5.444 Сравните дроби: a) 1/5 и 3/25; б) 3/4 и 11/12; в) 3/4 и 13/20; г) 4/9 и 16/36; д) 3/8 и 7/12; e) 7/12 и 7/16. 5.445 Вычислите: a) 1/2 + 1/3; б) 1/3 + 2/7; в) 2/5 + 1/3; г) 3/7 + 4/9; д) 5/9 - 1/6; e) 3/4 - 1/3; ж) 1/6 + 1/3; з) 9/5 - 7/10; и) 1/2 - 3/8; к) 7/15 - 3/10; л) 3/8 + 5/12; м) 5/9 - 1/6; н) 5/11 + 3/5; о) 17/30 - 3/6; п) 17/35 - 4/15.

5.444 Сравните дроби:

a) \(\frac{1}{5}\) и \(\frac{3}{25}\)

Приведем первую дробь к знаменателю 25: \(\frac{1}{5} = \frac{1 \cdot 5}{5 \cdot 5} = \frac{5}{25}\)

Сравним: \(\frac{5}{25} > \frac{3}{25}\), значит \(\frac{1}{5} > \frac{3}{25}\)

б) \(\frac{3}{4}\) и \(\frac{11}{12}\)

Приведем первую дробь к знаменателю 12: \(\frac{3}{4} = \frac{3 \cdot 3}{4 \cdot 3} = \frac{9}{12}\)

Сравним: \(\frac{9}{12} < \frac{11}{12}\), значит \(\frac{3}{4} < \frac{11}{12}\)

в) \(\frac{3}{4}\) и \(\frac{13}{20}\)

Приведем первую дробь к знаменателю 20: \(\frac{3}{4} = \frac{3 \cdot 5}{4 \cdot 5} = \frac{15}{20}\)

Сравним: \(\frac{15}{20} > \(\frac{13}{20}\), значит \(\frac{3}{4} > \frac{13}{20}\)

г) \(\frac{4}{9}\) и \(\frac{16}{36}\)

Приведем первую дробь к знаменателю 36: \(\frac{4}{9} = \frac{4 \cdot 4}{9 \cdot 4} = \frac{16}{36}\)

Сравним: \(\frac{16}{36} = \frac{16}{36}\), значит \(\frac{4}{9} = \frac{16}{36}\)

д) \(\frac{3}{8}\) и \(\frac{7}{12}\)

Приведем дроби к общему знаменателю 24: \(\frac{3}{8} = \frac{3 \cdot 3}{8 \cdot 3} = \frac{9}{24}\), \(\frac{7}{12} = \frac{7 \cdot 2}{12 \cdot 2} = \frac{14}{24}\)

Сравним: \(\frac{9}{24} < \frac{14}{24}\), значит \(\frac{3}{8} < \frac{7}{12}\)

e) \(\frac{7}{12}\) и \(\frac{7}{16}\)

У этих дробей одинаковые числители, значит, больше та дробь, у которой знаменатель меньше.

Сравним: \(12 < 16\), значит \(\frac{7}{12} > \frac{7}{16}\)

5.445 Вычислите:

а) \(\frac{1}{2} + \frac{1}{3}\) = \(\frac{1 \cdot 3 + 1 \cdot 2}{6}\) = \(\frac{3 + 2}{6}\) = \(\frac{5}{6}\)

б) \(\frac{1}{3} + \frac{2}{7}\) = \(\frac{1 \cdot 7 + 2 \cdot 3}{21}\) = \(\frac{7 + 6}{21}\) = \(\frac{13}{21}\)

в) \(\frac{2}{5} + \frac{1}{3}\) = \(\frac{2 \cdot 3 + 1 \cdot 5}{15}\) = \(\frac{6 + 5}{15}\) = \(\frac{11}{15}\)

г) \(\frac{3}{7} + \frac{4}{9}\) = \(\frac{3 \cdot 9 + 4 \cdot 7}{63}\) = \(\frac{27 + 28}{63}\) = \(\frac{55}{63}\)

д) \(\frac{5}{9} - \frac{1}{6}\) = \(\frac{5 \cdot 2 - 1 \cdot 3}{18}\) = \(\frac{10 - 3}{18}\) = \(\frac{7}{18}\)

е) \(\frac{3}{4} - \frac{1}{3}\) = \(\frac{3 \cdot 3 - 1 \cdot 4}{12}\) = \(\frac{9 - 4}{12}\) = \(\frac{5}{12}\)

ж) \(\frac{1}{6} + \frac{1}{3}\) = \(\frac{1 + 1 \cdot 2}{6}\) = \(\frac{1 + 2}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

з) \(\frac{9}{5} - \frac{7}{10}\) = \(\frac{9 \cdot 2 - 7}{10}\) = \(\frac{18 - 7}{10}\) = \(\frac{11}{10}\) = 1 \(\frac{1}{10}\)

и) \(\frac{1}{2} - \frac{3}{8}\) = \(\frac{1 \cdot 4 - 3}{8}\) = \(\frac{4 - 3}{8}\) = \(\frac{1}{8}\)

к) \(\frac{7}{15} - \frac{3}{10}\) = \(\frac{7 \cdot 2 - 3 \cdot 3}{30}\) = \(\frac{14 - 9}{30}\) = \(\frac{5}{30}\) = \(\frac{1}{6}\)

л) \(\frac{3}{8} + \frac{5}{12}\) = \(\frac{3 \cdot 3 + 5 \cdot 2}{24}\) = \(\frac{9 + 10}{24}\) = \(\frac{19}{24}\)

м) \(\frac{5}{9} - \frac{1}{6}\) = \(\frac{5 \cdot 2 - 1 \cdot 3}{18}\) = \(\frac{10 - 3}{18}\) = \(\frac{7}{18}\)

н) \(\frac{5}{11} + \frac{3}{5}\) = \(\frac{5 \cdot 5 + 3 \cdot 11}{55}\) = \(\frac{25 + 33}{55}\) = \(\frac{58}{55}\) = 1 \(\frac{3}{55}\)

о) \(\frac{17}{30} - \frac{3}{6}\) = \(\frac{17 - 3 \cdot 5}{30}\) = \(\frac{17 - 15}{30}\) = \(\frac{2}{30}\) = \(\frac{1}{15}\)

п) \(\frac{17}{35} - \frac{4}{15}\) = \(\frac{17 \cdot 3 - 4 \cdot 7}{105}\) = \(\frac{51 - 28}{105}\) = \(\frac{23}{105}\)

Ответ: См. решение