2.164 Найдите сумму: a) \(\frac{1}{6} + \frac{5}{8}\); б) \(\frac{7}{8} + \frac{5}{14}\); в) \(\frac{7}{10} + \frac{3}{25}\); г) \(\frac{27}{70} + \frac{16}{105}\); д) \(\frac{11}{18} + \frac{1}{81}\); e) \(\frac{5}{12} + \frac{3}{44}\); ж) \(\frac{15}{56} + \frac{11}{84}\); з) \(\frac{11}{21} + \frac{3}{49}\);

Решение:

1. a) \(\frac{1}{6} + \frac{5}{8} = \frac{1 \cdot 4}{6 \cdot 4} + \frac{5 \cdot 3}{8 \cdot 3} = \frac{4}{24} + \frac{15}{24} = \frac{4+15}{24} = \frac{19}{24}\)

   Ответ: \(\frac{19}{24}\)

2. б) \(\frac{7}{8} + \frac{5}{14} = \frac{7 \cdot 7}{8 \cdot 7} + \frac{5 \cdot 4}{14 \cdot 4} = \frac{49}{56} + \frac{20}{56} = \frac{49+20}{56} = \frac{69}{56} = 1\frac{13}{56}\)

   Ответ: \(1\frac{13}{56}\)

3. в) \(\frac{7}{10} + \frac{3}{25} = \frac{7 \cdot 5}{10 \cdot 5} + \frac{3 \cdot 2}{25 \cdot 2} = \frac{35}{50} + \frac{6}{50} = \frac{35+6}{50} = \frac{41}{50}\)

   Ответ: \(\frac{41}{50}\)

4. г) \(\frac{27}{70} + \frac{16}{105} = \frac{27 \cdot 3}{70 \cdot 3} + \frac{16 \cdot 2}{105 \cdot 2} = \frac{81}{210} + \frac{32}{210} = \frac{81+32}{210} = \frac{113}{210}\)

   Ответ: \(\frac{113}{210}\)

5. д) \(\frac{11}{18} + \frac{1}{81} = \frac{11 \cdot 9}{18 \cdot 9} + \frac{1 \cdot 2}{81 \cdot 2} = \frac{99}{162} + \frac{2}{162} = \frac{99+2}{162} = \frac{101}{162}\)

   Ответ: \(\frac{101}{162}\)

6. е) \(\frac{5}{12} + \frac{3}{44} = \frac{5 \cdot 11}{12 \cdot 11} + \frac{3 \cdot 3}{44 \cdot 3} = \frac{55}{132} + \frac{9}{132} = \frac{55+9}{132} = \frac{64}{132} = \frac{16}{33}\)

   Ответ: \(\frac{16}{33}\)

7. ж) \(\frac{15}{56} + \frac{11}{84} = \frac{15 \cdot 3}{56 \cdot 3} + \frac{11 \cdot 2}{84 \cdot 2} = \frac{45}{168} + \frac{22}{168} = \frac{45+22}{168} = \frac{67}{168}\)

   Ответ: \(\frac{67}{168}\)

8. з) \(\frac{11}{21} + \frac{3}{49} = \frac{11 \cdot 7}{21 \cdot 7} + \frac{3 \cdot 3}{49 \cdot 3} = \frac{77}{147} + \frac{9}{147} = \frac{77+9}{147} = \frac{86}{147}\)

   Ответ: \(\frac{86}{147}\)