5.84 Вычислите, применив распределительное свойство умножения: a) 8 * 129 + 8 * 171; б) 4,8 * 3,7 – 4,8 * 2,7; в) 6,35 * 4,4 + 4,4 * 2,65; г) \(\frac{5}{7} \cdot \frac{3}{4} + \frac{3}{4} \cdot \frac{3}{7}\); д) \(1\frac{1}{4} \cdot \frac{4}{21} - 1\frac{1}{4} \cdot \frac{2}{7}\); e) \(14,2 \cdot \frac{5}{9} - 12,4 \cdot \frac{5}{9}\);

a) \(8 \cdot 129 + 8 \cdot 171 = 8 \cdot (129 + 171) = 8 \cdot 300 = 2400\) б) \(4.8 \cdot 3.7 - 4.8 \cdot 2.7 = 4.8 \cdot (3.7 - 2.7) = 4.8 \cdot 1 = 4.8\) в) \(6.35 \cdot 4.4 + 4.4 \cdot 2.65 = 4.4 \cdot (6.35 + 2.65) = 4.4 \cdot 9 = 39.6\) г) \(\frac{5}{7} \cdot \frac{3}{4} + \frac{3}{4} \cdot \frac{3}{7} = \frac{3}{4} \cdot (\frac{5}{7} + \frac{3}{7}) = \frac{3}{4} \cdot \frac{8}{7} = \frac{3 \cdot 8}{4 \cdot 7} = \frac{3 \cdot 2}{1 \cdot 7} = \frac{6}{7}\) д) \(1\frac{1}{4} \cdot \frac{4}{21} - 1\frac{1}{4} \cdot \frac{2}{7} = \frac{5}{4} \cdot \frac{4}{21} - \frac{5}{4} \cdot \frac{2}{7} = \frac{5}{4} \cdot (\frac{4}{21} - \frac{2}{7}) = \frac{5}{4} \cdot (\frac{4}{21} - \frac{6}{21}) = \frac{5}{4} \cdot (-\frac{2}{21}) = -\frac{5 \cdot 2}{4 \cdot 21} = -\frac{5 \cdot 1}{2 \cdot 21} = -\frac{5}{42}\) е) \(14.2 \cdot \frac{5}{9} - 12.4 \cdot \frac{5}{9} = \frac{5}{9} \cdot (14.2 - 12.4) = \frac{5}{9} \cdot 1.8 = \frac{5}{9} \cdot \frac{18}{10} = \frac{5 \cdot 18}{9 \cdot 10} = \frac{5 \cdot 2}{1 \cdot 10} = \frac{10}{10} = 1\)