Question

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Answer 1

Bài 3:

a: \(A=49\dfrac{8}{23}-\left(5\dfrac{7}{32}+14\dfrac{8}{23}\right)\)

\(=49+\dfrac{8}{23}-\left(5+\dfrac{7}{32}+14+\dfrac{8}{23}\right)\)

\(=49+\dfrac{8}{23}-19-\dfrac{7}{32}-\dfrac{8}{23}\)

\(=30-\dfrac{7}{32}=\dfrac{953}{32}\)

b: \(B=71\dfrac{38}{45}-\left(43\dfrac{8}{45}-1\dfrac{17}{57}\right)\)

\(=71+\dfrac{38}{45}-\left(43+\dfrac{8}{45}-1-\dfrac{17}{57}\right)\)

\(=71+\dfrac{38}{45}-42-\dfrac{8}{45}+\dfrac{17}{57}\)

\(=29+\dfrac{30}{45}+\dfrac{17}{57}\)

\(=\dfrac{1708}{57}\)

c: \(C=\dfrac{-3}{7}\cdot\dfrac{5}{9}+\dfrac{4}{9}\cdot\dfrac{-3}{7}+2\dfrac{3}{7}\)

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

\(=-\dfrac{3}{7}+2+\dfrac{3}{7}\)

=2

d: \(D=\left(19\dfrac{5}{8}:\dfrac{7}{12}-13\dfrac{1}{4}:\dfrac{7}{12}\right):\dfrac{4}{5}\)

\(=\dfrac{12}{7}\left(19+\dfrac{5}{8}-13-\dfrac{1}{4}\right)\cdot\dfrac{5}{4}\)

\(=\dfrac{12}{7}\left(6+\dfrac{3}{8}\right)\cdot\dfrac{5}{4}\)

\(=\dfrac{60}{28}\cdot\dfrac{51}{8}=\dfrac{765}{56}\)

Bài 2:

a: \(-\dfrac{3}{7}+\dfrac{5}{13}+\dfrac{-4}{13}\)

\(=-\dfrac{3}{7}+\dfrac{5-4}{13}\)

\(=-\dfrac{3}{7}+\dfrac{1}{13}=\dfrac{-39+7}{91}=-\dfrac{22}{91}\)

b: \(-\dfrac{5}{21}+\dfrac{-2}{21}+\dfrac{8}{24}\)

\(=\dfrac{-5-2}{21}+\dfrac{1}{3}\)

\(=-\dfrac{7}{21}+\dfrac{7}{21}=0\)

c: \(-\dfrac{5}{9}+\dfrac{8}{15}+\dfrac{-2}{11}+\dfrac{4}{-9}+\dfrac{7}{15}\)

\(=\left(-\dfrac{5}{9}-\dfrac{4}{9}\right)+\left(\dfrac{8}{15}+\dfrac{7}{15}\right)-\dfrac{2}{11}\)

\(=-1+1-\dfrac{2}{11}=-\dfrac{2}{11}\)

d: \(\dfrac{7}{19}\cdot\dfrac{8}{11}+\dfrac{3}{11}\cdot\dfrac{7}{19}+\dfrac{-12}{19}\)

\(=\dfrac{7}{19}\left(\dfrac{8}{11}+\dfrac{3}{11}\right)-\dfrac{12}{19}\)

\(=\dfrac{7}{19}-\dfrac{12}{19}=-\dfrac{5}{19}\)

e: \(-\dfrac{7}{25}\cdot\dfrac{39}{-14}\cdot\dfrac{50}{78}\)

\(=\dfrac{7}{25}\cdot\dfrac{39}{14}\cdot\dfrac{25}{39}\)

\(=\dfrac{7}{14}=\dfrac{1}{2}\)

f: \(\left(\dfrac{3}{8}+\dfrac{-3}{4}+\dfrac{7}{12}\right):\dfrac{5}{6}+\dfrac{1}{2}\)

\(=\dfrac{9-18+14}{24}\cdot\dfrac{6}{5}+\dfrac{1}{2}\)

\(=\dfrac{5}{24}\cdot\dfrac{6}{5}+\dfrac{1}{2}=\dfrac{1}{4}+\dfrac{1}{2}=\dfrac{3}{4}\)

g: \(\dfrac{2}{5}\cdot\dfrac{1}{3}-\dfrac{2}{15}:\dfrac{1}{5}+\dfrac{3}{5}\cdot\dfrac{1}{3}\)

\(=\dfrac{2}{15}-\dfrac{2}{15}\cdot5+\dfrac{1}{5}\)

\(=\dfrac{2}{15}\left(1-5\right)+\dfrac{1}{5}=\dfrac{-8}{15}+\dfrac{5}{15}=-\dfrac{3}{15}=-\dfrac{1}{5}\)

h: \(\dfrac{9}{27}+\dfrac{8}{24}+\dfrac{18}{27}-\dfrac{-16}{24}+\dfrac{2}{3}\)

\(=\left(\dfrac{9}{27}+\dfrac{18}{27}\right)+\left(\dfrac{8}{24}+\dfrac{16}{24}\right)+\dfrac{2}{3}\)

\(=1+1+\dfrac{2}{3}=2+\dfrac{2}{3}=\dfrac{8}{3}\)

i: \(\left(4-\dfrac{5}{12}\right):2+\dfrac{5}{24}\)

\(=4:2-\dfrac{5}{12}:2+\dfrac{5}{24}\)

\(=2-\dfrac{5}{24}+\dfrac{5}{24}=2\)