1. Найдите значение выражения: a)(2/3 + 4/7) * 42; б) (2 1/4 - 1 1/2) * 8; в) 4 1/6 * 3 2/7 + 2 5/7 * 4 1/6.

Решение:

а) \( \left( \frac{2}{3} + \frac{4}{7} \right) \cdot 42 = \left( \frac{2 \cdot 7 + 4 \cdot 3}{3 \cdot 7} \right) \cdot 42 = \left( \frac{14 + 12}{21} \right) \cdot 42 = \frac{26}{21} \cdot 42 = 26 \cdot \frac{42}{21} = 26 \cdot 2 = 52 \)

б) \( \left( 2\frac{1}{4} - 1\frac{1}{2} \right) \cdot 8 = \left( \frac{2 \cdot 4 + 1}{4} - \frac{1 \cdot 2 + 1}{2} \right) \cdot 8 = \left( \frac{9}{4} - \frac{3}{2} \right) \cdot 8 = \left( \frac{9}{4} - \frac{3 \cdot 2}{2 \cdot 2} \right) \cdot 8 = \left( \frac{9}{4} - \frac{6}{4} \right) \cdot 8 = \frac{3}{4} \cdot 8 = 3 \cdot \frac{8}{4} = 3 \cdot 2 = 6 \)

в) \( 4\frac{1}{6} \cdot 3\frac{2}{7} + 2\frac{5}{7} \cdot 4\frac{1}{6} \)

Вынесем общий множитель \( 4\frac{1}{6} \) за скобки:

\[ 4\(\frac{1}{6}\) \(\cdot\) \(\left\)\(3\frac{2}{7} + 2\frac{5}{7} \right\) = \(\frac{4 \cdot 6 + 1}{6}\) \(\cdot\) \(\left\)\(\frac{3 \cdot 7 + 2}{7} + \frac{2 \cdot 7 + 5}{7} \right\) = \(\frac{25}{6}\) \(\cdot\) \(\left\)\(\frac{23}{7} + \frac{19}{7} \right\) = \(\frac{25}{6}\) \(\cdot\) \(\left\)\(\frac{23 + 19}{7} \right\) = \(\frac{25}{6}\) \(\cdot\) \(\frac{42}{7}\) = \(\frac{25}{6}\) \(\cdot\) 6 = 25 \)

Ответ: а) 52; б) 6; в) 25.