Đáp án:

$\begin{array}{l}
a)\dfrac{{ - 25}}{{37}} + \left[ {\left( { - 1} \right) + \dfrac{{ - 12}}{{37}}} \right]\\
 = \dfrac{{ - 25}}{{37}} - 1 - \dfrac{{12}}{{37}}\\
 = \dfrac{{ - 25 - 12}}{{37}} - 1\\
 = \dfrac{{ - 37}}{{37}} - 1\\
 =  - 1 - 1\\
 =  - 2\\
b)\dfrac{4}{5} + \dfrac{{2010}}{{2020}} + \dfrac{{ - 40}}{{50}}\\
 = \dfrac{4}{5} - \dfrac{4}{5} + \dfrac{{201}}{{202}}\\
 = \dfrac{{201}}{{202}}\\
c)\dfrac{{ - 13}}{{17}} + \dfrac{{17}}{{18}} + \dfrac{4}{{ - 17}}\\
 = \dfrac{{ - 13}}{{17}} - \dfrac{4}{{17}} + \dfrac{{17}}{{18}}\\
 =  - \dfrac{{17}}{{17}} + \dfrac{{17}}{{18}}\\
 =  - 1 + \dfrac{{17}}{{18}}\\
 = \dfrac{{ - 1}}{{18}}\\
d)\dfrac{{ - 1}}{3} + \dfrac{{25}}{{27}} + \dfrac{{ - 4}}{{16}} + \dfrac{5}{{ - 12}}\\
 = \dfrac{{ - 1}}{3} + \dfrac{{25}}{{27}} - \dfrac{1}{4} - \dfrac{5}{{12}}\\
 = \dfrac{{ - 4 - 3 - 5}}{{12}} + \dfrac{{25}}{{27}}\\
 =  - 1 + \dfrac{{25}}{{27}}\\
 = \dfrac{2}{{17}}\\
e)\dfrac{{ - 2}}{5} + \dfrac{{13}}{{15}} + \dfrac{{ - 45}}{{75}} + \dfrac{6}{{45}} + \dfrac{{2020}}{{2021}}\\
 = \dfrac{{ - 2}}{5} + \dfrac{{13}}{{15}} - \dfrac{3}{5} + \dfrac{2}{{15}} + \dfrac{{2020}}{{2021}}\\
 = \dfrac{{ - 2 - 3}}{5} + \dfrac{{13 + 2}}{{15}} + \dfrac{{2020}}{{2021}}\\
 =  - 1 + 1 + \dfrac{{2020}}{{2021}}\\
 = \dfrac{{2020}}{{2021}}
\end{array}$

Đáp án:

a)$\frac{-25}{37}$+ [(-1)+ $\frac{-12}{37}$]

=$\frac{-25}{37}$+ (-1)+ $\frac{-12}{37}$

= $\frac{-25}{37}$+ $\frac{-12}{37}$] + (-1)

= $\frac{-37}{37}$ + (-1)

= (-1)+(-1)

= (-2)

b) $\frac{4}{5}$+ $\frac{2019}{2020}$ +$\frac{-40}{50}$

= $\frac{40}{50}$+ $\frac{2019}{2020}$ +$\frac{-40}{50}$ 

= $\frac{40}{50}$ +$\frac{-40}{50}$ +$\frac{2019}{2020}$ 

= 0+ $\frac{2019}{2020}$ 

= $\frac{2019}{2020}$ 

c) $\frac{-13}{17}$+$\frac{17}{18}$+$\frac{4}{-17}$ 

= $\frac{-13}{17}$+$\frac{17}{18}$+$\frac{-4}{17}$ 

= $\frac{-13}{17}$+ $\frac{-4}{17}$ + $\frac{17}{18}$ 

= 1 + $\frac{17}{18}$ 

= $\frac{18}{18}$+$\frac{17}{18}$ 

=$\frac{35}{18}$ 

d) $\frac{-1}{3}$+$\frac{25}{27}$+$\frac{-4}{16}$ $\frac{5}{-12}$ 

= $\frac{-1}{3}$+$\frac{25}{27}$-$\frac{1}{4}$- $\frac{5}{12}$ 

=$\frac{-4-3-5}{12}$ +$\frac{25}{27}$ 

= -1+ $\frac{25}{27}$ 

=$\frac{2}{17}$ 

e)$\frac{-2}{5}$ +$\frac{13}{15}$+ $\frac{-45}{75}$+ $\frac{6}{45}$+ $\frac{2020}{2021}$

=$\frac{-2}{5}$+ $\frac{13}{15}$+ $\frac{3}{5}$+$\frac{2}{15}$+ $\frac{2020}{2021}$ 

=$\frac{-2-3}{5}$+ $\frac{13+2}{15}$ +$\frac{2020}{2021}$ 

=-1+1+$\frac{2020}{2021}$ 

=0+$\frac{2020}{2021}$ 

=$\frac{2020}{2021}$