Сократите дробь на наибольший общий делитель ее числителя нателя: 1) \(\frac{42}{24}\), \(\frac{35}{77}\), \(\frac{48}{60}\), \(\frac{72}{96}\); 3) \(\frac{72}{90}\), \(\frac{60}{105}\), \(\frac{45}{150}\), \(\frac{84}{120}\); 2) \(\frac{10}{100}\), \(\frac{400}{1000}\), \(\frac{600}{800}\), \(\frac{800}{1000}\); 4) \(\frac{56}{70}\), \(\frac{36}{90}\), \(\frac{66}{110}\), \(\frac{96}{160}\).

Ответ:

1. • \(\frac{42}{24}\): НОД(42, 24) = 6, \(\frac{42:6}{24:6} = \frac{7}{4}\)
   • \(\frac{35}{77}\): НОД(35, 77) = 7, \(\frac{35:7}{77:7} = \frac{5}{11}\)
   • \(\frac{48}{60}\): НОД(48, 60) = 12, \(\frac{48:12}{60:12} = \frac{4}{5}\)
   • \(\frac{72}{96}\): НОД(72, 96) = 24, \(\frac{72:24}{96:24} = \frac{3}{4}\)
2. • \(\frac{10}{100}\): НОД(10, 100) = 10, \(\frac{10:10}{100:10} = \frac{1}{10}\)
   • \(\frac{400}{1000}\): НОД(400, 1000) = 200, \(\frac{400:200}{1000:200} = \frac{2}{5}\)
   • \(\frac{600}{800}\): НОД(600, 800) = 200, \(\frac{600:200}{800:200} = \frac{3}{4}\)
   • \(\frac{800}{1000}\): НОД(800, 1000) = 200, \(\frac{800:200}{1000:200} = \frac{4}{5}\)
3. • \(\frac{72}{90}\): НОД(72, 90) = 18, \(\frac{72:18}{90:18} = \frac{4}{5}\)
   • \(\frac{60}{105}\): НОД(60, 105) = 15, \(\frac{60:15}{105:15} = \frac{4}{7}\)
   • \(\frac{45}{150}\): НОД(45, 150) = 15, \(\frac{45:15}{150:15} = \frac{3}{10}\)
   • \(\frac{84}{120}\): НОД(84, 120) = 12, \(\frac{84:12}{120:12} = \frac{7}{10}\)
4. • \(\frac{56}{70}\): НОД(56, 70) = 14, \(\frac{56:14}{70:14} = \frac{4}{5}\)
   • \(\frac{36}{90}\): НОД(36, 90) = 18, \(\frac{36:18}{90:18} = \frac{2}{5}\)
   • \(\frac{66}{110}\): НОД(66, 110) = 22, \(\frac{66:22}{110:22} = \frac{3}{5}\)
   • \(\frac{96}{160}\): НОД(96, 160) = 32, \(\frac{96:32}{160:32} = \frac{3}{5}\)

Ответ: 1) \(\frac{7}{4}\), \(\frac{5}{11}\), \(\frac{4}{5}\), \(\frac{3}{4}\); 2) \(\frac{1}{10}\), \(\frac{2}{5}\), \(\frac{3}{4}\), \(\frac{4}{5}\); 3) \(\frac{4}{5}\), \(\frac{4}{7}\), \(\frac{3}{10}\), \(\frac{7}{10}\); 4) \(\frac{4}{5}\), \(\frac{2}{5}\), \(\frac{3}{5}\), \(\frac{3}{5}\).