13: \(=\dfrac{4}{9}\cdot\left(-7\right)+\left(6+\dfrac{5}{9}\right)\cdot\left(-7\right)\)

\(=\left(-7\right)\left(\dfrac{4}{9}+6+\dfrac{5}{9}\right)=\left(-7\right)\cdot7=-49\)

14: \(=\left(\dfrac{-3}{4}+\dfrac{5}{13}\right)\cdot\dfrac{7}{2}-\left(\dfrac{9}{4}+\dfrac{8}{13}\right)\cdot\dfrac{7}{2}\)

\(=\dfrac{7}{2}\left(-\dfrac{3}{4}+\dfrac{5}{13}-\dfrac{9}{4}-\dfrac{8}{13}\right)\)

\(=\dfrac{7}{2}\left(-3-\dfrac{3}{13}\right)=\dfrac{7}{2}\cdot\dfrac{-42}{13}=\dfrac{-147}{13}\)

a)\(\dfrac{-10}{11}.\dfrac{8}{9}+\dfrac{7}{18}.\dfrac{10}{11}\)

=\(\dfrac{10}{11}.\dfrac{-8}{9}+\dfrac{7}{18}.\dfrac{10}{11}\)

=\(\dfrac{10}{11}(\dfrac{-8}{9}+\dfrac{7}{18})\)

=\(\dfrac{10}{11}.\dfrac{-1}{2}\)

=\(\dfrac{-5}{11}\)

b; 

B = \(\dfrac{3}{14}\) : \(\dfrac{1}{28}\) - \(\dfrac{13}{21}\): \(\dfrac{1}{28}\) + \(\dfrac{29}{42}\) : \(\dfrac{1}{28}\) - 8

B = (\(\dfrac{3}{14}\) - \(\dfrac{13}{21}\) + \(\dfrac{29}{42}\)) - 8

B = (\(\dfrac{9}{42}\) - \(\dfrac{26}{42}\) + \(\dfrac{29}{42}\)) - 8

B = (\(\dfrac{-17}{42}\) + \(\dfrac{29}{42}\)) - 8

B = \(\dfrac{2}{7}\) - 8

B = \(\dfrac{2}{7}-\dfrac{56}{7}\)

B = - \(\dfrac{54}{7}\)

c; C = -1\(\dfrac{5}{7}\).15 + \(\dfrac{2}{7}\)(-15) + (-105).(\(\dfrac{2}{3}\) - \(\dfrac{4}{5}\) + \(\dfrac{1}{7}\))

C = - 15.(- 1 - \(\dfrac{5}{7}\) + \(\dfrac{2}{7}\) + \(\dfrac{14}{3}\) - \(\dfrac{28}{5}\) + \(1\))

C = -15.[(1 - 1) - (\(\dfrac{5}{7}\) - \(\dfrac{2}{7}\)) + \(\dfrac{14}{3}\) - \(\dfrac{28}{5}\)]

C = -15.[0 - \(\dfrac{3}{7}\) + \(\dfrac{14}{3}\) - \(\dfrac{28}{5}\)]

C = -15 . [- \(\dfrac{45}{105}\) + \(\dfrac{490}{105}\)  - \(\dfrac{588}{105}\)]

C = -15. [ \(\dfrac{445}{105}\) - \(\dfrac{588}{105}\)]

C = - 15.(- \(\dfrac{143}{105}\))

C = \(\dfrac{143}{7}\)

7: \(=\dfrac{-12}{7}\cdot15+\dfrac{2}{7}\cdot\left(-15\right)+\left(-105\right)\cdot\dfrac{70-84+15}{105}\)

\(=\dfrac{-12\cdot15+2\cdot\left(-15\right)}{7}-1\)

\(=\dfrac{-15\cdot14}{7}-1=-15\cdot2-1=-31\)

8: \(=\dfrac{13}{29}\cdot\dfrac{29}{5}-\dfrac{13}{29}\cdot\dfrac{45}{8}-\dfrac{45}{8}\cdot\dfrac{9}{8}+\dfrac{45}{8}\cdot\dfrac{13}{29}\)

\(=-\dfrac{1193}{320}\)

a) \(\left(\dfrac{2}{3}-\dfrac{1}{2}-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{4}-\dfrac{1}{7}\right)\)

\(=-\dfrac{1}{6}\cdot\dfrac{17}{28}\)

\(=-\dfrac{17}{168}\)

b)  \(\left(\dfrac{15}{21}\div\dfrac{5}{7}\right)\div\left(\dfrac{6}{5}\div2\right)\)

\(=1\div\dfrac{3}{5}\)

\(=\dfrac{5}{3}\)

(2/3 - 1/2 - 1/3) . (1-1/4 - 1/7)

= -1/6 . 17/28

= -17/168

(15/21 : 5/7 ) : (6/5 : 2) 

= 1 : 3/5

= 5/3

11: \(=\dfrac{-5}{7}+\dfrac{5}{67}+\dfrac{13}{30}+\dfrac{1}{2}-\dfrac{11}{6}+\dfrac{17}{14}+\dfrac{2}{5}\)

\(=\left(\dfrac{-5}{7}+\dfrac{1}{2}+\dfrac{17}{14}\right)+\left(\dfrac{13}{30}-\dfrac{11}{6}+\dfrac{2}{5}\right)+\dfrac{5}{67}\)

\(=\dfrac{-10+7+17}{14}+\dfrac{13-55+12}{30}+\dfrac{5}{67}\)

\(=1-1+\dfrac{5}{67}=\dfrac{5}{67}\)

12: \(=\dfrac{-1}{4}\cdot\dfrac{152}{11}-\dfrac{1}{4}\cdot\dfrac{68}{11}\)

\(=\dfrac{-1}{4}\left(\dfrac{152}{11}+\dfrac{68}{11}\right)=-\dfrac{1}{4}\cdot20=-5\)

e)\(16\dfrac{2}{7}:\left(-\dfrac{3}{5}\right)+28\dfrac{2}{7}:\left(-\dfrac{3}{5}\right)\)

=\(\left(16\dfrac{2}{7}+28\dfrac{2}{7}\right):\left(-\dfrac{3}{5}\right)\)

=\(\dfrac{312}{7}\)\(:\left(-\dfrac{3}{5}\right)\)

=\(-\dfrac{516}{7}\)

a)\(\dfrac{7}{8}.\left(\dfrac{2}{12}+\dfrac{4}{10}\right)\)

=\(\dfrac{7}{8}.\left(\dfrac{1}{6}+\dfrac{2}{5}\right)\)

=\(\dfrac{7}{8}.\)\(\dfrac{17}{30}\)

=\(\dfrac{119}{240}\)

b)\(\dfrac{3}{2}-\dfrac{5}{6}:\left(\dfrac{1}{2}\right)^2+\sqrt{4}\)

=\(\dfrac{3}{2}-\dfrac{5}{6}:\dfrac{1}{4}+2\)

=\(\dfrac{3}{2}-\dfrac{10}{3}+2\)

=\(-\dfrac{11}{6}\) +2

=\(\dfrac{1}{6}\)

2: \(=\dfrac{203}{60}\cdot\dfrac{81}{1225}=\dfrac{783}{3500}\)

9: 

\(=5+\dfrac{1}{5}-\dfrac{2}{9}-2+\dfrac{1}{23}+\dfrac{73}{35}-\dfrac{5}{6}-8-\dfrac{2}{7}+\dfrac{1}{18}\)

\(=\left(5-2-8\right)+\left(\dfrac{1}{5}+\dfrac{73}{35}-\dfrac{2}{7}\right)+\left(-\dfrac{2}{9}+\dfrac{1}{18}-\dfrac{5}{6}\right)+\dfrac{1}{23}\)

\(=\left(-5\right)+\dfrac{7+73-10}{35}+\dfrac{-4+1-15}{18}+\dfrac{1}{23}\)

\(=-5+2-1+\dfrac{1}{23}=-4+\dfrac{1}{23}=-\dfrac{91}{23}\)

10: \(=\left(\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}\right)+\left(\dfrac{-3}{4}-\dfrac{2}{9}-\dfrac{1}{36}\right)+\dfrac{1}{64}\)

\(=\dfrac{5+9+1}{15}+\dfrac{-27-8-1}{36}+\dfrac{1}{64}\)

=1/64