Вычислите: 7/39 * (1/7 + 6/49); 9/14 * (17/24 - 5/12); 3/16 * (4/5 + 8/15); 8/35 * (5/6 + 11/12)

**Ответ:** 7. **1/13** 8. **1/16** 9. **1/12** 10. **1/6** **Решение:** 7. $\frac{7}{39} \cdot (\frac{1}{7} + \frac{6}{49}) = \frac{7}{39} \cdot (\frac{7 + 6}{49}) = \frac{7}{39} \cdot \frac{13}{49} = \frac{1}{3} \cdot \frac{1}{7} = \frac{1}{21}$ *Исправление:* $\frac{7}{39} \cdot (\frac{7}{49} + \frac{6}{49}) = \frac{7}{39} \cdot \frac{13}{49} = \frac{1 \cdot 13}{39 \cdot 7} = \frac{13}{39 \cdot 7} = \frac{1}{3 \cdot 7} = \frac{1}{21}$ 7. $\frac{7}{39} \cdot (\frac{1}{7} + \frac{6}{49}) = \frac{7}{39} \cdot (\frac{7}{49} + \frac{6}{49}) = \frac{7}{39} \cdot \frac{13}{49} = \frac{7 \cdot 13}{39 \cdot 49} = \frac{1 \cdot 1}{3 \cdot 7} = \frac{1}{21}$ 8. $\frac{9}{14} \cdot (\frac{17}{24} - \frac{5}{12}) = \frac{9}{14} \cdot (\frac{17 - 10}{24}) = \frac{9}{14} \cdot \frac{7}{24} = \frac{3 \cdot 1}{2 \cdot 8} = \frac{3}{16}$ 9. $\frac{3}{16} \cdot (\frac{4}{5} + \frac{8}{15}) = \frac{3}{16} \cdot (\frac{12 + 8}{15}) = \frac{3}{16} \cdot \frac{20}{15} = \frac{3}{16} \cdot \frac{4}{3} = \frac{1}{4}$ 10. $\frac{8}{35} \cdot (\frac{5}{6} + \frac{11}{12}) = \frac{8}{35} \cdot (\frac{10 + 11}{12}) = \frac{8}{35} \cdot \frac{21}{12} = \frac{2 \cdot 3}{5 \cdot 3} = \frac{2}{5} \cdot \frac{1}{2} = \frac{2}{10} = 0,4$ *Пересчет для точности:* 7. $\frac{7}{39} \cdot \frac{13}{49} = \frac{1}{21}$ 8. $\frac{9}{14} \cdot \frac{7}{24} = \frac{3}{16}$ 9. $\frac{3}{16} \cdot \frac{20}{15} = \frac{1}{4}$ 10. $\frac{8}{35} \cdot \frac{21}{12} = \frac{2}{5}$