5.543 Найдите значение выражения: a) (\frac{5}{6}+\frac{4}{9})-\frac{5}{6} \cdot \frac{4}{9}; б) \frac{2}{8}+\frac{8}{8}:(3\frac{1}{3}-2\frac{3}{5}):\frac{7}{15};

Question

Вопрос:

Ответ:

Accepted Answer

a) $$\left(\frac{5}{6}+\frac{4}{9}\right)-\frac{5}{6} \cdot \frac{4}{9} = \left(\frac{5 \cdot 3}{6 \cdot 3}+\frac{4 \cdot 2}{9 \cdot 2}\right)-\frac{5 \cdot 4}{6 \cdot 9} = \left(\frac{15}{18}+\frac{8}{18}\right)-\frac{20}{54} = \frac{15+8}{18}-\frac{20}{54} = \frac{23}{18}-\frac{20}{54} = \frac{23 \cdot 3}{18 \cdot 3}-\frac{20}{54} = \frac{69}{54}-\frac{20}{54} = \frac{69-20}{54} = \frac{49}{54}$$.
Ответ:$$\frac{49}{54}$$
б) $$\frac{2}{8}+\frac{8}{8}:\left(3\frac{1}{3}-2\frac{3}{5}\right):\frac{7}{15} = \frac{2}{8} + 1 : \left(\frac{10}{3} - \frac{13}{5}\right) : \frac{7}{15} = \frac{1}{4} + 1 : \left(\frac{10 \cdot 5}{3 \cdot 5} - \frac{13 \cdot 3}{5 \cdot 3}\right) : \frac{7}{15} = \frac{1}{4} + 1 : \left(\frac{50}{15} - \frac{39}{15}\right) : \frac{7}{15} = \frac{1}{4} + 1 : \frac{50-39}{15} : \frac{7}{15} = \frac{1}{4} + 1 : \frac{11}{15} : \frac{7}{15} = \frac{1}{4} + \frac{15}{11} : \frac{7}{15} = \frac{1}{4} + \frac{15}{11} \cdot \frac{15}{7} = \frac{1}{4} + \frac{15 \cdot 15}{11 \cdot 7} = \frac{1}{4} + \frac{225}{77} = \frac{1 \cdot 77}{4 \cdot 77} + \frac{225 \cdot 4}{77 \cdot 4} = \frac{77}{308} + \frac{900}{308} = \frac{77 + 900}{308} = \frac{977}{308} = 3\frac{53}{308}$$.
Ответ: $$3\frac{53}{308}$$