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a,\(\frac{4}{9}.\frac{2}{6}=\frac{4}{27}\)
b,\(1\frac{1}{3}.\left(0,5\right)+\left(\frac{8}{15}-\frac{19}{30}\right):\frac{6}{15}\)
=\(\frac{4}{3}.\frac{1}{2}+\left(\frac{16}{30}-\frac{19}{30}\right).\frac{15}{6}\)
=\(\frac{2}{3}+\frac{-1}{10}.\frac{15}{6}\)
=\(\frac{2}{3}+\frac{-1}{4}\)
=\(\frac{8}{12}+\frac{-3}{12}=\frac{5}{12}\)
bài2
a,\(\left(\frac{2}{7}.x+\frac{3}{7}\right):2\frac{1}{5}-\frac{3}{7}=1\)
=>\(\left(\frac{2}{7}.x+\frac{3}{7}\right):\frac{11}{5}=1+\frac{3}{7}=\frac{10}{7}\)
=>\(\frac{2}{7}.x+\frac{3}{7}=\frac{10}{7}.\frac{11}{5}\)
=>\(\frac{2}{7}.x+\frac{3}{7}=\frac{22}{7}\)
=>\(\frac{2}{7}.x=\frac{22}{7}-\frac{3}{7}=\frac{19}{7}\)
=>\(x=\frac{19}{7}:\frac{2}{7}=\frac{19}{7}.\frac{7}{2}=\frac{19}{2}\)
vậy x\(=\frac{19}{2}\)
\(=\frac{12}{7}\cdot\frac{3}{4}-\frac{6}{7}\cdot\frac{4}{3}+\frac{6}{7}\)
\(=\frac{6}{7}\left(\frac{3}{2}-\frac{4}{3}+1\right)\)
\(=\frac{6}{7}\left(\frac{1}{6}+1\right)=\frac{6}{7}\cdot\frac{7}{6}=1\)
2.
\(=2017\cdot2018\cdot\left[\left(2016\cdot2018\right)-\left(2016\cdot2017\right)\right]\)
\(=2017\cdot2018\cdot2016\left(2018-2017\right)=2016\cdot2017\cdot2018\)
3.
\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)....\left(\frac{1}{100}-1\right)=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot....\cdot\frac{99}{100}\)
\(=\frac{1}{100}\)
4.
\(=\frac{1+2+2^2+2^4+...+2^9}{2\left(1+2+2^2+2^3+2^4+...+2^9\right)}\)
\(=\frac{1}{2}\)
mình chỉ làm được câu 3 thôi
có \(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)....\left(\frac{1}{100}-1\right)\)
\(=\frac{-1}{2}\times\frac{-2}{3}\times....\times\frac{-99}{100}\)
\(=\frac{\left(-1\right)\left(-2\right)....\left(-99\right)}{2\times3\times....\times100}\)
\(=\frac{-\left(1\times2\times....\times99\right)}{2\times3\times....\times100}\)
\(=\frac{-1}{100}\)
Bài 1:
a) \(-\frac{4}{5}-\frac{8}{25}\left(\frac{-5}{2}-0,125\right)\\ =-\frac{4}{5}-\frac{8}{25}\left(\frac{-5}{2}-\frac{1}{8}\right)\\ =-\frac{4}{5}-\frac{8}{25}\left(\frac{-20}{8}-\frac{1}{8}\right)\\ =-\frac{4}{5}-\frac{8}{25}\cdot\frac{-21}{8}\\ =-\frac{4}{5}-\frac{-21}{25}\\ =\frac{-4}{5}+\frac{21}{25}\\ =\frac{-20}{25}+\frac{21}{25}=\frac{1}{25}\)
c) \(5\frac{1}{2}-4\frac{2}{3}:\frac{16}{9}-3\frac{1}{3}:\frac{16}{9}\\ =5\frac{1}{2}-\left(4\frac{2}{3}:\frac{16}{9}+3\frac{1}{3}:\frac{16}{9}\right)\\ =5\frac{1}{2}-\left(4\frac{2}{3}+3\frac{1}{3}\right):\frac{16}{9}\\ =5\frac{1}{2}-8\cdot\frac{9}{16}\\ =\frac{11}{2}-\frac{9}{2}=\frac{2}{2}=1\)
Bài 2:
a) \(\left(20\%x+\frac{2}{5}x-2\right):\frac{1}{3}=-2013\\ \left(\frac{1}{5}x+\frac{2}{5}x-2\right)\cdot3=-2013\\ \left[x\left(\frac{1}{5}+\frac{2}{5}\right)-2\right]=\left(-2013\right):3\\ x\cdot\frac{3}{5}-2=-671\\ x\cdot\frac{3}{5}=-671+2\\ x\cdot\frac{3}{5}=-669\\ x=\left(-669\right):\frac{3}{5}\\ x=\left(-669\right)\cdot\frac{5}{3}\\ x=-1115\)Vậy x = -1115
b) \(\left(4,5-2\left|x\right|\right)\cdot1\frac{4}{7}=\frac{11}{14}\\ \left(\frac{9}{2}-2\left|x\right|\right)\cdot\frac{11}{7}=\frac{11}{14}\\ \frac{9}{2}-2\left|x\right|=\frac{11}{14}:\frac{11}{7}\\ \frac{9}{2}-2\left|x\right|=\frac{11}{14}\cdot\frac{7}{11}\\ \frac{9}{2}-2\left|x\right|=\frac{1}{2}\\ 2\left|x\right|=\frac{9}{2}-\frac{1}{2}\\ 2\left|x\right|=4\\ \left|x\right|=4:2\\ \left|x\right|=2\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)Vậy x ∈ {2 ; -2}