6. Найти значение числового выражения: 1) \(\left(\frac{1}{2}+\frac{1}{3}\right)\cdot\left(\frac{1}{5}-\frac{1}{4}\right)\); 2) \(\left(\frac{2}{7}-\frac{3}{4}\right)\cdot\left(\frac{2}{13}-\frac{1}{2}\right)\); 3) \(4\frac{2}{3}+\frac{1}{4}\cdot\left(1\frac{7}{9}-\frac{4}{9}\right)\); 4) \(5\frac{1}{7}-\frac{1}{7}\cdot\left(1\frac{3}{4}+\frac{1}{4}\right)\); 5) \(\left(3\frac{1}{3}\cdot3^2-17\right):13-0{,}07\).

1. \(\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\), а \(\frac{1}{5}-\frac{1}{4}=-\frac{1}{20}\).

   \(\frac{5}{6}\cdot\left(-\frac{1}{20}\right)=-\frac{5}{120}=-\frac{1}{24}\).

2. \(\frac{2}{7}-\frac{3}{4}=\frac{8-21}{28}=-\frac{13}{28}\), а \(\frac{2}{13}-\frac{1}{2}=\frac{4-13}{26}=-\frac{9}{26}\).

   \(\left(-\frac{13}{28}\right)\cdot\left(-\frac{9}{26}\right)=\frac{9}{56}\).

3. \(1\frac{7}{9}-\frac{4}{9}=\frac{16}{9}-\frac{4}{9}=\frac{4}{3}\).

   \(4\frac{2}{3}+\frac{1}{4}\cdot\frac{4}{3}=\frac{14}{3}+\frac{1}{3}=5\).

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

   \(5\frac{1}{7}-\frac{1}{7}\cdot2=\frac{36}{7}-\frac{2}{7}=\frac{34}{7}=4\frac{6}{7}\).

5. \(3\frac{1}{3}\cdot3^2-17=\frac{10}{3}\cdot9-17=30-17=13\).

   \(13:13-0{,}07=1-0{,}07=0{,}93\).

Ответ: 1) \(-\frac{1}{24}\); 2) \(\frac{9}{56}\); 3) \(5\); 4) \(4\frac{6}{7}\); 5) \(0{,}93\).