Вопрос:

800. Приведите дроби к общему знаменателю: а) \(\frac{1}{4}\) и \(\frac{1}{6}\) б) \(\frac{1}{4}\) и \(\frac{1}{10}\) в) \(\frac{1}{6}\) и \(\frac{1}{8}\) г) \(\frac{1}{6}\) и \(\frac{1}{9}\) д) \(\frac{1}{10}\) и \(\frac{1}{15}\) е) \(\frac{1}{10}\) и \(\frac{1}{25}\) ж) \(\frac{1}{30}\) и \(\frac{1}{40}\) з) \(\frac{1}{30}\) и \(\frac{1}{50}\) и) \(\frac{1}{70}\) и \(\frac{1}{60}\) к) \(\frac{1}{50}\) и \(\frac{1}{80}\) л) \(\frac{1}{60}\) и \(\frac{1}{15}\) м) \(\frac{1}{24}\) и \(\frac{1}{120}\) н) \(\frac{3}{50}\) и \(\frac{7}{25}\) о) \(\frac{7}{200}\) и \(\frac{11}{40}\) п) \(\frac{8}{17}\) и \(\frac{9}{34}\) р) \(\frac{3}{40}\) и \(\frac{7}{25}\)

Ответ:

Приведем дроби к общему знаменателю: а) \(\frac{1}{4}\) и \(\frac{1}{6}\). НОЗ(4, 6) = 12. \(\frac{1}{4} = \frac{3}{12}\), \(\frac{1}{6} = \frac{2}{12}\). Дроби: \(\frac{3}{12}\) и \(\frac{2}{12}\). б) \(\frac{1}{4}\) и \(\frac{1}{10}\). НОЗ(4, 10) = 20. \(\frac{1}{4} = \frac{5}{20}\), \(\frac{1}{10} = \frac{2}{20}\). Дроби: \(\frac{5}{20}\) и \(\frac{2}{20}\). в) \(\frac{1}{6}\) и \(\frac{1}{8}\). НОЗ(6, 8) = 24. \(\frac{1}{6} = \frac{4}{24}\), \(\frac{1}{8} = \frac{3}{24}\). Дроби: \(\frac{4}{24}\) и \(\frac{3}{24}\). г) \(\frac{1}{6}\) и \(\frac{1}{9}\). НОЗ(6, 9) = 18. \(\frac{1}{6} = \frac{3}{18}\), \(\frac{1}{9} = \frac{2}{18}\). Дроби: \(\frac{3}{18}\) и \(\frac{2}{18}\). д) \(\frac{1}{10}\) и \(\frac{1}{15}\). НОЗ(10, 15) = 30. \(\frac{1}{10} = \frac{3}{30}\), \(\frac{1}{15} = \frac{2}{30}\). Дроби: \(\frac{3}{30}\) и \(\frac{2}{30}\). е) \(\frac{1}{10}\) и \(\frac{1}{25}\). НОЗ(10, 25) = 50. \(\frac{1}{10} = \frac{5}{50}\), \(\frac{1}{25} = \frac{2}{50}\). Дроби: \(\frac{5}{50}\) и \(\frac{2}{50}\). ж) \(\frac{1}{30}\) и \(\frac{1}{40}\). НОЗ(30, 40) = 120. \(\frac{1}{30} = \frac{4}{120}\), \(\frac{1}{40} = \frac{3}{120}\). Дроби: \(\frac{4}{120}\) и \(\frac{3}{120}\). з) \(\frac{1}{30}\) и \(\frac{1}{50}\). НОЗ(30, 50) = 150. \(\frac{1}{30} = \frac{5}{150}\), \(\frac{1}{50} = \frac{3}{150}\). Дроби: \(\frac{5}{150}\) и \(\frac{3}{150}\). и) \(\frac{1}{70}\) и \(\frac{1}{60}\). НОЗ(70, 60) = 420. \(\frac{1}{70} = \frac{6}{420}\), \(\frac{1}{60} = \frac{7}{420}\). Дроби: \(\frac{6}{420}\) и \(\frac{7}{420}\). к) \(\frac{1}{50}\) и \(\frac{1}{80}\). НОЗ(50, 80) = 400. \(\frac{1}{50} = \frac{8}{400}\), \(\frac{1}{80} = \frac{5}{400}\). Дроби: \(\frac{8}{400}\) и \(\frac{5}{400}\). л) \(\frac{1}{60}\) и \(\frac{1}{15}\). НОЗ(60, 15) = 60. \(\frac{1}{60}\) и \(\frac{1}{15} = \frac{4}{60}\). Дроби: \(\frac{1}{60}\) и \(\frac{4}{60}\). м) \(\frac{1}{24}\) и \(\frac{1}{120}\). НОЗ(24, 120) = 120. \(\frac{1}{24} = \frac{5}{120}\) и \(\frac{1}{120}\). Дроби: \(\frac{5}{120}\) и \(\frac{1}{120}\). н) \(\frac{3}{50}\) и \(\frac{7}{25}\). НОЗ(50, 25) = 50. \(\frac{3}{50}\) и \(\frac{7}{25} = \frac{14}{50}\). Дроби: \(\frac{3}{50}\) и \(\frac{14}{50}\). о) \(\frac{7}{200}\) и \(\frac{11}{40}\). НОЗ(200, 40) = 200. \(\frac{7}{200}\) и \(\frac{11}{40} = \frac{55}{200}\). Дроби: \(\frac{7}{200}\) и \(\frac{55}{200}\). п) \(\frac{8}{17}\) и \(\frac{9}{34}\). НОЗ(17, 34) = 34. \(\frac{8}{17} = \frac{16}{34}\) и \(\frac{9}{34}\). Дроби: \(\frac{16}{34}\) и \(\frac{9}{34}\). р) \(\frac{3}{40}\) и \(\frac{7}{25}\). НОЗ(40, 25) = 200. \(\frac{3}{40} = \frac{15}{200}\) и \(\frac{7}{25} = \frac{56}{200}\). Дроби: \(\frac{15}{200}\) и \(\frac{56}{200}\).
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