№6*. Выполни действие: 1 15 7 5 1 9 38:16-4(812-28):26-120 (25+21).1:112:(8+12)

Выполним действие по шагам:

1. $$3 \frac{1}{8} : 16 = \frac{3 \cdot 8 + 1}{8} : 16 = \frac{25}{8} \cdot \frac{1}{16} = \frac{25}{128}$$.
2. $$8 \frac{1}{12} - 2 \frac{5}{8} = \frac{8 \cdot 12 + 1}{12} - \frac{2 \cdot 8 + 5}{8} = \frac{97}{12} - \frac{21}{8} = \frac{97 \cdot 2}{12 \cdot 2} - \frac{21 \cdot 3}{8 \cdot 3} = \frac{194}{24} - \frac{63}{24} = \frac{131}{24}$$.
3. $$\frac{131}{24} \cdot \frac{7}{15} = \frac{131 \cdot 7}{24 \cdot 15} = \frac{917}{360}$$.
4. $$\frac{917}{360} : \frac{2}{6} = \frac{917}{360} \cdot \frac{6}{2} = \frac{917 \cdot 6}{360 \cdot 2} = \frac{5502}{720} = \frac{917}{120}$$.
5. $$\frac{25}{128} - 4 \cdot \frac{917}{120} = \frac{25}{128} - \frac{917}{30} = \frac{25 \cdot 15}{128 \cdot 15} - \frac{917 \cdot 64}{30 \cdot 64} = \frac{375}{1920} - \frac{58688}{1920} = \frac{-58313}{1920}$$.
6. $$\frac{-58313}{1920} - 1 = \frac{-58313}{1920} - \frac{1920}{1920} = \frac{-60233}{1920}$$.
7. $$2 \frac{5}{7} + 21 = \frac{2 \cdot 7 + 5}{7} + 21 = \frac{19}{7} + 21 = \frac{19}{7} + \frac{21 \cdot 7}{7} = \frac{19 + 147}{7} = \frac{166}{7}$$.
8. $$\frac{166}{7} \cdot 1 = \frac{166}{7}$$.
9. $$1 \frac{3}{12} = \frac{1 \cdot 12 + 3}{12} = \frac{15}{12} = \frac{5}{4}$$.
10. $$8 + 12 = 20$$.
11. $$\frac{5}{4} : 20 = \frac{5}{4} \cdot \frac{1}{20} = \frac{5}{80} = \frac{1}{16}$$.
12. $$\frac{166}{7} : \frac{1}{16} = \frac{166}{7} \cdot 16 = \frac{166 \cdot 16}{7} = \frac{2656}{7}$$.
13. $$\frac{-60233}{1920} : \frac{2656}{7} = \frac{-60233}{1920} \cdot \frac{7}{2656} = \frac{-60233 \cdot 7}{1920 \cdot 2656} = \frac{-421631}{5099520}$$.
14. Сократим дробь. Разделим числитель и знаменатель на 1: $$\frac{-421631}{5099520}$$.

Ответ: $$\frac{-421631}{5099520}$$