№ 1 Найдите значение выражения: а) 8-3-; б) 2-+3-; в) -; г) 2-1-; д) -; e) 4-:2-.

Решение:

a) $$8-3\frac{6}{7} = \frac{8 \cdot 7 - 3 \cdot 7 - 6}{7} = \frac{56 - 21 - 6}{7} = \frac{29}{7} = 4\frac{1}{7}$$

б) $$2\frac{1}{8}+3\frac{5}{12} = \frac{2 \cdot 8 + 1}{8} + \frac{3 \cdot 12 + 5}{12} = \frac{17}{8} + \frac{41}{12} = \frac{17 \cdot 3 + 41 \cdot 2}{24} = \frac{51 + 82}{24} = \frac{133}{24} = 5\frac{13}{24}$$

в) $$\frac{6}{25}:\frac{5}{18} = \frac{6}{25} \cdot \frac{18}{5} = \frac{6 \cdot 18}{25 \cdot 5} = \frac{108}{125}$$

г) $$2\frac{1}{10} \cdot 1\frac{1}{14} = \frac{2 \cdot 10 + 1}{10} \cdot \frac{1 \cdot 14 + 1}{14} = \frac{21}{10} \cdot \frac{15}{14} = \frac{21 \cdot 15}{10 \cdot 14} = \frac{3 \cdot 3}{2 \cdot 2} = \frac{9}{4} = 2\frac{1}{4}$$

д) $$\frac{5}{9}:\frac{10}{27} = \frac{5}{9} \cdot \frac{27}{10} = \frac{5 \cdot 27}{9 \cdot 10} = \frac{1 \cdot 3}{1 \cdot 2} = \frac{3}{2} = 1\frac{1}{2}$$

e) $$4\frac{4}{9}:2\frac{2}{3} = \frac{4 \cdot 9 + 4}{9} : \frac{2 \cdot 3 + 2}{3} = \frac{40}{9} : \frac{8}{3} = \frac{40}{9} \cdot \frac{3}{8} = \frac{40 \cdot 3}{9 \cdot 8} = \frac{5 \cdot 1}{3 \cdot 1} = \frac{5}{3} = 1\frac{2}{3}$$

Ответ: a) $$4\frac{1}{7}$$, б) $$5\frac{13}{24}$$, в) $$\frac{108}{125}$$, г) $$2\frac{1}{4}$$, д) $$1\frac{1}{2}$$, e) $$1\frac{2}{3}$$