65. Найдите значение выражения: 1) 8 1/3 · 9 - 2 2/3 · 3 1/4 - 4 4/7 · 3 5/24; 2) 1 1/48 · 2 2/5 - (9 1/6 · 4/15 + 2 5/9) · 1/4.

65. Найдите значение выражения:

1) $$8 \frac{1}{3} \cdot 9 - 2 \frac{2}{3} \cdot 3 \frac{1}{4} - 4 \frac{4}{7} \cdot 3 \frac{5}{24};$$

• $$8 \frac{1}{3} = \frac{8 \cdot 3 + 1}{3} = \frac{24 + 1}{3} = \frac{25}{3}$$
• $$2 \frac{2}{3} = \frac{2 \cdot 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}$$
• $$3 \frac{1}{4} = \frac{3 \cdot 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}$$
• $$4 \frac{4}{7} = \frac{4 \cdot 7 + 4}{7} = \frac{28 + 4}{7} = \frac{32}{7}$$
• $$3 \frac{5}{24} = \frac{3 \cdot 24 + 5}{24} = \frac{72 + 5}{24} = \frac{77}{24}$$

$$\frac{25}{3} \cdot 9 - \frac{8}{3} \cdot \frac{13}{4} - \frac{32}{7} \cdot \frac{77}{24} = 25 \cdot 3 - \frac{2}{3} \cdot 13 - \frac{4}{1} \cdot \frac{11}{3} = 75 - \frac{26}{3} - \frac{44}{3} = 75 - \frac{26 + 44}{3} = 75 - \frac{70}{3} = 75 - 23 \frac{1}{3} = 51 \frac{2}{3}$$

Ответ: $$51 \frac{2}{3}$$

2) $$1 \frac{1}{48} \cdot 2 \frac{2}{5} - (9 \frac{1}{6} \cdot \frac{4}{15} + 2 \frac{5}{9}) \cdot \frac{1}{4};$$

• $$1 \frac{1}{48} = \frac{1 \cdot 48 + 1}{48} = \frac{48 + 1}{48} = \frac{49}{48}$$
• $$2 \frac{2}{5} = \frac{2 \cdot 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}$$
• $$9 \frac{1}{6} = \frac{9 \cdot 6 + 1}{6} = \frac{54 + 1}{6} = \frac{55}{6}$$
• $$2 \frac{5}{9} = \frac{2 \cdot 9 + 5}{9} = \frac{18 + 5}{9} = \frac{23}{9}$$

$$\frac{49}{48} \cdot \frac{12}{5} - (\frac{55}{6} \cdot \frac{4}{15} + \frac{23}{9}) \cdot \frac{1}{4} = \frac{49}{4 \cdot 5} - (\frac{11}{3} \cdot \frac{2}{3} + \frac{23}{9}) \cdot \frac{1}{4} = \frac{49}{20} - (\frac{22}{9} + \frac{23}{9}) \cdot \frac{1}{4} = \frac{49}{20} - \frac{45}{9} \cdot \frac{1}{4} = \frac{49}{20} - 5 \cdot \frac{1}{4} = \frac{49}{20} - \frac{5}{4} = \frac{49}{20} - \frac{5 \cdot 5}{4 \cdot 5} = \frac{49}{20} - \frac{25}{20} = \frac{24}{20} = \frac{6}{5} = 1 \frac{1}{5}$$

Ответ: $$1 \frac{1}{5}$$