Приведите дроби к наименьшему общему знаменателю:
а) $\frac{3}{28}$ и $\frac{17}{42}$;
б) $\frac{4}{15}, \frac{7}{20}$ и $\frac{3}{10}$;
в) $\frac{25}{104}$ и $\frac{37}{520}$;
г) $\frac{1}{12}, \frac{1}{18}$ и $\frac{1}{20}$;
д) $\frac{7}{132}$ и $\frac{9}{154}$;
е) $\frac{2}{15}, \frac{3}{35}$ и $\frac{5}{21}$.
$28 = 2^2 * 7$;
$42 = 2 * 3 * 7$;
$НОК(28;42) = 2^2 * 3 * 7 = 4 * 21 = 84$;
$\frac{3}{28} = \frac{3 * 3}{3 * 28} = \frac{9}{84}$;
$\frac{17}{42} = \frac{2 * 17}{2 * 42} = \frac{34}{84}$.
$15 = 3 * 5$;
$20 = 2^2 * 5$;
$10 = 2 * 5$;
$НОК(10;15;20) = 2^2 * 3 * 5 = 4 * 15 = 60$;
$\frac{4}{15} = \frac{4 * 4}{4 * 15} = \frac{16}{60}$;
$\frac{7}{20} = \frac{3 * 7}{3 * 20} = \frac{21}{60}$;
$\frac{3}{10} = \frac{6 * 3}{6 * 10} = \frac{18}{60}$.
$
\begin{array}{r|l}
104 & 2\\
52 & 2\\
26 & 2\\
13 & 13\\
1 &
\end{array}
$
$
\begin{array}{r|l}
520 & 2\\
260 & 2\\
130 & 2\\
65 & 5\\
13 & 13\\
1 &
\end{array}
$
$104 = 2^3 * 13$;
$520 = 2^3 * 5 * 13$;
$НОК(104;520) = 2^3 * 5 * 13 = 8 * 5 * 13 = 40 * 13 = 520$;
$\frac{25}{104} = \frac{5 * 25}{5 * 104} = \frac{125}{502}$;
$\frac{37}{520}$.
$12 = 2^2 * 3$;
$18 = 2 * 3^2$;
$20 = 2^2 * 5$;
$НОК(12;18;20) = 2^2 * 3^2 * 5 = 4 * 9 * 5 = 20 * 9 = 180$;
$\frac{1}{12} = \frac{15 * 1}{15 * 12} = \frac{15}{180}$;
$\frac{1}{18} = \frac{10 * 1}{10 * 18} = \frac{10}{180}$;
$\frac{1}{20} = \frac{9 * 1}{9 * 20} = \frac{9}{180}$.
$
\begin{array}{r|l}
132 & 2\\
66 & 2\\
33 & 3\\
11 & 11\\
1 &
\end{array}
$
$
\begin{array}{r|l}
154 & 2\\
77 & 7\\
11 & 11\\
1 &
\end{array}
$
$132 = 2^2 * 3 * 11$;
$154 = 2 * 7 * 11$;
$НОК(132;154) = 2^2 * 3 * 7 * 11 = 4 * 3 * 77 = 12 * 77 = 924$;
$\frac{7}{132} = \frac{7 * 7}{7 * 132} = \frac{49}{924}$;
$\frac{9}{154} = \frac{6 * 9}{6 * 132} = \frac{54}{924}$.
$15 = 3 * 5$;
$35 = 5 * 7$;
$21 = 3 * 7$;
НОК(15;21;35) = 3 * 5 * 7 = 15 * 7 = 105;
$\frac{2}{15} = \frac{7 * 2}{7 * 15} = \frac{14}{105}$;
$\frac{3}{35} = \frac{3 * 3}{3 * 35} = \frac{9}{105}$;
$\frac{5}{21} = \frac{5 * 5}{5 * 21} = \frac{25}{105}$.
Пожауйста, оцените решение