1. Закончите действия. a) 7\(\frac{5}{8}\) + 3\(\frac{1}{8}\) = 10 + \(\frac{5}{8} + \frac{1}{8}\) = 10 + \(\frac{6}{8}\) = 10\(\frac{6}{8}\) б) 5\(\frac{3}{10}\) + 2\(\frac{1}{5}\) = 5\(\frac{3}{10}\) + 2\(\frac{2}{10}\) = 7 + \(\frac{3}{10} + \frac{2}{10}\) = 7 + \(\frac{5}{10}\) = 7\(\frac{5}{10}\) в) 5\(\frac{3}{10}\) - 2\(\frac{2}{5}\) = 5\(\frac{3}{10}\) - 2\(\frac{4}{10}\) = 3 + \(\frac{13}{10} - \frac{4}{10}\) = 3 + \(\frac{9}{10}\) = 3\(\frac{9}{10}\) г) 3\(\frac{1}{2}\) - 1\(\frac{3}{4}\) = 3\(\frac{2}{4}\) - 1\(\frac{3}{4}\) = 2\(\frac{6}{4}\) - 1\(\frac{3}{4}\) = 1 + \(\frac{3}{4}\) = 1\(\frac{3}{4}\) д) 5 - 1\(\frac{1}{3}\) = 4\(\frac{3}{3}\) - 1\(\frac{1}{3}\) = 4 + \(\frac{2}{3}\) = 4\(\frac{2}{3}\)

Решение:

1. а) \( 7\frac{5}{8} + 3\frac{1}{8} = (7+3) + (\frac{5}{8} + \frac{1}{8}) = 10 + \frac{6}{8} = 10\frac{6}{8} \)


2. б) \( 5\frac{3}{10} + 2\frac{1}{5} = 5\frac{3}{10} + 2\frac{2}{10} = (5+2) + (\frac{3}{10} + \frac{2}{10}) = 7 + \frac{5}{10} = 7\frac{5}{10} \)


3. в) \( 5\frac{3}{10} - 2\frac{2}{5} = 5\frac{3}{10} - 2\frac{4}{10} \). Чтобы вычесть дробь \(\frac{4}{10}\) из \(\frac{3}{10}\), представим 5 как \( 4 + \frac{10}{10} \), тогда \( 4\frac{13}{10} - 2\frac{4}{10} = (4-2) + (\frac{13}{10} - \frac{4}{10}) = 2 + \frac{9}{10} = 2\frac{9}{10} \).


4. г) \( 3\frac{1}{2} - 1\frac{3}{4} = 3\frac{2}{4} - 1\frac{3}{4} \). Чтобы вычесть \(\frac{3}{4}\) из \(\frac{2}{4}\), представим 3 как \( 2 + \frac{4}{4} \), тогда \( 2\frac{6}{4} - 1\frac{3}{4} = (2-1) + (\frac{6}{4} - \frac{3}{4}) = 1 + \frac{3}{4} = 1\frac{3}{4} \)


5. д) \( 5 - 1\frac{1}{3} = 4\frac{3}{3} - 1\frac{1}{3} = (4-1) + (\frac{3}{3} - \frac{1}{3}) = 3 + \frac{2}{3} = 3\frac{2}{3} \)

Ответ: а) \( 10\frac{6}{8} \); б) \( 7\frac{5}{10} \); в) \( 2\frac{9}{10} \); г) \( 1\frac{3}{4} \); д) \( 3\frac{2}{3} \).