Найдите значение выражения: a) $$2\frac{3}{7} + 3\frac{2}{7} =$$ b) $$8 - 4\frac{2}{13} =$$ v) $$\frac{4}{15} - \frac{2}{9} =$$ г) $$4\frac{1}{7} - \frac{5}{21} =$$ д) $$\frac{55}{7} \cdot \frac{21}{44} =$$ e) $$3\frac{5}{26} \cdot 13 =$$ ж) $$\frac{5}{6} : \frac{10}{27} =$$ з) $$\frac{0,63}{4,5} =$$ и) $$7,5 : \frac{15}{16} =$$

Решаем по действиям:

1. a) $$2\frac{3}{7} + 3\frac{2}{7} = (2+3) + (\frac{3}{7} + \frac{2}{7}) = 5 + \frac{5}{7} = 5\frac{5}{7}$$
2. б) $$8 - 4\frac{2}{13} = 8 - \frac{4 \cdot 13 + 2}{13} = 8 - \frac{54}{13} = \frac{8 \cdot 13}{13} - \frac{54}{13} = \frac{104 - 54}{13} = \frac{50}{13} = 3\frac{11}{13}$$
3. в) $$\frac{4}{15} - \frac{2}{9} = \frac{4 \cdot 3}{15 \cdot 3} - \frac{2 \cdot 5}{9 \cdot 5} = \frac{12}{45} - \frac{10}{45} = \frac{12 - 10}{45} = \frac{2}{45}$$
4. г) $$4\frac{1}{7} - \frac{5}{21} = \frac{4 \cdot 7 + 1}{7} - \frac{5}{21} = \frac{29}{7} - \frac{5}{21} = \frac{29 \cdot 3}{7 \cdot 3} - \frac{5}{21} = \frac{87}{21} - \frac{5}{21} = \frac{87 - 5}{21} = \frac{82}{21} = 3\frac{19}{21}$$
5. д) $$\frac{55}{7} \cdot \frac{21}{44} = \frac{55 \cdot 21}{7 \cdot 44} = \frac{5 \cdot 11 \cdot 3 \cdot 7}{7 \cdot 4 \cdot 11} = \frac{5 \cdot 3}{4} = \frac{15}{4} = 3\frac{3}{4}$$
6. е) $$3\frac{5}{26} \cdot 13 = \frac{3 \cdot 26 + 5}{26} \cdot 13 = \frac{83}{26} \cdot 13 = \frac{83 \cdot 13}{26} = \frac{83 \cdot 13}{2 \cdot 13} = \frac{83}{2} = 41\frac{1}{2}$$
7. ж) $$\frac{5}{6} : \frac{10}{27} = \frac{5}{6} \cdot \frac{27}{10} = \frac{5 \cdot 27}{6 \cdot 10} = \frac{5 \cdot 9 \cdot 3}{2 \cdot 3 \cdot 5 \cdot 2} = \frac{9}{4} = 2\frac{1}{4}$$
8. з) $$\frac{0,63}{4,5} = \frac{63}{450} = \frac{9 \cdot 7}{9 \cdot 50} = \frac{7}{50} = \frac{7 \cdot 2}{50 \cdot 2} = \frac{14}{100} = 0,14$$
9. и) $$7,5 : \frac{15}{16} = \frac{75}{10} : \frac{15}{16} = \frac{75}{10} \cdot \frac{16}{15} = \frac{75 \cdot 16}{10 \cdot 15} = \frac{5 \cdot 15 \cdot 8 \cdot 2}{5 \cdot 2 \cdot 15} = 8$$