Выполните действие и сократите результат: 1) $\frac{7}{15} + \frac{5}{15}$

1) $$\frac{7}{15} + \frac{5}{15} = \frac{7+5}{15} = \frac{12}{15} = \frac{12 \div 3}{15 \div 3} = \frac{4}{5}$$ **Ответ:** $\frac{4}{5}$ 2) $$\frac{43}{54} - \frac{17}{54} = \frac{43-17}{54} = \frac{26}{54} = \frac{26 \div 2}{54 \div 2} = \frac{13}{27}$$ **Ответ:** $\frac{13}{27}$ 3) $$4\frac{11}{56} + 5\frac{29}{56} = (4+5) + (\frac{11}{56} + \frac{29}{56}) = 9 + \frac{11+29}{56} = 9 + \frac{40}{56} = 9 + \frac{40 \div 8}{56 \div 8} = 9 + \frac{5}{7} = 9\frac{5}{7}$$ **Ответ:** $9\frac{5}{7}$ 4) $$18\frac{59}{84} - 9\frac{23}{84} = (18-9) + (\frac{59}{84} - \frac{23}{84}) = 9 + \frac{59-23}{84} = 9 + \frac{36}{84} = 9 + \frac{36 \div 12}{84 \div 12} = 9 + \frac{3}{7} = 9\frac{3}{7}$$ **Ответ:** $9\frac{3}{7}$ 40. Сократите: 1) $$\frac{17 \cdot 5}{20 \cdot 34} = \frac{17 \cdot 5}{(4 \cdot 5) \cdot (2 \cdot 17)} = \frac{\cancel{17} \cdot \cancel{5}}{4 \cdot \cancel{5} \cdot 2 \cdot \cancel{17}} = \frac{1}{4 \cdot 2} = \frac{1}{8}$$ **Ответ:** $\frac{1}{8}$ 2) $$\frac{36 \cdot 9}{15 \cdot 30} = \frac{(12 \cdot 3) \cdot 9}{(5 \cdot 3) \cdot (10 \cdot 3)} = \frac{12 \cdot \cancel{3} \cdot 9}{5 \cdot \cancel{3} \cdot 10 \cdot 3} = \frac{12 \cdot 9}{5 \cdot 10 \cdot 3} = \frac{(4 \cdot \cancel{3}) \cdot \cancel{9}}{5 \cdot 10 \cdot \cancel{3}} = \frac{4 \cdot 9}{5 \cdot 10} = \frac{36}{50} = \frac{18}{25}$$ **Ответ:** $\frac{18}{25}$ 3) $$\frac{7 \cdot 6 \cdot 11}{33 \cdot 21 \cdot 30} = \frac{7 \cdot 6 \cdot 11}{(3 \cdot 11) \cdot (3 \cdot 7) \cdot (5 \cdot 6)} = \frac{\cancel{7} \cdot \cancel{6} \cdot \cancel{11}}{3 \cdot \cancel{11} \cdot 3 \cdot \cancel{7} \cdot 5 \cdot \cancel{6}} = \frac{1}{3 \cdot 3 \cdot 5} = \frac{1}{45}$$ **Ответ:** $\frac{1}{45}$ 4) $$\frac{19 \cdot 9 + 19 \cdot 6}{19 \cdot 70 - 19 \cdot 25} = \frac{19 \cdot (9+6)}{19 \cdot (70-25)} = \frac{\cancel{19} \cdot 15}{\cancel{19} \cdot 45} = \frac{15}{45} = \frac{1}{3}$$ **Ответ:** $\frac{1}{3}$