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МатематикаВопрос:
Приведите дроби к общему знаменателю (800, 801). 800. a) \(\frac{1}{4}\) 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 \(\frac{7}{25}\); o) \(\frac{7}{200}\) и \(\frac{11}{40}\); п) \(\frac{8}{17}\) и \(\frac{9}{34}\); р) \(\frac{3}{40}\) и \(\frac{7}{25}\).
Ответ:
Чтобы привести дроби к общему знаменателю, нужно найти наименьший общий знаменатель (НОЗ) и привести каждую дробь к этому знаменателю.
а) \(\frac{1}{4}\) и \(\frac{1}{6}\). НОЗ(4, 6) = 12. \(\frac{1}{4} = \frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}\); \(\frac{1}{6} = \frac{1 \cdot 2}{6 \cdot 2} = \frac{2}{12}\)
б) \(\frac{1}{4}\) и \(\frac{1}{10}\). НОЗ(4, 10) = 20. \(\frac{1}{4} = \frac{1 \cdot 5}{4 \cdot 5} = \frac{5}{20}\); \(\frac{1}{10} = \frac{1 \cdot 2}{10 \cdot 2} = \frac{2}{20}\)
в) \(\frac{1}{6}\) и \(\frac{1}{8}\). НОЗ(6, 8) = 24. \(\frac{1}{6} = \frac{1 \cdot 4}{6 \cdot 4} = \frac{4}{24}\); \(\frac{1}{8} = \frac{1 \cdot 3}{8 \cdot 3} = \frac{3}{24}\)
г) \(\frac{1}{6}\) и \(\frac{1}{9}\). НОЗ(6, 9) = 18. \(\frac{1}{6} = \frac{1 \cdot 3}{6 \cdot 3} = \frac{3}{18}\); \(\frac{1}{9} = \frac{1 \cdot 2}{9 \cdot 2} = \frac{2}{18}\)
д) \(\frac{1}{10}\) и \(\frac{1}{15}\). НОЗ(10, 15) = 30. \(\frac{1}{10} = \frac{1 \cdot 3}{10 \cdot 3} = \frac{3}{30}\); \(\frac{1}{15} = \frac{1 \cdot 2}{15 \cdot 2} = \frac{2}{30}\)
е) \(\frac{1}{10}\) и \(\frac{1}{25}\). НОЗ(10, 25) = 50. \(\frac{1}{10} = \frac{1 \cdot 5}{10 \cdot 5} = \frac{5}{50}\); \(\frac{1}{25} = \frac{1 \cdot 2}{25 \cdot 2} = \frac{2}{50}\)
ж) \(\frac{1}{30}\) и \(\frac{1}{40}\). НОЗ(30, 40) = 120. \(\frac{1}{30} = \frac{1 \cdot 4}{30 \cdot 4} = \frac{4}{120}\); \(\frac{1}{40} = \frac{1 \cdot 3}{40 \cdot 3} = \frac{3}{120}\)
з) \(\frac{1}{30}\) и \(\frac{1}{50}\). НОЗ(30, 50) = 150. \(\frac{1}{30} = \frac{1 \cdot 5}{30 \cdot 5} = \frac{5}{150}\); \(\frac{1}{50} = \frac{1 \cdot 3}{50 \cdot 3} = \frac{3}{150}\)
и) \(\frac{1}{70}\) и \(\frac{1}{60}\). НОЗ(70, 60) = 420. \(\frac{1}{70} = \frac{1 \cdot 6}{70 \cdot 6} = \frac{6}{420}\); \(\frac{1}{60} = \frac{1 \cdot 7}{60 \cdot 7} = \frac{7}{420}\)
к) \(\frac{1}{50}\) и \(\frac{1}{80}\). НОЗ(50, 80) = 400. \(\frac{1}{50} = \frac{1 \cdot 8}{50 \cdot 8} = \frac{8}{400}\); \(\frac{1}{80} = \frac{1 \cdot 5}{80 \cdot 5} = \frac{5}{400}\)
л) \(\frac{1}{60}\) и \(\frac{1}{15}\). НОЗ(60, 15) = 60. \(\frac{1}{60}\); \(\frac{1}{15} = \frac{1 \cdot 4}{15 \cdot 4} = \frac{4}{60}\)
м) \(\frac{1}{24}\) и \(\frac{1}{120}\). НОЗ(24, 120) = 120. \(\frac{1}{24} = \frac{1 \cdot 5}{24 \cdot 5} = \frac{5}{120}\); \(\frac{1}{120}\)
н) \(\frac{3}{50}\) и \(\frac{7}{25}\). НОЗ(50, 25) = 50. \(\frac{3}{50}\); \(\frac{7}{25} = \frac{7 \cdot 2}{25 \cdot 2} = \frac{14}{50}\)
о) \(\frac{7}{200}\) и \(\frac{11}{40}\). НОЗ(200, 40) = 200. \(\frac{7}{200}\); \(\frac{11}{40} = \frac{11 \cdot 5}{40 \cdot 5} = \frac{55}{200}\)
п) \(\frac{8}{17}\) и \(\frac{9}{34}\). НОЗ(17, 34) = 34. \(\frac{8}{17} = \frac{8 \cdot 2}{17 \cdot 2} = \frac{16}{34}\); \(\frac{9}{34}\)
р) \(\frac{3}{40}\) и \(\frac{7}{25}\). НОЗ(40, 25) = 200. \(\frac{3}{40} = \frac{3 \cdot 5}{40 \cdot 5} = \frac{15}{200}\); \(\frac{7}{25} = \frac{7 \cdot 8}{25 \cdot 8} = \frac{56}{200}\)
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