2 Действия с обыкновенными дробями 1. Вычислите $$\frac{5}{12} \cdot (\frac{1}{5} + \frac{3}{25})$$ 2. Вычислите $$\frac{7}{39} \cdot (\frac{1}{7} + \frac{6}{49})$$ 3. Вычислите $$\frac{9}{14} \cdot (\frac{17}{24} - \frac{5}{12})$$ 4. Вычислите $$\frac{3}{16} \cdot (\frac{4}{5} - \frac{8}{15})$$ 5. Вычислите $$\frac{8}{35} \cdot (\frac{5}{6} + \frac{11}{12})$$ 6. Вычислите $$\frac{8}{15} \cdot (\frac{7}{8} + \frac{11}{16})$$ 7. Вычислите $$\frac{9}{10} \cdot (\frac{11}{12} - \frac{2}{9})$$ 8. Вычислите $$\frac{7}{39} \cdot (\frac{11}{14} - \frac{1}{6})$$ 9. Вычислите $$\frac{15}{32} : (\frac{5}{8} + \frac{3}{20})$$ 10. Вычислите $$\frac{24}{49} : (\frac{6}{7} + \frac{1}{14})$$ 11. Вычислите $$\frac{3}{11} + \frac{15}{17} : \frac{11}{34}$$ 12. Вычислите $$\frac{14}{25} \cdot \frac{7}{45} - 3$$ 13. Вычислите $$\frac{18}{35} : 12 + \frac{1}{10}$$ 14. Вычислите $$\frac{11}{8} - \frac{15}{16} : \frac{25}{28}$$

1. $$\frac{5}{12} \cdot (\frac{1}{5} + \frac{3}{25}) = \frac{5}{12} \cdot (\frac{5}{25} + \frac{3}{25}) = \frac{5}{12} \cdot \frac{8}{25} = \frac{5 \cdot 8}{12 \cdot 25} = \frac{40}{300} = \frac{2}{15}$$

2. $$\frac{7}{39} \cdot (\frac{1}{7} + \frac{6}{49}) = \frac{7}{39} \cdot (\frac{7}{49} + \frac{6}{49}) = \frac{7}{39} \cdot \frac{13}{49} = \frac{7 \cdot 13}{39 \cdot 49} = \frac{91}{1911} = \frac{1}{21}$$

3. $$\frac{9}{14} \cdot (\frac{17}{24} - \frac{5}{12}) = \frac{9}{14} \cdot (\frac{17}{24} - \frac{10}{24}) = \frac{9}{14} \cdot \frac{7}{24} = \frac{9 \cdot 7}{14 \cdot 24} = \frac{63}{336} = \frac{3}{16}$$

4. $$\frac{3}{16} \cdot (\frac{4}{5} - \frac{8}{15}) = \frac{3}{16} \cdot (\frac{12}{15} - \frac{8}{15}) = \frac{3}{16} \cdot \frac{4}{15} = \frac{3 \cdot 4}{16 \cdot 15} = \frac{12}{240} = \frac{1}{20}$$

5. $$\frac{8}{35} \cdot (\frac{5}{6} + \frac{11}{12}) = \frac{8}{35} \cdot (\frac{10}{12} + \frac{11}{12}) = \frac{8}{35} \cdot \frac{21}{12} = \frac{8 \cdot 21}{35 \cdot 12} = \frac{168}{420} = \frac{2}{5}$$

6. $$\frac{8}{15} \cdot (\frac{7}{8} + \frac{11}{16}) = \frac{8}{15} \cdot (\frac{14}{16} + \frac{11}{16}) = \frac{8}{15} \cdot \frac{25}{16} = \frac{8 \cdot 25}{15 \cdot 16} = \frac{200}{240} = \frac{5}{6}$$

7. $$\frac{9}{10} \cdot (\frac{11}{12} - \frac{2}{9}) = \frac{9}{10} \cdot (\frac{33}{36} - \frac{8}{36}) = \frac{9}{10} \cdot \frac{25}{36} = \frac{9 \cdot 25}{10 \cdot 36} = \frac{225}{360} = \frac{5}{8}$$

8. $$\frac{7}{39} \cdot (\frac{11}{14} - \frac{1}{6}) = \frac{7}{39} \cdot (\frac{33}{42} - \frac{7}{42}) = \frac{7}{39} \cdot \frac{26}{42} = \frac{7 \cdot 26}{39 \cdot 42} = \frac{182}{1638} = \frac{1}{9}$$

9. $$\frac{15}{32} : (\frac{5}{8} + \frac{3}{20}) = \frac{15}{32} : (\frac{25}{40} + \frac{6}{40}) = \frac{15}{32} : \frac{31}{40} = \frac{15}{32} \cdot \frac{40}{31} = \frac{15 \cdot 40}{32 \cdot 31} = \frac{600}{992} = \frac{9}{10}$$

10. $$\frac{24}{49} : (\frac{6}{7} + \frac{1}{14}) = \frac{24}{49} : (\frac{12}{14} + \frac{1}{14}) = \frac{24}{49} : \frac{13}{14} = \frac{24}{49} \cdot \frac{14}{13} = \frac{24 \cdot 14}{49 \cdot 13} = \frac{336}{637} = \frac{9}{14}$$

11. $$\frac{3}{11} + \frac{15}{17} : \frac{11}{34} = \frac{3}{11} + \frac{15}{17} \cdot \frac{34}{11} = \frac{3}{11} + \frac{15 \cdot 34}{17 \cdot 11} = \frac{3}{11} + \frac{510}{187} = \frac{3}{11} + \frac{30}{11} = \frac{33}{11} = 3$$

12. $$\frac{14}{25} \cdot \frac{7}{45} - 3 = \frac{14 \cdot 7}{25 \cdot 45} - 3 = \frac{98}{1125} - 3 = \frac{98 - 3375}{1125} = \frac{-3277}{1125} = \frac{3}{5}$$

13. $$\frac{18}{35} : 12 + \frac{1}{10} = \frac{18}{35} \cdot \frac{1}{12} + \frac{1}{10} = \frac{18}{420} + \frac{1}{10} = \frac{3}{70} + \frac{1}{10} = \frac{3}{70} + \frac{7}{70} = \frac{10}{70} = \frac{1}{7}$$

14. $$\frac{11}{8} - \frac{15}{16} : \frac{25}{28} = \frac{11}{8} - \frac{15}{16} \cdot \frac{28}{25} = \frac{11}{8} - \frac{15 \cdot 28}{16 \cdot 25} = \frac{11}{8} - \frac{420}{400} = \frac{11}{8} - \frac{21}{20} = \frac{55}{40} - \frac{42}{40} = \frac{13}{40}$$