1. \(2\frac{4}{37} - 1\frac{5}{37}\) 2. \(7\frac{8}{41} - \frac{9}{41}\) 3. \(10\frac{12}{55} - 5\frac{25}{55}\) 4. \(1\frac{9}{20} - \frac{19}{20}\) 5. \(6\frac{2}{7} - 1\frac{5}{7}\)

Решение:

1. \(2\frac{4}{37} - 1\frac{5}{37} = \frac{2 \cdot 37 + 4}{37} - \frac{1 \cdot 37 + 5}{37} = \frac{74+4}{37} - \frac{37+5}{37} = \frac{78}{37} - \frac{42}{37} = \frac{78-42}{37} = \frac{36}{37}\)
2. \(7\frac{8}{41} - \frac{9}{41} = \frac{7 \cdot 41 + 8}{41} - \frac{9}{41} = \frac{287+8}{41} - \frac{9}{41} = \frac{295}{41} - \frac{9}{41} = \frac{295-9}{41} = \frac{286}{41}\)
3. \(10\frac{12}{55} - 5\frac{25}{55} = \frac{10 \cdot 55 + 12}{55} - \frac{5 \cdot 55 + 25}{55} = \frac{550+12}{55} - \frac{275+25}{55} = \frac{562}{55} - \frac{300}{55} = \frac{562-300}{55} = \frac{262}{55}\)
4. \(1\frac{9}{20} - \frac{19}{20} = \frac{1 \cdot 20 + 9}{20} - \frac{19}{20} = \frac{20+9}{20} - \frac{19}{20} = \frac{29}{20} - \frac{19}{20} = \frac{29-19}{20} = \frac{10}{20} = \frac{1}{2}\)
5. \(6\frac{2}{7} - 1\frac{5}{7} = \frac{6 \cdot 7 + 2}{7} - \frac{1 \cdot 7 + 5}{7} = \frac{42+2}{7} - \frac{7+5}{7} = \frac{44}{7} - \frac{12}{7} = \frac{44-12}{7} = \frac{32}{7}\)

Ответ: 1. \(\frac{36}{37}\) 2. \(\frac{286}{41}\) 3. \(\frac{262}{55}\) 4. \(\frac{1}{2}\) 5. \(\frac{32}{7}\)