-1/9 . 17/5 + -1/9 . -2/5
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a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
\(\dfrac{5}{9}\cdot\dfrac{14}{17}+\dfrac{1}{17}\cdot\dfrac{5}{9}+\dfrac{2}{9}\cdot\dfrac{5}{17}\\ =\dfrac{5}{9}\cdot\dfrac{14}{17}+\dfrac{1}{17}\cdot\dfrac{5}{9}+\dfrac{5}{9}\cdot\dfrac{2}{17}\\ =\dfrac{5}{9}\left(\dfrac{14}{17}+\dfrac{1}{17}+\dfrac{2}{17}\right)\\ =\dfrac{5}{9}\cdot1\\ =\dfrac{5}{9}\)
bài 1.
A) \(\dfrac{-5}{9}+\dfrac{3}{5}-\dfrac{3}{9}+\dfrac{-2}{5}=\left(\dfrac{-5}{9}-\dfrac{3}{9}\right)+\left(\dfrac{3}{5}+\dfrac{-2}{5}\right)=\dfrac{-8}{9}+\dfrac{1}{5}=-\dfrac{31}{45}\)
B)\(-\dfrac{5}{13}+\left(\dfrac{3}{5}+\dfrac{3}{1}-\dfrac{4}{10}\right)=-\dfrac{5}{13}+3+\left(\dfrac{3}{5}-\dfrac{4}{10}\right)=-\dfrac{5+3.13}{13}+\dfrac{1}{5}=-\dfrac{207}{65}\)C)\(\dfrac{5}{17}-\dfrac{9}{15}-\dfrac{2}{-17}+\dfrac{-3}{15}=\left(\dfrac{5}{17}+\dfrac{2}{17}\right)+\left(\dfrac{-9}{15}+\dfrac{-3}{15}\right)=\dfrac{7}{17}-\dfrac{12}{15}=-\dfrac{33}{85}\)D)\(\left(\dfrac{1}{9}-\dfrac{9}{17}\right)+\dfrac{3}{6}-\left(\dfrac{12}{17}-\dfrac{1}{2}\right)+\dfrac{-1}{9}=\left(\dfrac{1}{9}+\dfrac{-1}{9}\right)+\left(\dfrac{3}{6}+\dfrac{1}{2}\right)-\dfrac{12}{17}=1-\dfrac{12}{17}=\dfrac{5}{17}\)
\(=\frac{5\cdot14+5+2\cdot5}{9\cdot17}=\frac{5\left(14+2+1\right)}{9\cdot17}=\frac{5\cdot17}{9\cdot17}=\frac{5}{9}\)
\((\frac{1}{9}-\frac{9}{17})+\frac{3}{6}-(\frac{-8}{17}-\frac{1}{2})+\frac{5}{9}=\)
=\(\frac{1}{9}-\frac{9}{17}+\frac{1}{2}+\frac{8}{17}+\frac{1}{2}+\frac{5}{9}\)
= \((\frac{1}{9}+\frac{5}{9})+(\frac{-9}{17}+\frac{8}{17})+(\frac{1}{2}+\frac{1}{2})\)
=\(\frac{2}{3}-\frac{1}{17}+1\)
=\(\frac{34}{51}-\frac{3}{51}+\frac{51}{51}\)
=\(\frac{82}{51}\)
1:
a: =23/27-11/17+4/27+28/17
=23/27+4/27+28/17-11/17
=1+1=2
b: \(=\dfrac{2}{3}\cdot\left(\dfrac{7}{9}+\dfrac{2}{9}\right)-\dfrac{2}{9}\)
=2/3-2/9
=6/9-2/9
=4/9
c: \(=\dfrac{11}{5}\cdot\dfrac{7}{3}-\dfrac{1}{3}\cdot\dfrac{11}{5}\)
=11/5(7/3-1/3)
=11/5*2
=22/5
d: \(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{2024}{2023}=\dfrac{2024}{2}=1012\)
e: \(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{2022}{2023}=\dfrac{1}{2023}\)
-1/9 . 17/5 + -1/9 . -2/5
=-1/9.(17/5+(-2/5))
=-1/9. 3
=-3/9
\(\frac{-1}{9}.\frac{17}{5}+\frac{-1}{9}.\frac{-2}{5}\)
\(=\frac{-1}{9}.\left(\frac{17}{5}+\frac{-2}{5}\right)\)
\(=\frac{-1}{9}.\frac{15}{5}\)
\(=\frac{-1}{9}.3\)
\(=\frac{-3}{9}=\frac{-1}{3}\)