15. Сократите дробь: 6/12 = ? 35/42 = ? 6/60 = ? 22/55 = ? 8/10 = ? 150/400 = ? 12/16 = ? 12/144 = ? 58/377 = ? 7/49 = ? 16/28 = ? 14/91 = ? 18/54 = ? 52/65 = ? 600/850 = ? 20/30 = ? 144/216 = ? 57/342 = ? 36/96 = ? 18/81 = ? 24/30 = ? 9/24 = ? 8/14 = ? 23/115 = ? 50/75 = ? 56/126 = ? 15/1656 = ? 5/55 = ? 32/48 = ? 10/15 = ? 10/22 = ? 20/30 = ? 126/840 = ? 4/4 = ? 78/390 = ? 88/484 = ?

Решение:

Чтобы сократить дробь, нужно найти наибольший общий делитель (НОД) числителя и знаменателя и разделить на него оба числа.

• \(\frac{6}{12} = \frac{6 \div 6}{12 \div 6} = \frac{1}{2}\)
• \(\frac{35}{42} = \frac{35 \div 7}{42 \div 7} = \frac{5}{6}\)
• \(\frac{6}{60} = \frac{6 \div 6}{60 \div 6} = \frac{1}{10}\)
• \(\frac{22}{55} = \frac{22 \div 11}{55 \div 11} = \frac{2}{5}\)
• \(\frac{8}{10} = \frac{8 \div 2}{10 \div 2} = \frac{4}{5}\)
• \(\frac{150}{400} = \frac{150 \div 50}{400 \div 50} = \frac{3}{8}\)
• \(\frac{12}{16} = \frac{12 \div 4}{16 \div 4} = \frac{3}{4}\)
• \(\frac{12}{144} = \frac{12 \div 12}{144 \div 12} = \frac{1}{12}\)
• \(\frac{58}{377} = \frac{58 \div 29}{377 \div 29} = \frac{2}{13}\)
• \(\frac{7}{49} = \frac{7 \div 7}{49 \div 7} = \frac{1}{7}\)
• \(\frac{16}{28} = \frac{16 \div 4}{28 \div 4} = \frac{4}{7}\)
• \(\frac{14}{91} = \frac{14 \div 7}{91 \div 7} = \frac{2}{13}\)
• \(\frac{18}{54} = \frac{18 \div 18}{54 \div 18} = \frac{1}{3}\)
• \(\frac{52}{65} = \frac{52 \div 13}{65 \div 13} = \frac{4}{5}\)
• \(\frac{600}{850} = \frac{600 \div 50}{850 \div 50} = \frac{12}{17}\)
• \(\frac{20}{30} = \frac{20 \div 10}{30 \div 10} = \frac{2}{3}\)
• \(\frac{144}{216} = \frac{144 \div 72}{216 \div 72} = \frac{2}{3}\)
• \(\frac{57}{342} = \frac{57 \div 19}{342 \div 19} = \frac{3}{18} = \frac{1}{6}\)
• \(\frac{36}{96} = \frac{36 \div 12}{96 \div 12} = \frac{3}{8}\)
• \(\frac{18}{81} = \frac{18 \div 9}{81 \div 9} = \frac{2}{9}\)
• \(\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}\)
• \(\frac{9}{24} = \frac{9 \div 3}{24 \div 3} = \frac{3}{8}\)
• \(\frac{8}{14} = \frac{8 \div 2}{14 \div 2} = \frac{4}{7}\)
• \(\frac{23}{115} = \frac{23 \div 23}{115 \div 23} = \frac{1}{5}\)
• \(\frac{50}{75} = \frac{50 \div 25}{75 \div 25} = \frac{2}{3}\)
• \(\frac{56}{126} = \frac{56 \div 14}{126 \div 14} = \frac{4}{9}\)
• \(\frac{15}{1656} = \frac{15 \div 3}{1656 \div 3} = \frac{5}{552}\)
• \(\frac{5}{55} = \frac{5 \div 5}{55 \div 5} = \frac{1}{11}\)
• \(\frac{32}{48} = \frac{32 \div 16}{48 \div 16} = \frac{2}{3}\)
• \(\frac{10}{15} = \frac{10 \div 5}{15 \div 5} = \frac{2}{3}\)
• \(\frac{10}{22} = \frac{10 \div 2}{22 \div 2} = \frac{5}{11}\)
• \(\frac{20}{30} = \frac{20 \div 10}{30 \div 10} = \frac{2}{3}\)
• \(\frac{126}{840} = \frac{126 \div 42}{840 \div 42} = \frac{3}{20}\)
• \(\frac{4}{4} = 1\)
• \(\frac{78}{390} = \frac{78 \div 78}{390 \div 78} = \frac{1}{5}\)
• \(\frac{88}{484} = \frac{88 \div 44}{484 \div 44} = \frac{2}{11}\)

Ответ: 1/2, 5/6, 1/10, 2/5, 4/5, 3/8, 3/4, 1/12, 2/13, 1/7, 4/7, 2/13, 1/3, 4/5, 12/17, 2/3, 2/3, 1/6, 3/8, 2/9, 4/5, 3/8, 4/7, 1/5, 2/3, 4/9, 5/552, 1/11, 2/3, 2/3, 5/11, 2/3, 3/20, 1, 1/5, 2/11.