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27 tháng 7

Bài 3:

\(a.\dfrac{5}{3}+\left(7+\dfrac{-5}{3}\right)\\ =\dfrac{5}{3}+7+\dfrac{-5}{3}\\ =\left(\dfrac{5}{3}-\dfrac{5}{3}\right)+7\\ =7\\ b.\dfrac{-7}{31}+\left(\dfrac{24}{17}+\dfrac{7}{31}\right)\\ =\dfrac{-7}{31}+\dfrac{24}{17}+\dfrac{7}{31}\\ =\left(\dfrac{7}{31}-\dfrac{7}{31}\right)+\dfrac{24}{17}\\ =\dfrac{24}{17}\\ c.\dfrac{3}{7}+\left(\dfrac{-1}{5}+\dfrac{-3}{7}\right)\\ =\dfrac{3}{7}+\dfrac{-1}{5}+\dfrac{-3}{7}\\ =\left(\dfrac{3}{7}-\dfrac{3}{7}\right)+\dfrac{-1}{5}\\ =-\dfrac{1}{5}\)

Bài 2:

a: \(\dfrac{2}{7}+\dfrac{3}{7}=\dfrac{2+3}{7}=\dfrac{5}{7}\)

b: \(\dfrac{3}{8}+\dfrac{5}{8}=\dfrac{3+5}{8}=\dfrac{8}{8}=1\)

c: \(\dfrac{1}{7}+\dfrac{-4}{7}=\dfrac{1-4}{7}=-\dfrac{3}{7}\)

d: \(\dfrac{7}{-25}+\dfrac{-8}{25}=\dfrac{-7}{25}+\dfrac{-8}{25}=-\dfrac{15}{25}=-\dfrac{3}{5}\)

e: \(\dfrac{6}{18}+\dfrac{-14}{21}=\dfrac{1}{3}-\dfrac{2}{3}=-\dfrac{1}{3}\)

f: \(\dfrac{6}{13}+\dfrac{-14}{39}=\dfrac{18}{39}-\dfrac{14}{39}=\dfrac{4}{39}\)

g: \(-\dfrac{3}{21}+\dfrac{6}{42}=-\dfrac{3}{21}+\dfrac{3}{21}=0\)

h: \(\dfrac{7}{21}+\dfrac{9}{-36}=\dfrac{1}{3}-\dfrac{1}{4}=\dfrac{1}{12}\)

Bài 4:

a: \(\dfrac{6}{5}+\left(3+\dfrac{-1}{5}\right)\)

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

=1+3=4

b: \(-\dfrac{3}{5}+\left(-\dfrac{2}{5}+2\right)\)

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

c: \(-\dfrac{3}{5}+\left(-\dfrac{2}{5}+2\right)\)

\(=-\dfrac{3}{5}-\dfrac{2}{5}+2\)

=2-1=1

d: \(-\dfrac{5}{11}+\left(-\dfrac{6}{11}+1\right)\)

\(=-\dfrac{5}{11}-\dfrac{6}{11}+1=1-1=0\)

e: \(-\dfrac{17}{13}+\left(\dfrac{25}{101}+\dfrac{4}{13}\right)\)

\(=-\dfrac{17}{13}+\dfrac{4}{13}+\dfrac{25}{101}\)

\(=-1+\dfrac{25}{101}=-\dfrac{76}{101}\)