1163. 1) [(6 1/6-1 1/24):(8 3/8+7,2)+418/623]:[(16/17-45/68)·17/20]

Выполним вычисления:

1. $$6\frac{1}{6} = \frac{37}{6}$$
2. $$1\frac{1}{24} = \frac{25}{24}$$
3. $$8\frac{3}{8} = \frac{67}{8}$$
4. $$\frac{37}{6} - \frac{25}{24} = \frac{37 \cdot 4 - 25}{24} = \frac{148 - 25}{24} = \frac{123}{24} = \frac{41}{8}$$
5. $$7,2 = \frac{72}{10} = \frac{36}{5}$$
6. $$\frac{67}{8} + \frac{36}{5} = \frac{67 \cdot 5 + 36 \cdot 8}{40} = \frac{335 + 288}{40} = \frac{623}{40}$$
7. $$\frac{41}{8} : \frac{623}{40} = \frac{41}{8} \cdot \frac{40}{623} = \frac{41}{1} \cdot \frac{5}{623} = \frac{205}{623}$$
8. $$\frac{205}{623} + \frac{418}{623} = \frac{623}{623} = 1$$
9. $$\frac{16}{17} - \frac{45}{68} = \frac{16 \cdot 4 - 45}{68} = \frac{64 - 45}{68} = \frac{19}{68}$$
10. $$\frac{19}{68} \cdot \frac{17}{20} = \frac{19}{4} \cdot \frac{1}{20} = \frac{19}{80}$$
11. $$1 : \frac{19}{80} = \frac{80}{19}$$

Ответ: 80/19