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МатематикаВопрос:
801. a) \(\frac{2}{15}\) и \(\frac{5}{12}\); б) \(\frac{5}{12}\) и \(\frac{7}{8}\); в) \(\frac{6}{15}\) и \(\frac{11}{18}\); г) \(\frac{5}{16}\) и \(\frac{5}{12}\); д) \(\frac{7}{33}\) и \(\frac{3}{77}\); e) \(\frac{2}{55}\) и \(\frac{5}{22}\); ж) \(\frac{4}{15}\) и \(\frac{3}{20}\); з) \(\frac{5}{121}\) и \(\frac{8}{99}\); и) \(\frac{1}{72}\) и \(\frac{1}{56}\); к) \(\frac{1}{48}\) и \(\frac{1}{72}\); л) \(\frac{2}{77}\) и \(\frac{3}{44}\); м) \(\frac{1}{51}\) и \(\frac{1}{68}\); н) \(\frac{5}{36}\) и \(\frac{7}{54}\); o) \(\frac{9}{35}\) и \(\frac{11}{42}\); п) \(\frac{4}{49}\) и \(\frac{5}{63}\); p) \(\frac{15}{98}\) и \(\frac{13}{72}\).
Ответ:
a) \(\frac{2}{15}\) и \(\frac{5}{12}\). НОЗ(15, 12) = 60. \(\frac{2}{15} = \frac{2 \cdot 4}{15 \cdot 4} = \frac{8}{60}\); \(\frac{5}{12} = \frac{5 \cdot 5}{12 \cdot 5} = \frac{25}{60}\)
б) \(\frac{5}{12}\) и \(\frac{7}{8}\). НОЗ(12, 8) = 24. \(\frac{5}{12} = \frac{5 \cdot 2}{12 \cdot 2} = \frac{10}{24}\); \(\frac{7}{8} = \frac{7 \cdot 3}{8 \cdot 3} = \frac{21}{24}\)
в) \(\frac{6}{15}\) и \(\frac{11}{18}\). НОЗ(15, 18) = 90. \(\frac{6}{15} = \frac{6 \cdot 6}{15 \cdot 6} = \frac{36}{90}\); \(\frac{11}{18} = \frac{11 \cdot 5}{18 \cdot 5} = \frac{55}{90}\)
г) \(\frac{5}{16}\) и \(\frac{5}{12}\). НОЗ(16, 12) = 48. \(\frac{5}{16} = \frac{5 \cdot 3}{16 \cdot 3} = \frac{15}{48}\); \(\frac{5}{12} = \frac{5 \cdot 4}{12 \cdot 4} = \frac{20}{48}\)
д) \(\frac{7}{33}\) и \(\frac{3}{77}\). НОЗ(33, 77) = 231. \(\frac{7}{33} = \frac{7 \cdot 7}{33 \cdot 7} = \frac{49}{231}\); \(\frac{3}{77} = \frac{3 \cdot 3}{77 \cdot 3} = \frac{9}{231}\)
е) \(\frac{2}{55}\) и \(\frac{5}{22}\). НОЗ(55, 22) = 110. \(\frac{2}{55} = \frac{2 \cdot 2}{55 \cdot 2} = \frac{4}{110}\); \(\frac{5}{22} = \frac{5 \cdot 5}{22 \cdot 5} = \frac{25}{110}\)
ж) \(\frac{4}{15}\) и \(\frac{3}{20}\). НОЗ(15, 20) = 60. \(\frac{4}{15} = \frac{4 \cdot 4}{15 \cdot 4} = \frac{16}{60}\); \(\frac{3}{20} = \frac{3 \cdot 3}{20 \cdot 3} = \frac{9}{60}\)
з) \(\frac{5}{121}\) и \(\frac{8}{99}\). НОЗ(121, 99) = 1089. \(\frac{5}{121} = \frac{5 \cdot 9}{121 \cdot 9} = \frac{45}{1089}\); \(\frac{8}{99} = \frac{8 \cdot 11}{99 \cdot 11} = \frac{88}{1089}\)
и) \(\frac{1}{72}\) и \(\frac{1}{56}\). НОЗ(72, 56) = 504. \(\frac{1}{72} = \frac{1 \cdot 7}{72 \cdot 7} = \frac{7}{504}\); \(\frac{1}{56} = \frac{1 \cdot 9}{56 \cdot 9} = \frac{9}{504}\)
к) \(\frac{1}{48}\) и \(\frac{1}{72}\). НОЗ(48, 72) = 144. \(\frac{1}{48} = \frac{1 \cdot 3}{48 \cdot 3} = \frac{3}{144}\); \(\frac{1}{72} = \frac{1 \cdot 2}{72 \cdot 2} = \frac{2}{144}\)
л) \(\frac{2}{77}\) и \(\frac{3}{44}\). НОЗ(77, 44) = 308. \(\frac{2}{77} = \frac{2 \cdot 4}{77 \cdot 4} = \frac{8}{308}\); \(\frac{3}{44} = \frac{3 \cdot 7}{44 \cdot 7} = \frac{21}{308}\)
м) \(\frac{1}{51}\) и \(\frac{1}{68}\). НОЗ(51, 68) = 204. \(\frac{1}{51} = \frac{1 \cdot 4}{51 \cdot 4} = \frac{4}{204}\); \(\frac{1}{68} = \frac{1 \cdot 3}{68 \cdot 3} = \frac{3}{204}\)
н) \(\frac{5}{36}\) и \(\frac{7}{54}\). НОЗ(36, 54) = 108. \(\frac{5}{36} = \frac{5 \cdot 3}{36 \cdot 3} = \frac{15}{108}\); \(\frac{7}{54} = \frac{7 \cdot 2}{54 \cdot 2} = \frac{14}{108}\)
о) \(\frac{9}{35}\) и \(\frac{11}{42}\). НОЗ(35, 42) = 210. \(\frac{9}{35} = \frac{9 \cdot 6}{35 \cdot 6} = \frac{54}{210}\); \(\frac{11}{42} = \frac{11 \cdot 5}{42 \cdot 5} = \frac{55}{210}\)
п) \(\frac{4}{49}\) и \(\frac{5}{63}\). НОЗ(49, 63) = 441. \(\frac{4}{49} = \frac{4 \cdot 9}{49 \cdot 9} = \frac{36}{441}\); \(\frac{5}{63} = \frac{5 \cdot 7}{63 \cdot 7} = \frac{35}{441}\)
р) \(\frac{15}{98}\) и \(\frac{13}{72}\). НОЗ(98, 72) = 3528. \(\frac{15}{98} = \frac{15 \cdot 36}{98 \cdot 36} = \frac{540}{3528}\); \(\frac{13}{72} = \frac{13 \cdot 49}{72 \cdot 49} = \frac{637}{3528}\)
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