2.134 Приведите к наименьшему общему знаменателю дроби: а) \frac{7}{16} и \frac{3}{8}; б) \frac{14}{75} и \frac{13}{30}; д) \frac{12}{55} и \frac{17}{22}; ж) \frac{13}{750} и \frac{7}{450}; и \frac{21}{60}; г) \frac{17}{20} и \frac{7}{25}; е) \frac{25}{42} и \frac{55}{147}; з) \frac{21}{225} и \frac{14}{375}

a) \(\frac{7}{16}\) и \(\frac{3}{8}\). Наименьший общий знаменатель (НОЗ) равен 16. \(\frac{3}{8} = \frac{3 \cdot 2}{8 \cdot 2} = \frac{6}{16}\). Получаем: \(\frac{7}{16}\) и \(\frac{6}{16}\).

б) \(\frac{14}{75}\) и \(\frac{13}{30}\). НОЗ равен 150. \(\frac{14}{75} = \frac{14 \cdot 2}{75 \cdot 2} = \frac{28}{150}\). \(\frac{13}{30} = \frac{13 \cdot 5}{30 \cdot 5} = \frac{65}{150}\). Получаем: \(\frac{28}{150}\) и \(\frac{65}{150}\).

д) \(\frac{12}{55}\) и \(\frac{17}{22}\). НОЗ равен 110. \(\frac{12}{55} = \frac{12 \cdot 2}{55 \cdot 2} = \frac{24}{110}\). \(\frac{17}{22} = \frac{17 \cdot 5}{22 \cdot 5} = \frac{85}{110}\). Получаем: \(\frac{24}{110}\) и \(\frac{85}{110}\).

ж) \(\frac{13}{750}\) и \(\frac{7}{450}\). НОЗ равен 2250. \(\frac{13}{750} = \frac{13 \cdot 3}{750 \cdot 3} = \frac{39}{2250}\). \(\frac{7}{450} = \frac{7 \cdot 5}{450 \cdot 5} = \frac{35}{2250}\). Получаем: \(\frac{39}{2250}\) и \(\frac{35}{2250}\).

и \(\frac{9}{20}\) и \(\frac{21}{60}\). НОЗ = 60. \(\frac{9}{20} = \frac{9 \cdot 3}{20 \cdot 3} = \frac{27}{60}\). Получаем: \(\frac{27}{60}\) и \(\frac{21}{60}\).

г) \(\frac{17}{20}\) и \(\frac{7}{25}\). НОЗ = 100. \(\frac{17}{20} = \frac{17 \cdot 5}{20 \cdot 5} = \frac{85}{100}\). \(\frac{7}{25} = \frac{7 \cdot 4}{25 \cdot 4} = \frac{28}{100}\). Получаем: \(\frac{85}{100}\) и \(\frac{28}{100}\).

е) \(\frac{25}{42}\) и \(\frac{55}{147}\). НОЗ равен 294. \(\frac{25}{42} = \frac{25 \cdot 7}{42 \cdot 7} = \frac{175}{294}\). \(\frac{55}{147} = \frac{55 \cdot 2}{147 \cdot 2} = \frac{110}{294}\). Получаем: \(\frac{175}{294}\) и \(\frac{110}{294}\).

з) \(\frac{21}{225}\) и \(\frac{14}{375}\). НОЗ равен 1125. \(\frac{21}{225} = \frac{21 \cdot 5}{225 \cdot 5} = \frac{105}{1125}\). \(\frac{14}{375} = \frac{14 \cdot 3}{375 \cdot 3} = \frac{42}{1125}\). Получаем: \(\frac{105}{1125}\) и \(\frac{42}{1125}\).

Ответ: a) \(\frac{7}{16}\) и \(\frac{6}{16}\); б) \(\frac{28}{150}\) и \(\frac{65}{150}\); д) \(\frac{24}{110}\) и \(\frac{85}{110}\); ж) \(\frac{39}{2250}\) и \(\frac{35}{2250}\); и) \(\frac{27}{60}\) и \(\frac{21}{60}\); г) \(\frac{85}{100}\) и \(\frac{28}{100}\); е) \(\frac{175}{294}\) и \(\frac{110}{294}\); з) \(\frac{105}{1125}\) и \(\frac{42}{1125}\)