Упражнение 5.491 к § 37

1. \(\dfrac{7}{12} - \dfrac{5}{14} = \dfrac{49}{84} - \dfrac{30}{84} = \dfrac{19}{84}\).

2. \(\dfrac{13}{16} + \dfrac{1}{2} = \dfrac{13}{16} + \dfrac{8}{16} = \dfrac{21}{16}\).

3. \(\dfrac{19}{84} \cdot \dfrac{21}{16} = \dfrac{19 \cdot 1}{4 \cdot 16} = \dfrac{19}{64}\).

4. \(\dfrac{61}{64} - \dfrac{19}{64} = \dfrac{42}{64} = \dfrac{21}{32}\).

1. \(1 - \dfrac{11}{17} = \dfrac{6}{17}\).

2. \(\dfrac{3}{4} - \dfrac{5}{12} + \dfrac{11}{18} = \dfrac{27}{36} - \dfrac{15}{36} + \dfrac{22}{36} = \dfrac{34}{36} = \dfrac{17}{18}\).

3. \(\dfrac{6}{17} \cdot \dfrac{17}{18} = \dfrac{6}{18} = \dfrac{1}{3}\).

Общий знаменатель 60:

\(\dfrac{60 - 30 + 20 - 15 + 12 - 10}{60} = \dfrac{37}{60}\).

Сгруппируем дроби с одинаковыми знаменателями:

\(\left(\dfrac{1}{8} + \dfrac{3}{8}\right) + \left(\dfrac{1}{12} + \dfrac{5}{12}\right) + \left(\dfrac{1}{16} + \dfrac{7}{16}\right) + \left(\dfrac{1}{20} + \dfrac{9}{20}\right) = \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2} = 2\).