Выполните действия (13-16).

Решение:

13.

1. \( \frac{48}{4 \cdot 8} = \frac{48}{32} = \frac{3}{2} = 1.5 \)
2. \( \frac{2}{3} \cdot \frac{6}{7} \cdot \frac{1}{10} = \frac{2 \cdot 6 \cdot 1}{3 \cdot 7 \cdot 10} = \frac{12}{210} = \frac{2}{35} \)
3. \( \frac{1}{3} \cdot 90 \cdot \frac{1}{5} = \frac{90}{15} = 6 \)
4. \( \frac{6}{7} : \frac{7}{12} : \frac{5}{16} = \frac{6}{7} \cdot \frac{12}{7} \cdot \frac{16}{5} = \frac{6 \cdot 12 \cdot 16}{7 \cdot 7 \cdot 5} = \frac{1152}{245} \)

14.

1. \( \frac{2 \cdot 5 \cdot 9}{3 \cdot 6 \cdot 10} = \frac{90}{180} = \frac{1}{2} \)
2. \( \frac{3}{5} \cdot \frac{15}{17} \cdot \frac{4}{9} = \frac{3 \cdot 15 \cdot 4}{5 \cdot 17 \cdot 9} = \frac{180}{765} = \frac{4}{17} \)
3. \( 36 \cdot \frac{1}{12} \cdot \frac{1}{3} = \frac{36}{36} = 1 \)
4. \( \frac{7}{25} : \frac{3}{10} \cdot \frac{5}{6} = \frac{7}{25} \cdot \frac{10}{3} \cdot \frac{5}{6} = \frac{7 \cdot 10 \cdot 5}{25 \cdot 3 \cdot 6} = \frac{350}{450} = \frac{7}{9} \)

15.

1. \( \frac{9 \cdot 11 \cdot 21}{10 \cdot 10 \cdot 10} = \frac{2079}{1000} = 2.079 \)
2. \( \frac{6}{7} \cdot \frac{3}{5} \cdot \frac{5}{6} = \frac{6 \cdot 3 \cdot 5}{7 \cdot 5 \cdot 6} = \frac{90}{210} = \frac{3}{7} \)
3. \( \frac{1}{7} \cdot 42 \cdot \frac{1}{3} = \frac{42}{21} = 2 \)
4. \( \frac{2}{9} \cdot \frac{3}{7} : \frac{5}{2} = \frac{2}{9} \cdot \frac{3}{7} \cdot \frac{2}{5} = \frac{2 \cdot 3 \cdot 2}{9 \cdot 7 \cdot 5} = \frac{12}{315} = \frac{4}{105} \)

Ответ: 13. а) 1.5; б) \(\frac{2}{35}\); в) 6; г) \(\frac{1152}{245}\). 14. а) \(\frac{1}{2}\); б) \(\frac{4}{17}\); в) 1; г) \(\frac{7}{9}\). 15. а) 2.079; б) \(\frac{3}{7}\); в) 2; г) \(\frac{4}{105}\).