1). 2 1/3 : (5/8 - 8/3) - 2 * 1 3/7.

Привет! Давай решим эти примеры на дроби. Будем выполнять действия строго по порядку: сначала в скобках, затем умножение/деление, в конце сложение/вычитание. ### 1. $2\frac{1}{3} : (\frac{5}{8} - \frac{8}{3}) - 2 \cdot 1\frac{3}{7}$ 1) $\frac{5}{8} - \frac{8}{3} = \frac{15}{24} - \frac{64}{24} = -\frac{49}{24}$ 2) $\frac{7}{3} : (-\frac{49}{24}) = \frac{7}{3} \cdot (-\frac{24}{49}) = -\frac{1}{1} \cdot \frac{8}{7} = -\frac{8}{7} = -1\frac{1}{7}$ 3) $2 \cdot \frac{10}{7} = \frac{20}{7} = 2\frac{6}{7}$ 4) $-\frac{8}{7} - \frac{20}{7} = -\frac{28}{7} = -4$ **Ответ: -4** ### 2. $\frac{7}{15} : (\frac{6}{10} - \frac{8}{3}) + 19 \cdot \frac{2}{31}$ 1) $\frac{6}{10} - \frac{8}{3} = \frac{3}{5} - \frac{8}{3} = \frac{9}{15} - \frac{40}{15} = -\frac{31}{15}$ 2) $\frac{7}{15} : (-\frac{31}{15}) = \frac{7}{15} \cdot (-\frac{15}{31}) = -\frac{7}{31}$ 3) $19 \cdot \frac{2}{31} = \frac{38}{31} = 1\frac{7}{31}$ 4) $-\frac{7}{31} + \frac{38}{31} = \frac{31}{31} = 1$ **Ответ: 1** ### 3. $(7 - 1\frac{5}{9} : \frac{7}{24}) : \frac{20}{27}$ 1) $1\frac{5}{9} : \frac{7}{24} = \frac{14}{9} \cdot \frac{24}{7} = \frac{2}{3} \cdot \frac{8}{1} = \frac{16}{3} = 5\frac{1}{3}$ 2) $7 - 5\frac{1}{3} = 6\frac{3}{3} - 5\frac{1}{3} = 1\frac{2}{3} = \frac{5}{3}$ 3) $\frac{5}{3} : \frac{20}{27} = \frac{5}{3} \cdot \frac{27}{20} = \frac{1}{1} \cdot \frac{9}{4} = \frac{9}{4} = 2\frac{1}{4}$ **Ответ: 2,25** ### 4. $(1\frac{1}{35} : \frac{4}{5} - 1\frac{8}{35}) \cdot 3\frac{1}{3}$ 1) $\frac{36}{35} : \frac{4}{5} = \frac{36}{35} \cdot \frac{5}{4} = \frac{9}{7} = 1\frac{2}{7}$ 2) $1\frac{2}{7} - 1\frac{8}{35} = \frac{9}{7} - \frac{43}{35} = \frac{45}{35} - \frac{43}{35} = \frac{2}{35}$ 3) $\frac{2}{35} \cdot \frac{10}{3} = \frac{2}{7} \cdot \frac{2}{3} = \frac{4}{21}$ **Ответ: 4/21** ### 5. $1\frac{31}{35} : (2 - \frac{8}{9} : 1\frac{19}{45})$ 1) $\frac{8}{9} : \frac{64}{45} = \frac{8}{9} \cdot \frac{45}{64} = \frac{1}{1} \cdot \frac{5}{8} = \frac{5}{8}$ 2) $2 - \frac{5}{8} = 1\frac{3}{8} = \frac{11}{8}$ 3) $\frac{66}{35} : \frac{11}{8} = \frac{66}{35} \cdot \frac{8}{11} = \frac{6}{35} \cdot 8 = \frac{48}{35} = 1\frac{13}{35}$ **Ответ: 1 13/35** ### 6. $2\frac{7}{9} \cdot \frac{18}{25} + \frac{9}{60} : (\frac{7}{12} - \frac{3}{5})$ 1) $\frac{25}{9} \cdot \frac{18}{25} = \frac{1}{1} \cdot \frac{2}{1} = 2$ 2) $\frac{7}{12} - \frac{3}{5} = \frac{35}{60} - \frac{36}{60} = -\frac{1}{60}$ 3) $\frac{9}{60} : (-\frac{1}{60}) = \frac{3}{20} \cdot (-60) = 3 \cdot (-3) = -9$ 4) $2 + (-9) = -7$ **Ответ: -7** ### 7. $(5\frac{1}{16} - 1\frac{1}{8}) (\frac{5}{6} + \frac{3}{14})$ 1) $5\frac{1}{16} - 1\frac{2}{16} = 4\frac{17}{16} - 1\frac{2}{16} = 3\frac{15}{16} = \frac{63}{16}$ 2) $\frac{5}{6} + \frac{3}{14} = \frac{35}{42} + \frac{9}{42} = \frac{44}{42} = \frac{22}{21}$ 3) $\frac{63}{16} \cdot \frac{22}{21} = \frac{3}{8} \cdot \frac{11}{1} = \frac{33}{8} = 4\frac{1}{8}$ **Ответ: 4,125** ### 8. $(\frac{4}{5} + \frac{4}{7}) (3\frac{3}{8} + 2\frac{11}{4})$ 1) $\frac{28}{35} + \frac{20}{35} = \frac{48}{35}$ 2) $3\frac{3}{8} + 2\frac{22}{8} = 5\frac{25}{8} = 8\frac{1}{8} = \frac{65}{8}$ 3) $\frac{48}{35} \cdot \frac{65}{8} = \frac{6}{7} \cdot \frac{13}{1} = \frac{78}{7} = 11\frac{1}{7}$ **Ответ: 11 1/7** ### 9. $(2\frac{13}{48} + 2\frac{5}{12}) : 3\frac{3}{4} - 9\frac{3}{4} : 12$ 1) $2\frac{13}{48} + 2\frac{20}{48} = 4\frac{33}{48} = 4\frac{11}{16} = \frac{75}{16}$ 2) $\frac{75}{16} : \frac{15}{4} = \frac{75}{16} \cdot \frac{4}{15} = \frac{5}{4} = 1\frac{1}{4}$ 3) $9\frac{3}{4} : 12 = \frac{39}{4} : 12 = \frac{39}{48} = \frac{13}{16}$ 4) $1\frac{4}{16} - \frac{13}{16} = \frac{20}{16} - \frac{13}{16} = \frac{7}{16}$ **Ответ: 7/16** ### 10. $-3\frac{1}{7} \cdot (-8) - 2,9 : 0,1 + \frac{11}{21} : (-3\frac{2}{3})$ 1) $-\frac{22}{7} \cdot (-8) = \frac{176}{7} = 25\frac{1}{7}$ 2) $2,9 : 0,1 = 29$ 3) $\frac{11}{21} : (-\frac{11}{3}) = \frac{11}{21} \cdot (-\frac{3}{11}) = -\frac{1}{7}$ 4) $25\frac{1}{7} - 29 - \frac{1}{7} = 25 - 29 = -4$ **Ответ: -4** ### 11. $4\frac{1}{3} \cdot 5 + 2,4 : (-0,1) - \frac{14}{15} : 1\frac{2}{5}$ 1) $\frac{13}{3} \cdot 5 = \frac{65}{3} = 21\frac{2}{3}$ 2) $2,4 : (-0,1) = -24$ 3) $\frac{14}{15} : \frac{7}{5} = \frac{14}{15} \cdot \frac{5}{7} = \frac{2}{3}$ 4) $21\frac{2}{3} - 24 - \frac{2}{3} = 21 - 24 = -3$ **Ответ: -3** ### 12. $(6 - 2\frac{4}{5}) \cdot 3\frac{1}{8} - 1\frac{3}{5} : \frac{1}{4}$ 1) $6 - 2\frac{4}{5} = 3\frac{1}{5} = \frac{16}{5}$ 2) $\frac{16}{5} \cdot \frac{25}{8} = 2 \cdot 5 = 10$ 3) $\frac{8}{5} \cdot 4 = \frac{32}{5} = 6,4$ 4) $10 - 6,4 = 3,6$ **Ответ: 3,6** ### 13. $3\frac{1}{7} \cdot (-4) - 1,8 : (-0,1) + \frac{20}{21} : 1\frac{2}{3}$ 1) $\frac{22}{7} \cdot (-4) = -\frac{88}{7} = -12\frac{4}{7}$ 2) $1,8 : (-0,1) = -18$ 3) $\frac{20}{21} : \frac{5}{3} = \frac{20}{21} \cdot \frac{3}{5} = \frac{4}{7}$ 4) $-12\frac{4}{7} - (-18) + \frac{4}{7} = -12\frac{4}{7} + 18 + \frac{4}{7} = -12 + 18 = 6$ **Ответ: 6** ### 14. $4\frac{1}{6} \cdot (1\frac{1}{2} - \frac{3}{5}) + (\frac{3}{4} + \frac{5}{6}) \cdot 6$ 1) $1\frac{5}{10} - \frac{6}{10} = \frac{15}{10} - \frac{6}{10} = \frac{9}{10}$ 2) $\frac{25}{6} \cdot \frac{9}{10} = \frac{5}{2} \cdot \frac{3}{2} = \frac{15}{4} = 3\frac{3}{4}$ 3) $\frac{9}{12} + \frac{10}{12} = \frac{19}{12}$ 4) $\frac{19}{12} \cdot 6 = \frac{19}{2} = 9,5$ 5) $3,75 + 9,5 = 13,25$ **Ответ: 13,25** ### 15. $\frac{7}{9} : 1\frac{1}{6} + 2,7 : (-0,1) - 4\frac{1}{3} \cdot (-4)$ 1) $\frac{7}{9} : \frac{7}{6} = \frac{7}{9} \cdot \frac{6}{7} = \frac{2}{3}$ 2) $2,7 : (-0,1) = -27$ 3) $\frac{13}{3} \cdot (-4) = -\frac{52}{3} = -17\frac{1}{3}$ 4) $\frac{2}{3} - 27 - (-17\frac{1}{3}) = \frac{2}{3} - 27 + 17\frac{1}{3} = 18 - 27 = -9$ **Ответ: -9** ### 16. $7 \cdot 2\frac{6}{7} + \frac{53}{12} : (\frac{7}{9} - \frac{9}{4})$ 1) $7 \cdot \frac{20}{7} = 20$ 2) $\frac{7}{9} - \frac{9}{4} = \frac{28}{36} - \frac{81}{36} = -\frac{53}{36}$ 3) $\frac{53}{12} : (-\frac{53}{36}) = \frac{53}{12} \cdot (-\frac{36}{53}) = -\frac{36}{12} = -3$ 4) $20 - 3 = 17$ **Ответ: 17**