Задание 1. Найдите значение выражения: a) 3 \frac{14}{45} \cdot 15; б) 6 \cdot (5 \frac{2}{3} + 7 \frac{1}{2}); в) 6 \frac{5}{14} \cdot \frac{14}{27} - \frac{14}{27} \cdot 3 \frac{5}{14}

Задание 1

а) 3 \frac{14}{45} \cdot 15 = \frac{3 \cdot 45 + 14}{45} \cdot 15 = \frac{135 + 14}{45} \cdot 15 = \frac{149}{45} \cdot 15 = \frac{149 \cdot 15}{45} = \frac{149 \cdot 1}{3} = \frac{149}{3} = 49 \frac{2}{3}

б) 6 \cdot (5 \frac{2}{3} + 7 \frac{1}{2}) = 6 \cdot (\frac{5 \cdot 3 + 2}{3} + \frac{7 \cdot 2 + 1}{2}) = 6 \cdot (\frac{15 + 2}{3} + \frac{14 + 1}{2}) = 6 \cdot (\frac{17}{3} + \frac{15}{2}) = 6 \cdot (\frac{17 \cdot 2 + 15 \cdot 3}{6}) = 6 \cdot (\frac{34 + 45}{6}) = 6 \cdot \frac{79}{6} = 79

в) 6 \frac{5}{14} \cdot \frac{14}{27} - \frac{14}{27} \cdot 3 \frac{5}{14} = \frac{6 \cdot 14 + 5}{14} \cdot \frac{14}{27} - \frac{14}{27} \cdot \frac{3 \cdot 14 + 5}{14} = \frac{84 + 5}{14} \cdot \frac{14}{27} - \frac{14}{27} \cdot \frac{42 + 5}{14} = \frac{89}{14} \cdot \frac{14}{27} - \frac{14}{27} \cdot \frac{47}{14} = \frac{89 \cdot 14}{14 \cdot 27} - \frac{14 \cdot 47}{27 \cdot 14} = \frac{89}{27} - \frac{47}{27} = \frac{89 - 47}{27} = \frac{42}{27} = \frac{14}{9} = 1 \frac{5}{9}