Tính nhanh nếu có thể
a)$\frac{-25}{37}$ + [(-1) + $\frac{-12}{37}$]
b)$\frac{4}{5}$ + $\frac{2019}{2020}$ + $\frac{-40}{50}$
c)$\frac{-13}{17}$ + $\frac{17}{18}$ + $\frac{4}{-17}$
d)$\frac{-1}{3}$ + $\frac{25}{27}$ + $\frac{-4}{16}$ + $\frac{5}{-12}$
e)$\frac{-2}{5}$ + $\frac{13}{15}$ + $\frac{-45}{75}$ + $\frac{6}{45}$ + $\frac{2020}{2021}$
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+$\frac{2020}{2021}$
=$\frac{2020}{2021}$