Задание №4

Вычислите обыкновенные дроби, а потом сократите.

1. $$\frac{9}{14} - \frac{2}{7} + \frac{9}{35} = \frac{9}{14} - \frac{4}{14} + \frac{9}{35} = \frac{5}{14} + \frac{9}{35}$$ $$\frac{5}{14} + \frac{9}{35} = \frac{5 \cdot 5}{14 \cdot 5} + \frac{9 \cdot 2}{35 \cdot 2} = \frac{25}{70} + \frac{18}{70} = \frac{43}{70}$$ $$\frac{43}{70}$$
2. $$\frac{7}{18} - \frac{1}{6} + \frac{7}{9} = \frac{7}{18} - \frac{3}{18} + \frac{14}{18} = \frac{4}{18} + \frac{14}{18} = \frac{18}{18} = 1$$ $$\frac{18}{18} = 1$$
3. $$\frac{3}{4} - \frac{1}{6} + \frac{7}{12} = \frac{9}{12} - \frac{2}{12} + \frac{7}{12} = \frac{7}{12} + \frac{7}{12} = \frac{14}{12}$$ $$\frac{14}{12} = \frac{7}{6}$$
4. $$\frac{12}{170} + \frac{13}{17} - \frac{2}{34} = \frac{6}{85} + \frac{13}{17} - \frac{1}{17} = \frac{6}{85} + \frac{12}{17} = \frac{6}{85} + \frac{60}{85} = \frac{66}{85}$$ $$\frac{66}{85}$$
5. $$\frac{7}{15} + \frac{8}{9} - \frac{5}{6} = \frac{7}{15} + \frac{16}{18} - \frac{15}{18} = \frac{7}{15} + \frac{1}{18}$$ $$\frac{7}{15} + \frac{1}{18} = \frac{7 \cdot 6}{15 \cdot 6} + \frac{1 \cdot 5}{18 \cdot 5} = \frac{42}{90} + \frac{5}{90} = \frac{47}{90}$$ $$\frac{47}{90}$$
6. $$\frac{15}{17} - (\frac{1}{5} + \frac{1}{6}) = \frac{15}{17} - (\frac{6}{30} + \frac{5}{30}) = \frac{15}{17} - \frac{11}{30}$$ $$\frac{15}{17} - \frac{11}{30} = \frac{15 \cdot 30}{17 \cdot 30} - \frac{11 \cdot 17}{30 \cdot 17} = \frac{450}{510} - \frac{187}{510} = \frac{263}{510}$$ $$\frac{263}{510}$$