5.334 Сократите дробь: a) \(\frac{33}{99}\), \(\frac{150}{125}\), \(\frac{25}{100}\), \(\frac{14}{210}\), \(\frac{150}{1000}\), \(\frac{1000}{2500}\), \(\frac{264}{148}\); б) \(\frac{45}{630}\), \(\frac{30}{64}\), \(\frac{125}{500}\), \(\frac{7}{217}\), \(\frac{12}{600}\), \(\frac{75}{300}\), \(\frac{140}{210}\).

Чтобы сократить дробь, нужно:

1. Найти наибольший общий делитель (НОД) числителя и знаменателя.
2. Разделить числитель и знаменатель на их НОД.

• \(\frac{33}{99} = \frac{33:33}{99:33} = \frac{1}{3}\)
• \(\frac{150}{125} = \frac{150:25}{125:25} = \frac{6}{5}\)
• \(\frac{25}{100} = \frac{25:25}{100:25} = \frac{1}{4}\)
• \(\frac{14}{210} = \frac{14:14}{210:14} = \frac{1}{15}\)
• \(\frac{150}{1000} = \frac{150:50}{1000:50} = \frac{3}{20}\)
• \(\frac{1000}{2500} = \frac{1000:500}{2500:500} = \frac{2}{5}\)
• \(\frac{264}{148} = \frac{264:4}{148:4} = \frac{66}{37}\)

• \(\frac{45}{630} = \frac{45:45}{630:45} = \frac{1}{14}\)
• \(\frac{30}{64} = \frac{30:2}{64:2} = \frac{15}{32}\)
• \(\frac{125}{500} = \frac{125:125}{500:125} = \frac{1}{4}\)
• \(\frac{7}{217} = \frac{7:7}{217:7} = \frac{1}{31}\)
• \(\frac{12}{600} = \frac{12:12}{600:12} = \frac{1}{50}\)
• \(\frac{75}{300} = \frac{75:75}{300:75} = \frac{1}{4}\)
• \(\frac{140}{210} = \frac{140:70}{210:70} = \frac{2}{3}\)

Ответ: а) \(\frac{1}{3}\), \(\frac{6}{5}\), \(\frac{1}{4}\), \(\frac{1}{15}\), \(\frac{3}{20}\), \(\frac{2}{5}\), \(\frac{66}{37}\); б) \(\frac{1}{14}\), \(\frac{15}{32}\), \(\frac{1}{4}\), \(\frac{1}{31}\), \(\frac{1}{50}\), \(\frac{1}{4}\), \(\frac{2}{3}\).