Сократите дроби, используя признаки делимости: 1) \(\frac{14}{21}\), \(\frac{18}{24}\), \(\frac{24}{15}\), \(\frac{25}{35}\), \(\frac{81}{108}\); 3) \(\frac{30}{42}\), \(\frac{33}{39}\), \(\frac{45}{51}\), \(\frac{36}{60}\), \(\frac{50}{100}\); 2) \(\frac{12}{51}\), \(\frac{4}{26}\), \(\frac{10}{90}\), \(\frac{35}{45}\), \(\frac{15}{93}\); 4) \(\frac{15}{95}\), \(\frac{33}{48}\), \(\frac{63}{108}\), \(\frac{34}{82}\), \(\frac{105}{200}\).

Ответ:

1. • \(\frac{14}{21} = \frac{2 \cdot 7}{3 \cdot 7} = \frac{2}{3}\)
   • \(\frac{18}{24} = \frac{3 \cdot 6}{4 \cdot 6} = \frac{3}{4}\)
   • \(\frac{24}{15} = \frac{8 \cdot 3}{5 \cdot 3} = \frac{8}{5}\)
   • \(\frac{25}{35} = \frac{5 \cdot 5}{7 \cdot 5} = \frac{5}{7}\)
   • \(\frac{81}{108} = \frac{9 \cdot 9}{12 \cdot 9} = \frac{9}{12} = \frac{3 \cdot 3}{4 \cdot 3} = \frac{3}{4}\)
2. • \(\frac{12}{51} = \frac{4 \cdot 3}{17 \cdot 3} = \frac{4}{17}\)
   • \(\frac{4}{26} = \frac{2 \cdot 2}{13 \cdot 2} = \frac{2}{13}\)
   • \(\frac{10}{90} = \frac{1 \cdot 10}{9 \cdot 10} = \frac{1}{9}\)
   • \(\frac{35}{45} = \frac{7 \cdot 5}{9 \cdot 5} = \frac{7}{9}\)
   • \(\frac{15}{93} = \frac{5 \cdot 3}{31 \cdot 3} = \frac{5}{31}\)
3. • \(\frac{30}{42} = \frac{5 \cdot 6}{7 \cdot 6} = \frac{5}{7}\)
   • \(\frac{33}{39} = \frac{11 \cdot 3}{13 \cdot 3} = \frac{11}{13}\)
   • \(\frac{45}{51} = \frac{15 \cdot 3}{17 \cdot 3} = \frac{15}{17}\)
   • \(\frac{36}{60} = \frac{6 \cdot 6}{10 \cdot 6} = \frac{6}{10} = \frac{3 \cdot 2}{5 \cdot 2} = \frac{3}{5}\)
   • \(\frac{50}{100} = \frac{1 \cdot 50}{2 \cdot 50} = \frac{1}{2}\)
4. • \(\frac{15}{95} = \frac{3 \cdot 5}{19 \cdot 5} = \frac{3}{19}\)
   • \(\frac{33}{48} = \frac{11 \cdot 3}{16 \cdot 3} = \frac{11}{16}\)
   • \(\frac{63}{108} = \frac{7 \cdot 9}{12 \cdot 9} = \frac{7}{12}\)
   • \(\frac{34}{82} = \frac{17 \cdot 2}{41 \cdot 2} = \frac{17}{41}\)
   • \(\frac{105}{200} = \frac{21 \cdot 5}{40 \cdot 5} = \frac{21}{40}\)

Ответ: 1) \(\frac{2}{3}\), \(\frac{3}{4}\), \(\frac{8}{5}\), \(\frac{5}{7}\), \(\frac{3}{4}\); 2) \(\frac{4}{17}\), \(\frac{2}{13}\), \(\frac{1}{9}\), \(\frac{7}{9}\), \(\frac{5}{31}\); 3) \(\frac{5}{7}\), \(\frac{11}{13}\), \(\frac{15}{17}\), \(\frac{3}{5}\), \(\frac{1}{2}\); 4) \(\frac{3}{19}\), \(\frac{11}{16}\), \(\frac{7}{12}\), \(\frac{17}{41}\), \(\frac{21}{40}\).