2. Вычислите: a) 4 1/3 * 3 1/4 b) 1 2/13 : 1 4/11 c) 2 2/3 * 1 1/8 : 6 2/3

Решение:

1. а)\[ 4 \frac{1}{3} \times 3 \frac{1}{4} = \frac{4 \times 3 + 1}{3} \times \frac{3 \times 3 + 1}{4} = \frac{13}{3} \times \frac{10}{4} = \frac{13 \times 10}{3 \times 4} = \frac{130}{12} = \frac{65}{6} = 10 \frac{5}{6} \]
2. б)\[ 1 \frac{2}{13} : 1 \frac{4}{11} = \frac{1 \times 13 + 2}{13} : \frac{1 \times 11 + 4}{11} = \frac{15}{13} : \frac{15}{11} = \frac{15}{13} \times \frac{11}{15} = \frac{15 \times 11}{13 \times 15} = \frac{11}{13} \]
3. в)\[ 2 \frac{2}{3} \times 1 \frac{1}{8} : 6 \frac{2}{3} = \frac{2 \times 3 + 2}{3} \times \frac{1 \times 8 + 1}{8} : \frac{6 \times 3 + 2}{3} = \frac{8}{3} \times \frac{9}{8} : \frac{20}{3} \]Сначала умножаем:\[ \frac{8}{3} \times \frac{9}{8} = \frac{8 \times 9}{3 \times 8} = \frac{9}{3} = 3 \]Теперь делим:\[ 3 : \frac{20}{3} = 3 \times \frac{3}{20} = \frac{3 \times 3}{20} = \frac{9}{20} \]

Ответ: а) 10 5/6; б) 11/13; в) 9/20