6.58 Найдите сумму: a) 8/13 + 3/13; б) 31/60 + 29/60; в) 18 + 4/19; г) 23 + 9/10; д) 2 7/9 + 8/9; e) 15 8/11 + 4 3/11; ж) 4 1/2 + 3 1/4; з) 5 1/7 + 3 20/21. Найдите разность: a) 7 3/5 - 1 2/5; б) 28 6/13 - 7 1/13; в) 6 - 2/5; г) 21 - 5/9; д) 4 1/7 - 1 4/7; e) 12 2/5 - 1 4/5; ж) 4 1/2 - 3 1/4; з) 5 1/7 - 3 20/21.

Сумма:

1. а) \[ \frac{8}{13} + \frac{3}{13} = \frac{8+3}{13} = \frac{11}{13} \]
2. б) \[ \frac{31}{60} + \frac{29}{60} = \frac{31+29}{60} = \frac{60}{60} = 1 \]
3. в) \[ 18 + \frac{4}{19} = 18\frac{4}{19} \]
4. г) \[ 23 + \frac{9}{10} = 23\frac{9}{10} \]
5. д) \[ 2\frac{7}{9} + \frac{8}{9} = 2 + \frac{7}{9} + \frac{8}{9} = 2 + \frac{15}{9} = 2 + 1\frac{6}{9} = 3\frac{6}{9} = 3\frac{2}{3} \]
6. е) \[ 15\frac{8}{11} + 4\frac{3}{11} = 15 + 4 + \frac{8}{11} + \frac{3}{11} = 19 + \frac{11}{11} = 19 + 1 = 20 \]
7. ж) \[ 4\frac{1}{2} + 3\frac{1}{4} = 4\frac{2}{4} + 3\frac{1}{4} = 4 + 3 + \frac{2}{4} + \frac{1}{4} = 7 + \frac{3}{4} = 7\frac{3}{4} \]
8. з) \[ 5\frac{1}{7} + 3\frac{20}{21} = 5\frac{3}{21} + 3\frac{20}{21} = 5 + 3 + \frac{3}{21} + \frac{20}{21} = 8 + \frac{23}{21} = 8 + 1\frac{2}{21} = 9\frac{2}{21} \]

Разность:

1. а) \[ 7\frac{3}{5} - 1\frac{2}{5} = 7 - 1 + \frac{3}{5} - \frac{2}{5} = 6 + \frac{1}{5} = 6\frac{1}{5} \]
2. б) \[ 28\frac{6}{13} - 7\frac{1}{13} = 28 - 7 + \frac{6}{13} - \frac{1}{13} = 21 + \frac{5}{13} = 21\frac{5}{13} \]
3. в) \[ 6 - \frac{2}{5} = 5\frac{5}{5} - \frac{2}{5} = 5\frac{3}{5} \]
4. г) \[ 21 - \frac{5}{9} = 20\frac{9}{9} - \frac{5}{9} = 20\frac{4}{9} \]
5. д) \[ 4\frac{1}{7} - 1\frac{4}{7} = 3\frac{8}{7} - 1\frac{4}{7} = 3 - 1 + \frac{8}{7} - \frac{4}{7} = 2 + \frac{4}{7} = 2\frac{4}{7} \]
6. е) \[ 12\frac{2}{5} - 1\frac{4}{5} = 11\frac{7}{5} - 1\frac{4}{5} = 11 - 1 + \frac{7}{5} - \frac{4}{5} = 10 + \frac{3}{5} = 10\frac{3}{5} \]
7. ж) \[ 4\frac{1}{2} - 3\frac{1}{4} = 4\frac{2}{4} - 3\frac{1}{4} = 4 - 3 + \frac{2}{4} - \frac{1}{4} = 1 + \frac{1}{4} = 1\frac{1}{4} \]
8. з) \[ 5\frac{1}{7} - 3\frac{20}{21} = 5\frac{3}{21} - 3\frac{20}{21} = 4\frac{24}{21} - 3\frac{20}{21} = 4 - 3 + \frac{24}{21} - \frac{20}{21} = 1 + \frac{4}{21} = 1\frac{4}{21} \]