Вариант № 1. 1. Сократите дроби \frac{30}{15}, \frac{12}{18}, \frac{24}{48}, \frac{28}{35}, \frac{35}{42}, \frac{13}{78}, \frac{7}{14}, \frac{75}{100} 2. Сократите: а) \frac{4}{5} : \frac{5}{6} б) \frac{12}{49} : \frac{14}{15} в) \frac{8}{33} : \frac{11}{4} г) \frac{2}{6} : \frac{9}{8} : \frac{12}{3}

1. Сократим дроби: $$\frac{30}{15} = \frac{15 \cdot 2}{15 \cdot 1} = \frac{2}{1} = 2$$ $$\frac{12}{18} = \frac{6 \cdot 2}{6 \cdot 3} = \frac{2}{3}$$ $$\frac{24}{48} = \frac{24 \cdot 1}{24 \cdot 2} = \frac{1}{2}$$ $$\frac{28}{35} = \frac{7 \cdot 4}{7 \cdot 5} = \frac{4}{5}$$ $$\frac{35}{42} = \frac{7 \cdot 5}{7 \cdot 6} = \frac{5}{6}$$ $$\frac{13}{78} = \frac{13 \cdot 1}{13 \cdot 6} = \frac{1}{6}$$ $$\frac{7}{14} = \frac{7 \cdot 1}{7 \cdot 2} = \frac{1}{2}$$ $$\frac{75}{100} = \frac{25 \cdot 3}{25 \cdot 4} = \frac{3}{4}$$ 2. Сократим выражения: а) $$\frac{4}{5} : \frac{5}{6} = \frac{4}{5} \cdot \frac{6}{5} = \frac{4 \cdot 6}{5 \cdot 5} = \frac{24}{25}$$ б) $$\frac{12}{49} : \frac{14}{15} = \frac{12}{49} \cdot \frac{15}{14} = \frac{6 \cdot 2}{7 \cdot 7} \cdot \frac{15}{7 \cdot 2} = \frac{6 \cdot 15}{7 \cdot 7 \cdot 7} = \frac{90}{343}$$ в) $$\frac{8}{33} : \frac{11}{4} = \frac{8}{33} \cdot \frac{4}{11} = \frac{8 \cdot 4}{33 \cdot 11} = \frac{32}{363}$$ г) $$\frac{2}{6} : \frac{9}{8} : \frac{12}{3} = \frac{2}{6} \cdot \frac{8}{9} \cdot \frac{3}{12} = \frac{1}{3} \cdot \frac{8}{9} \cdot \frac{1}{4} = \frac{8}{3 \cdot 9 \cdot 4} = \frac{2}{27 \cdot 1} = \frac{2}{27}$$