Solve the following math problems, showing your work.

Решение:

Столбец Г:

• \( \frac{4}{5} \cdot 10 = \frac{4 \cdot 10}{5} = \frac{40}{5} = 8 \)
• \( \frac{5}{1} : \frac{1}{4} = \frac{5}{1} \cdot \frac{4}{1} = 20 \)
• \( \frac{6}{9} : \frac{10}{3} = \frac{6}{9} \cdot \frac{3}{10} = \frac{18}{90} = \frac{1}{5} \)
• \( \frac{3}{5} \cdot \frac{5}{7} = \frac{3 \cdot 5}{5 \cdot 7} = \frac{15}{35} = \frac{3}{7} \)
• \( 1 \frac{3}{8} : \frac{1}{2} = \frac{11}{8} \cdot \frac{2}{1} = \frac{22}{8} = \frac{11}{4} \)
• \( \frac{4}{7} : \frac{7}{8} = \frac{4}{7} \cdot \frac{8}{7} = \frac{32}{49} \)
• \( \frac{12}{13} : 6 = \frac{12}{13} \cdot \frac{1}{6} = \frac{12}{78} = \frac{2}{13} \)
• \( \frac{3}{4} \cdot \frac{8}{9} = \frac{3 \cdot 8}{4 \cdot 9} = \frac{24}{36} = \frac{2}{3} \)
• \( 7 \frac{1}{12} : 3 = \frac{85}{12} \cdot \frac{1}{3} = \frac{85}{36} \)
• \( \frac{3}{8} : \frac{4}{4} = \frac{3}{8} : 1 = \frac{3}{8} \)
• \( 6 \cdot \frac{2}{3} = \frac{6 \cdot 2}{3} = \frac{12}{3} = 4 \)
• \( \frac{3}{5} \cdot \frac{1}{9} = \frac{3 \cdot 1}{5 \cdot 9} = \frac{3}{45} = \frac{1}{15} \)
• \( 5 \frac{2}{6} : 3 = \frac{32}{6} \cdot \frac{1}{3} = \frac{32}{18} = \frac{16}{9} \)
• \( \frac{3}{7} \cdot 7 = 3 \)

Столбец Д:

• \( \frac{4}{5} : 20 = \frac{4}{5} \cdot \frac{1}{20} = \frac{4}{100} = \frac{1}{25} \)
• \( 42 \frac{6}{7} = \frac{294+6}{7} = \frac{300}{7} \)
• \( 2,4 : \frac{3}{8} = \frac{24}{10} \cdot \frac{8}{3} = \frac{8}{10} \cdot \frac{8}{1} = \frac{64}{10} = 6,4 \)
• \( \frac{4}{9} \cdot 7 = \frac{28}{9} \)
• \( 2 \frac{1}{4} \cdot \frac{4}{9} = \frac{9}{4} \cdot \frac{4}{9} = 1 \)
• \( \frac{8}{2} : 5 = 4 : 5 = \frac{4}{5} \)
• \( 5 \cdot \frac{1}{7} = \frac{5}{7} \)
• \( \frac{4}{25} : \frac{1}{5} = \frac{4}{25} \cdot \frac{5}{1} = \frac{20}{25} = \frac{4}{5} \)
• \( \frac{3}{2} \cdot \frac{4}{9} = \frac{12}{18} = \frac{2}{3} \)
• \( 1 \frac{1}{2} : 0,3 = \frac{3}{2} : \frac{3}{10} = \frac{3}{2} \cdot \frac{10}{3} = 5 \)
• \( 20 : \frac{5}{7} = 20 \cdot \frac{7}{5} = 4 \cdot 7 = 28 \)
• \( \frac{3}{4} : \frac{7}{8} = \frac{3}{4} \cdot \frac{8}{7} = \frac{24}{28} = \frac{6}{7} \)
• \( 3 \frac{1}{4} \cdot \frac{1}{3} = \frac{13}{4} \cdot \frac{1}{3} = \frac{13}{12} \)
• \( 1,5 : \frac{3}{5} = \frac{3}{2} \cdot \frac{5}{3} = \frac{5}{2} = 2,5 \)

Столбец Е:

• \( \frac{4}{20} = \frac{1}{5} \)
• \( 42 \frac{6}{7} \)
• \( 2,4 : \frac{3}{8} \)
• \( \frac{8}{15} : \frac{2}{5} = \frac{8}{15} \cdot \frac{5}{2} = \frac{40}{30} = \frac{4}{3} \)
• \( 5 \cdot \frac{1}{7} = \frac{5}{7} \)
• \( \frac{2}{7} \cdot \frac{1}{5} = \frac{2}{35} \)
• \( 1 \frac{1}{5} : \frac{1}{5} = \frac{6}{5} \cdot \frac{5}{1} = 6 \)
• \( \frac{3}{2} \cdot \frac{4}{9} = \frac{12}{18} = \frac{2}{3} \)
• \( 1 \frac{1}{2} : 0,7 = \frac{3}{2} : \frac{7}{10} = \frac{3}{2} \cdot \frac{10}{7} = \frac{30}{14} = \frac{15}{7} \)
• \( 2 \frac{1}{7} \cdot \frac{2}{3} = \frac{15}{7} \cdot \frac{2}{3} = \frac{30}{21} = \frac{10}{7} \)
• \( \frac{7}{8} : \frac{1}{16} = \frac{7}{8} \cdot \frac{16}{1} = 14 \)
• \( 3 \frac{1}{3} \cdot \frac{1}{6} = \frac{10}{3} \cdot \frac{1}{6} = \frac{10}{18} = \frac{5}{9} \)
• \( 5 \frac{1}{7} : 3 = \frac{36}{7} \cdot \frac{1}{3} = \frac{12}{7} \)
• \( \frac{3}{8} \cdot \frac{3}{5} = \frac{9}{40} \)
• \( 30 \cdot \frac{5}{6} = 5 \cdot 5 = 25 \)

Ответ: Выполнены вычисления в столбцах Г, Д, Е.