2. Сократите дроби: a) 8/12, 12/16, 12/18, 24/40, 18/27, 20/70, 8/36, 30/75 б) 2/4, 3/9, 4/16, 9/45, 11/66, 5/35

Решение:

Для сокращения дробей найдем наибольший общий делитель (НОД) числителя и знаменателя.

а)

• \( \frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \)
• \( \frac{12}{16} = \frac{12 \div 4}{16 \div 4} = \frac{3}{4} \)
• \( \frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3} \)
• \( \frac{24}{40} = \frac{24 \div 8}{40 \div 8} = \frac{3}{5} \)
• \( \frac{18}{27} = \frac{18 \div 9}{27 \div 9} = \frac{2}{3} \)
• \( \frac{20}{70} = \frac{20 \div 10}{70 \div 10} = \frac{2}{7} \)
• \( \frac{8}{36} = \frac{8 \div 4}{36 \div 4} = \frac{2}{9} \)
• \( \frac{30}{75} = \frac{30 \div 15}{75 \div 15} = \frac{2}{5} \)

б)

• \( \frac{2}{4} = \frac{2 \div 2}{4 \div 2} = \frac{1}{2} \)
• \( \frac{3}{9} = \frac{3 \div 3}{9 \div 3} = \frac{1}{3} \)
• \( \frac{4}{16} = \frac{4 \div 4}{16 \div 4} = \frac{1}{4} \)
• \( \frac{9}{45} = \frac{9 \div 9}{45 \div 9} = \frac{1}{5} \)
• \( \frac{11}{66} = \frac{11 \div 11}{66 \div 11} = \frac{1}{6} \)
• \( \frac{5}{35} = \frac{5 \div 5}{35 \div 5} = \frac{1}{7} \)

Ответ: а) 2/3, 3/4, 2/3, 3/5, 2/3, 2/7, 2/9, 2/5; б) 1/2, 1/3, 1/4, 1/5, 1/6, 1/7.