Приведите дроби к наименьшему общему знаменате- лю (9-11). 9. a) 1,1 2'3 и 1; 4' 13 19. 10. a) и ; 16 24 б) 1. 1 и 1: 3' 45' 7. и; 15 20 в) 1 и 1 и 1; 3' 5 30' 22 11; 27 18' г) 1 1 и 1. 2' 416 7 12 г) и 15 25

Ответ:

9. a) \(\frac{1}{2}\), \(\frac{1}{3}\) и \(\frac{1}{4}\). НОК(2, 3, 4) = 12. Приводим дроби к знаменателю 12:

• \(\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}\)
• \(\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}\)
• \(\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}\)

б) \(\frac{1}{3}\), \(\frac{1}{4}\) и \(\frac{1}{5}\). НОК(3, 4, 5) = 60. Приводим дроби к знаменателю 60:

• \(\frac{1}{3} = \frac{1 \times 20}{3 \times 20} = \frac{20}{60}\)
• \(\frac{1}{4} = \frac{1 \times 15}{4 \times 15} = \frac{15}{60}\)
• \(\frac{1}{5} = \frac{1 \times 12}{5 \times 12} = \frac{12}{60}\)

в) \(\frac{1}{3}\), \(\frac{1}{5}\) и \(\frac{1}{30}\). НОК(3, 5, 30) = 30. Приводим дроби к знаменателю 30:

• \(\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}\)
• \(\frac{1}{5} = \frac{1 \times 6}{5 \times 6} = \frac{6}{30}\)
• \(\frac{1}{30} = \frac{1}{30}\)

г) \(\frac{1}{2}\), \(\frac{1}{4}\) и \(\frac{1}{16}\). НОК(2, 4, 16) = 16. Приводим дроби к знаменателю 16:

• \(\frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16}\)
• \(\frac{1}{4} = \frac{1 \times 4}{4 \times 4} = \frac{4}{16}\)
• \(\frac{1}{16} = \frac{1}{16}\)

10. a) \(\frac{13}{16}\) и \(\frac{19}{24}\). НОК(16, 24) = 48. Приводим дроби к знаменателю 48:

• \(\frac{13}{16} = \frac{13 \times 3}{16 \times 3} = \frac{39}{48}\)
• \(\frac{19}{24} = \frac{19 \times 2}{24 \times 2} = \frac{38}{48}\)

б) \(\frac{8}{15}\) и \(\frac{7}{20}\). НОК(15, 20) = 60. Приводим дроби к знаменателю 60:

• \(\frac{8}{15} = \frac{8 \times 4}{15 \times 4} = \frac{32}{60}\)
• \(\frac{7}{20} = \frac{7 \times 3}{20 \times 3} = \frac{21}{60}\)

в) \(\frac{22}{27}\) и \(\frac{11}{18}\). НОК(27, 18) = 54. Приводим дроби к знаменателю 54:

• \(\frac{22}{27} = \frac{22 \times 2}{27 \times 2} = \frac{44}{54}\)
• \(\frac{11}{18} = \frac{11 \times 3}{18 \times 3} = \frac{33}{54}\)

г) \(\frac{7}{15}\) и \(\frac{12}{25}\). НОК(15, 25) = 75. Приводим дроби к знаменателю 75:

• \(\frac{7}{15} = \frac{7 \times 5}{15 \times 5} = \frac{35}{75}\)
• \(\frac{12}{25} = \frac{12 \times 3}{25 \times 3} = \frac{36}{75}\)

Ответ: a) \[\frac{6}{12}, \frac{4}{12}, \frac{3}{12}\]; б) \(\frac{20}{60}, \frac{15}{60}, \frac{12}{60}\); в) \(\frac{10}{30}, \frac{6}{30}, \frac{1}{30}\); г) \(\frac{8}{16}, \frac{4}{16}, \frac{1}{16}\); 10. a) \(\frac{39}{48}, \frac{38}{48}\); б) \(\frac{32}{60}, \frac{21}{60}\); в) \(\frac{44}{54}, \frac{33}{54}\); г) \(\frac{35}{75}, \frac{36}{75}\)