№7. Найди значение выражений 1) $$2\frac{1}{2}+1\frac{3}{4} \cdot 2$$ 2) $$5\frac{1}{3}-2\frac{1}{2}:1\frac{1}{4}$$ 3) $$3\frac{2}{5} \cdot 1\frac{1}{2}+4\frac{1}{10}$$ 4) $$6\frac{3}{4}:2\frac{1}{4}-1\frac{1}{2}$$ 5) $$1\frac{5}{6}+2\frac{1}{3} \cdot 3\frac{1}{2}$$

Решение:

1. $$2\frac{1}{2}+1\frac{3}{4} \cdot 2$$
   1. $$1\frac{3}{4} \cdot 2 = \frac{7}{4} \cdot 2 = \frac{7 \cdot 2}{4} = \frac{14}{4} = \frac{7}{2} = 3\frac{1}{2}$$
   2. $$2\frac{1}{2} + 3\frac{1}{2} = 2 + \frac{1}{2} + 3 + \frac{1}{2} = 5 + \frac{1}{2} + \frac{1}{2} = 5 + 1 = 6$$

   Ответ: 6

2. $$5\frac{1}{3}-2\frac{1}{2}:1\frac{1}{4}$$
   1. $$2\frac{1}{2}:1\frac{1}{4} = \frac{5}{2}:\frac{5}{4} = \frac{5}{2} \cdot \frac{4}{5} = \frac{5 \cdot 4}{2 \cdot 5} = \frac{4}{2} = 2$$
   2. $$5\frac{1}{3} - 2 = 5 + \frac{1}{3} - 2 = 3\frac{1}{3}$$

   Ответ: $$3\frac{1}{3}$$

3. $$3\frac{2}{5} \cdot 1\frac{1}{2}+4\frac{1}{10}$$
   1. $$3\frac{2}{5} \cdot 1\frac{1}{2} = \frac{17}{5} \cdot \frac{3}{2} = \frac{17 \cdot 3}{5 \cdot 2} = \frac{51}{10} = 5\frac{1}{10}$$
   2. $$5\frac{1}{10} + 4\frac{1}{10} = 5 + \frac{1}{10} + 4 + \frac{1}{10} = 9 + \frac{1}{10} + \frac{1}{10} = 9 + \frac{2}{10} = 9 + \frac{1}{5} = 9\frac{1}{5}$$

   Ответ: $$9\frac{1}{5}$$

4. $$6\frac{3}{4}:2\frac{1}{4}-1\frac{1}{2}$$
   1. $$6\frac{3}{4}:2\frac{1}{4} = \frac{27}{4}:\frac{9}{4} = \frac{27}{4} \cdot \frac{4}{9} = \frac{27 \cdot 4}{4 \cdot 9} = \frac{27}{9} = 3$$
   2. $$3 - 1\frac{1}{2} = 3 - 1 - \frac{1}{2} = 2 - \frac{1}{2} = 1\frac{1}{2}$$

   Ответ: $$1\frac{1}{2}$$

5. $$1\frac{5}{6}+2\frac{1}{3} \cdot 3\frac{1}{2}$$
   1. $$2\frac{1}{3} \cdot 3\frac{1}{2} = \frac{7}{3} \cdot \frac{7}{2} = \frac{7 \cdot 7}{3 \cdot 2} = \frac{49}{6} = 8\frac{1}{6}$$
   2. $$1\frac{5}{6} + 8\frac{1}{6} = 1 + \frac{5}{6} + 8 + \frac{1}{6} = 9 + \frac{5}{6} + \frac{1}{6} = 9 + \frac{6}{6} = 9 + 1 = 10$$

   Ответ: 10