Решебник по математике 5 класс Ткачева рабочая тетрадь | Страница 65

\[\boxed{\mathbf{3.}}\]

\[1)\ \frac{2}{3}\ и\ \frac{3}{4}\]

\[НОК(3,4) = 3 \cdot 4 = 12\]

\[\frac{2^{\backslash 4}}{3} = \frac{8}{12};\ \ \frac{3^{\backslash 3}}{4} = \frac{9}{12}\]

\[\frac{8}{12} < \frac{9}{12}\]

\[\frac{2}{3} < \frac{3}{4}.\]

\[2)\ \frac{7}{12}\ и\ \frac{11}{18}\]

\[НОК(12,\ 18) = 36\]

\[\frac{7^{\backslash 3}}{12} = \frac{21}{36};\ \frac{11^{\backslash 2}}{18} = \frac{22}{36}\text{\ \ }\]

\[\frac{21}{36} < \frac{22}{36}\]

\[\frac{7}{12} < \frac{11}{18}.\]

\[3)\ \frac{7}{66}\ и\ \frac{5}{44}\]

\[НОК(66,\ 44) = 132\]

\[\frac{7^{\backslash 2}}{66} = \frac{14}{132};\ \ \frac{5}{44} = \frac{15}{132}.\]

\[\frac{14}{132} < \frac{15}{132}\]

\[\frac{7}{66} < \frac{5}{44}.\]

\[\mathbf{38.\ Сложение\ и\ вычитание\ дробей\ с\ разными\ знаменателями}\]

\[\boxed{\mathbf{1.}}\]

\[1)\ \frac{2}{5}\ и\ \frac{3}{7}\]

\[НОК(5,\ 7) = 35\]

\[\frac{2^{\backslash 7}}{5} + \frac{3^{\backslash 5}}{7} = \frac{14 + 15}{35} = \frac{29}{35}.\]

\[2)\ \frac{5}{21}\ и\ \frac{9}{14}\]

\[НОК(21,\ 14) = 42\]

\[\frac{5^{\backslash 2}}{21} + \frac{9^{\backslash 3}}{14} = \frac{10 + 27}{42} = \frac{37}{42}.\]

\[3)\ \frac{7}{15}\ и\ \frac{3}{40}\]

\[НОК(15,\ 40) = 120\]

\[\frac{7^{\backslash 8}}{15} + \frac{3^{\backslash 3}}{40} = \frac{56 + 9}{120} = \frac{65}{120} = \frac{13}{40}.\]