5.389 Приведите к общему знаменателю дроби: a) \(\frac{5}{9}\) и \(\frac{1}{4}\); в) \(\frac{3}{20}\) и \(\frac{5}{24}\); д) \(\frac{6}{17}\) и \(\frac{2}{11}\); б) \(\frac{7}{10}\) и \(\frac{4}{15}\); г) \(\frac{8}{11}\) и \(\frac{35}{44}\); e) \(\frac{17}{24}\) и \(\frac{5}{8}\).

a) \(\frac{5}{9}\) и \(\frac{1}{4}\); общий знаменатель 36. \(\frac{5 \cdot 4}{9 \cdot 4} = \frac{20}{36}\); \(\frac{1 \cdot 9}{4 \cdot 9} = \frac{9}{36}\)

в) \(\frac{3}{20}\) и \(\frac{5}{24}\); общий знаменатель 120. \(\frac{3 \cdot 6}{20 \cdot 6} = \frac{18}{120}\); \(\frac{5 \cdot 5}{24 \cdot 5} = \frac{25}{120}\)

д) \(\frac{6}{17}\) и \(\frac{2}{11}\); общий знаменатель 187. \(\frac{6 \cdot 11}{17 \cdot 11} = \frac{66}{187}\); \(\frac{2 \cdot 17}{11 \cdot 17} = \frac{34}{187}\)

б) \(\frac{7}{10}\) и \(\frac{4}{15}\); общий знаменатель 30. \(\frac{7 \cdot 3}{10 \cdot 3} = \frac{21}{30}\); \(\frac{4 \cdot 2}{15 \cdot 2} = \frac{8}{30}\)

г) \(\frac{8}{11}\) и \(\frac{35}{44}\); общий знаменатель 44. \(\frac{8 \cdot 4}{11 \cdot 4} = \frac{32}{44}\); \(\frac{35}{44}\)

e) \(\frac{17}{24}\) и \(\frac{5}{8}\); общий знаменатель 24. \(\frac{17}{24}\); \(\frac{5 \cdot 3}{8 \cdot 3} = \frac{15}{24}\)

Ответ: а) \(\frac{20}{36}\) и \(\frac{9}{36}\); в) \(\frac{18}{120}\) и \(\frac{25}{120}\); д) \(\frac{66}{187}\) и \(\frac{34}{187}\); б) \(\frac{21}{30}\) и \(\frac{8}{30}\); г) \(\frac{32}{44}\) и \(\frac{35}{44}\); e) \(\frac{17}{24}\) и \(\frac{15}{24}\)