Контрольные задания > №1. Приведите к наименьшему общему знаменателю дроби: a) $$ rac{1}{6}$$ и $$ rac{3}{8}$$; б) $$ rac{4}{9}$$ и $$ rac{7}{15}$$; в) $$ rac{5}{12}$$ и $$ rac{1}{8}$$; г) $$ rac{8}{15}$$ и $$ rac{11}{12}$$; д) $$ rac{9}{10}$$ и $$ rac{5}{12}$$; e) $$ rac{13}{12}$$ и $$ rac{13}{18}$$; ж) $$ rac{11}{30}$$ и $$ rac{8}{45}$$; з) $$ rac{11}{20}$$ и $$ rac{9}{16}$$; и) $$ rac{8}{33}$$ и $$ rac{9}{77}$$; к) $$ rac{9}{98}$$ и $$ rac{5}{56}$$; л) $$ rac{13}{750}$$ и $$ rac{7}{450}$$; м) $$ rac{10}{297}$$ и $$ rac{14}{363}$$
Вопрос:

№1. Приведите к наименьшему общему знаменателю дроби: a) $$ rac{1}{6}$$ и $$ rac{3}{8}$$; б) $$ rac{4}{9}$$ и $$ rac{7}{15}$$; в) $$ rac{5}{12}$$ и $$ rac{1}{8}$$; г) $$ rac{8}{15}$$ и $$ rac{11}{12}$$; д) $$ rac{9}{10}$$ и $$ rac{5}{12}$$; e) $$ rac{13}{12}$$ и $$ rac{13}{18}$$; ж) $$ rac{11}{30}$$ и $$ rac{8}{45}$$; з) $$ rac{11}{20}$$ и $$ rac{9}{16}$$; и) $$ rac{8}{33}$$ и $$ rac{9}{77}$$; к) $$ rac{9}{98}$$ и $$ rac{5}{56}$$; л) $$ rac{13}{750}$$ и $$ rac{7}{450}$$; м) $$ rac{10}{297}$$ и $$ rac{14}{363}$$

Ответ:

Решение:

  1. a) $$ rac{1}{6}$$ и $$ rac{3}{8}$$: НОЗ(6, 8) = 24. $$ rac{1}{6} = \frac{4}{24}$$, $$ rac{3}{8} = \frac{9}{24}$$
  2. б) $$ rac{4}{9}$$ и $$ rac{7}{15}$$: НОЗ(9, 15) = 45. $$ rac{4}{9} = \frac{20}{45}$$, $$ rac{7}{15} = \frac{21}{45}$$
  3. в) $$ rac{5}{12}$$ и $$ rac{1}{8}$$: НОЗ(12, 8) = 24. $$ rac{5}{12} = \frac{10}{24}$$, $$ rac{1}{8} = \frac{3}{24}$$
  4. г) $$ rac{8}{15}$$ и $$ rac{11}{12}$$: НОЗ(15, 12) = 60. $$ rac{8}{15} = \frac{32}{60}$$, $$ rac{11}{12} = \frac{55}{60}$$
  5. д) $$ rac{9}{10}$$ и $$ rac{5}{12}$$: НОЗ(10, 12) = 60. $$ rac{9}{10} = \frac{54}{60}$$, $$ rac{5}{12} = \frac{25}{60}$$
  6. e) $$ rac{13}{12}$$ и $$ rac{13}{18}$$: НОЗ(12, 18) = 36. $$ rac{13}{12} = \frac{39}{36}$$, $$ rac{13}{18} = \frac{26}{36}$$
  7. ж) $$ rac{11}{30}$$ и $$ rac{8}{45}$$: НОЗ(30, 45) = 90. $$ rac{11}{30} = \frac{33}{90}$$, $$ rac{8}{45} = \frac{16}{90}$$
  8. з) $$ rac{11}{20}$$ и $$ rac{9}{16}$$: НОЗ(20, 16) = 80. $$ rac{11}{20} = \frac{44}{80}$$, $$ rac{9}{16} = \frac{45}{80}$$
  9. и) $$ rac{8}{33}$$ и $$ rac{9}{77}$$: НОЗ(33, 77) = 231. $$ rac{8}{33} = \frac{56}{231}$$, $$ rac{9}{77} = \frac{27}{231}$$
  10. к) $$ rac{9}{98}$$ и $$ rac{5}{56}$$: НОЗ(98, 56) = 392. $$ rac{9}{98} = \frac{36}{392}$$, $$ rac{5}{56} = \frac{35}{392}$$
  11. л) $$ rac{13}{750}$$ и $$ rac{7}{450}$$: НОЗ(750, 450) = 2250. $$ rac{13}{750} = \frac{39}{2250}$$, $$ rac{7}{450} = \frac{35}{2250}$$
  12. м) $$ rac{10}{297}$$ и $$ rac{14}{363}$$: НОЗ(297, 363) = 35937. $$ rac{10}{297} = \frac{1210}{35937}$$, $$ rac{14}{363} = \frac{1386}{35937}$$
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