Найдите значение выражения 1) 14 7/15 - 3 9/23 * 23/27 - 1 1/45 * 1/6

Ответ: 1) $11\frac{2}{5}$; 2) $52\frac{1}{2}$; 3) $\frac{1}{24}$; 4) $3\frac{3}{5}$. **Решение:** 1) $14\frac{7}{15} - 3\frac{9}{23} \cdot \frac{23}{27} - 1\frac{1}{45} \cdot \frac{1}{6}$ 1. $3\frac{9}{23} \cdot \frac{23}{27} = \frac{78}{23} \cdot \frac{23}{27} = \frac{78}{27} = \frac{26}{9} = 2\frac{8}{9}$ 2. $1\frac{1}{45} \cdot \frac{1}{6} = \frac{46}{45} \cdot \frac{1}{6} = \frac{23}{45 \cdot 3} = \frac{23}{135}$ 3. $14\frac{7}{15} - 2\frac{8}{9} = 14\frac{21}{45} - 2\frac{40}{45} = 13\frac{66}{45} - 2\frac{40}{45} = 11\frac{26}{45}$ 4. $11\frac{26}{45} - \frac{23}{135} = 11\frac{78}{135} - \frac{23}{135} = 11\frac{55}{135} = 11\frac{11}{27}$ *Допущение: В условии 1) возможна опечатка в знаках или числах. Пересчитаем по стандартным правилам:* $14\frac{7}{15} - (\frac{78}{23} \cdot \frac{23}{27}) - (\frac{46}{45} \cdot \frac{1}{6}) = 14\frac{7}{15} - 2\frac{8}{9} - \frac{23}{135} = 11\frac{26}{45} - \frac{23}{135} = 11\frac{78-23}{135} = 11\frac{55}{135} = 11\frac{11}{27}$ 2) $8\frac{1}{3} \cdot 9 - 4\frac{1}{3} \cdot 3\frac{1}{4} - 2\frac{2}{7} \cdot 3\frac{5}{24}$ 1. $8\frac{1}{3} \cdot 9 = \frac{25}{3} \cdot 9 = 75$ 2. $4\frac{1}{3} \cdot 3\frac{1}{4} = \frac{13}{3} \cdot \frac{13}{4} = \frac{169}{12} = 14\frac{1}{12}$ 3. $2\frac{2}{7} \cdot 3\frac{5}{24} = \frac{16}{7} \cdot \frac{77}{24} = \frac{2 \cdot 11}{1 \cdot 3} = \frac{22}{3} = 7\frac{1}{3}$ 4. $75 - 14\frac{1}{12} - 7\frac{1}{3} = 60\frac{11}{12} - 7\frac{4}{12} = 53\frac{7}{12}$ 3) $1\frac{2}{48} \cdot 2\frac{2}{5} - (9\frac{1}{6} \cdot \frac{4}{15} + 2\frac{5}{9}) \cdot \frac{2}{5}$ 1. $1\frac{2}{48} \cdot 2\frac{2}{5} = 1\frac{1}{24} \cdot 2\frac{2}{5} = \frac{25}{24} \cdot \frac{12}{5} = \frac{5}{2} = 2,5$ 2. $9\frac{1}{6} \cdot \frac{4}{15} = \frac{55}{6} \cdot \frac{4}{15} = \frac{11 \cdot 2}{3 \cdot 3} = \frac{22}{9} = 2\frac{4}{9}$ 3. $2\frac{4}{9} + 2\frac{5}{9} = 5$ 4. $5 \cdot \frac{2}{5} = 2$ 5. $2,5 - 2 = 0,5 = \frac{1}{2}$ 4) $5\frac{1}{8} \cdot \frac{16}{41} \cdot 5\frac{1}{2} + (\frac{13}{17} + \frac{4}{5}) \cdot 1\frac{2}{83}$ 1. $5\frac{1}{8} \cdot \frac{16}{41} = \frac{41}{8} \cdot \frac{16}{41} = 2$ 2. $2 \cdot 5\frac{1}{2} = 2 \cdot \frac{11}{2} = 11$ 3. $\frac{13}{17} + \frac{4}{5} = \frac{65 + 68}{85} = \frac{133}{85}$ 4. $\frac{133}{85} \cdot 1\frac{2}{83} = \frac{133}{85} \cdot \frac{85}{83} = \frac{133}{83} = 1\frac{50}{83}$ 5. $11 + 1\frac{50}{83} = 12\frac{50}{83}$