Расположите числа в порядке убывания:
а) $\frac{5}{6}, \frac{11}{12}, \frac{13}{14}, \frac{20}{11}$;
б) $\frac{7}{12}, \frac{9}{14}, \frac{11}{21}, \frac{23}{24}$.
6 = 2 * 3;
11 = 11 * 1;
$12 = 2^2 * 3$;
$14 = 2 * 7$;
$НОК(6;11;12;14) = 2^2 * 3 * 7 * 11 = 4 * 21 * 11 = 84 * 11 = 924$;
$\frac{5}{6} = \frac{154 * 5}{154 * 6} = \frac{770}{924}$;
$\frac{11}{12} = \frac{77 * 11}{77 * 12} = \frac{847}{924}$;
$\frac{13}{14} = \frac{66 * 13}{66 * 14} = \frac{858}{924}$;
$\frac{20}{11} = \frac{84 * 20}{84 * 11} = \frac{1680}{924}$;
$\frac{1680}{924} > \frac{858}{924} > \frac{847}{924} > \frac{770}{924}$;
$\frac{20}{11} > \frac{13}{14} > \frac{11}{12} > \frac{5}{6}$.
$12 = 2^2 * 3$;
$14 = 2 * 7$;
$21 = 3 * 7$;
$24 = 2^3 * 3$;
$НОК = 2^3 * 3 * 7 = 8 * 21 = 168$;
$\frac{7}{12} = \frac{14 * 7}{14 * 12} = \frac{98}{168}$;
$\frac{9}{14} = \frac{12 * 9}{12 * 14} = \frac{108}{168}$;
$\frac{11}{21} = \frac{8 * 11}{8 * 21} = \frac{88}{168}$;
$\frac{23}{24} = \frac{7 * 23}{7 * 24} = \frac{161}{168}$;
$\frac{161}{168} > \frac{108}{168} > \frac{98}{168} > \frac{88}{168}$;
$\frac{23}{24} > \frac{9}{14} > \frac{7}{12} > \frac{11}{21}$.
Пожауйста, оцените решение
