Приведите дроби к наименьшему общему знаменателю:
а) $\frac{2}{5}, \frac{7}{10}, \frac{13}{15}$ и $\frac{9}{20}$;
б) $\frac{5}{6}, \frac{7}{9}, \frac{1}{4}$ и $\frac{2}{3}$;
в) $\frac{5}{24}, \frac{7}{18}, \frac{3}{40}$ и $\frac{11}{20}$;
г) $\frac{3}{4}, \frac{13}{20}, \frac{41}{60}, \frac{17}{75}$ и $\frac{11}{25}$.
$5 = 1 * 5$;
$10 = 2 * 5$;
$15 = 3 * 5$;
$20 = 2^2 * 5$;
$НОК(5;10;15;20) = 2^2 * 3 * 5 = 12 * 5 = 60$;
$\frac{2}{5} = \frac{12 * 2}{12 * 5} = \frac{24}{60}$;
$\frac{7}{10} = \frac{6 * 7}{6 * 10} = \frac{42}{60}$;
$\frac{13}{15} = \frac{4 * 13}{4 * 15} = \frac{52}{60}$;
$\frac{9}{20} = \frac{3 * 9}{3 * 20} = \frac{27}{60}$.
$3 = 1 * 3$;
$4 = 2^2$;
$6 = 2 * 3$;
$9 = 3^2$;
$НОК(3;4;6;9) = 2^2 * 3^2 = 4 * 9 = 36$;
$\frac{5}{6} = \frac{6 * 5}{6 * 6} = \frac{30}{36}$;
$\frac{7}{9} = \frac{4 * 7}{4 * 9} = \frac{28}{36}$;
$\frac{1}{4} = \frac{9 * 1}{9 * 4} = \frac{9}{36}$;
$\frac{2}{3} = \frac{12 * 2}{12 * 3} = \frac{24}{36}$.
$18 = 2 * 3^2$;
$20 = 2^2 * 5$;
$24 = 2^3 * 3$;
$40 = 2^3 * 5$;
$НОК(18;20;24;40) = 2^3 * 3^2 * 5 = 8 * 9 * 5 = 9 * 40 = 360$;
$\frac{5}{24} = \frac{15 * 5}{15 * 24} = \frac{75}{360}$;
$\frac{7}{18} = \frac{20 * 7}{20 * 18} = \frac{140}{360}$;
$\frac{3}{40} = \frac{9 * 3}{9 * 40} = \frac{27}{360}$;
$\frac{11}{20} = \frac{18 * 11}{18 * 20} = \frac{198}{360}$.
$4 = 2^2$;
$20 = 2^2 * 5$;
$25 = 5^2$;
$60 = 2^2 * 3 * 5$;
$75 = 3 * 5^2$;
$НОК(4;20;25;60;75) = 2^2 * 3 * 5^2 = 4 * 3 * 25 = 3 * 100 = 300$;
$\frac{3}{4} = \frac{75 * 3}{75 * 4} = \frac{225}{300}$;
$\frac{13}{20} = \frac{15 * 13}{15 * 20} = \frac{195}{300}$;
$\frac{41}{60} = \frac{5 * 41}{5 * 60} = \frac{205}{300}$;
$\frac{17}{75} = \frac{4 * 17}{4 * 75} = \frac{68}{300}$;
$\frac{11}{25} = \frac{12 * 11}{12 * 25} = \frac{132}{300}$.
Пожауйста, оцените решение
