frac{1}{6}$$; в) $$rac{5}{8} + \frac{1}{3} + \frac{7}{12}$$; г) $$rac{5}{6} - \frac{1}{8} + \frac{5}{12}$$; д) $$3 \frac{5}{7} + 4 \frac{9}{14} - 2 \frac{5}{21}$$; е) $$2 \frac{1}{3} + \frac{1}{5} - 1 \frac{1}{8}$$

Решим каждый пример по действиям:

а)

$$\frac{1}{2} + \frac{3}{4} + \frac{5}{8} = \frac{4}{8} + \frac{6}{8} + \frac{5}{8} = \frac{4+6+5}{8} = \frac{15}{8} = 1\frac{7}{8}$$

б)

$$\frac{23}{24} - \frac{5}{12} - \frac{1}{6} = \frac{23}{24} - \frac{10}{24} - \frac{4}{24} = \frac{23-10-4}{24} = \frac{9}{24} = \frac{3}{8}$$

в)

$$\frac{5}{8} + \frac{1}{3} + \frac{7}{12} = \frac{45}{72} + \frac{24}{72} + \frac{42}{72} = \frac{45+24+42}{72} = \frac{111}{72} = \frac{37}{24} = 1\frac{13}{24}$$

г)

$$\frac{5}{6} - \frac{1}{8} + \frac{5}{12} = \frac{20}{24} - \frac{3}{24} + \frac{10}{24} = \frac{20-3+10}{24} = \frac{27}{24} = \frac{9}{8} = 1\frac{1}{8}$$

д)

$$3 \frac{5}{7} + 4 \frac{9}{14} - 2 \frac{5}{21} = \frac{26}{7} + \frac{65}{14} - \frac{47}{21} = \frac{78}{21} + \frac{97.5}{21} - \frac{47}{21} = \frac{233.5}{21} - \frac{47}{21} = \frac{186.5}{21} = 8 \frac{17}{42} $$

е)

$$2 \frac{1}{3} + \frac{1}{5} - 1 \frac{1}{8} = \frac{7}{3} + \frac{1}{5} - \frac{9}{8} = \frac{280}{120} + \frac{24}{120} - \frac{135}{120} = \frac{280+24-135}{120} = \frac{169}{120} = 1 \frac{49}{120}$$