Bài 1: Tính a) \(\frac{2}{7}+\frac{5}{7}:\frac{2}{21}+\frac{19}{21}\) b) \(\frac{14^{1005}\cdot5^{1006}}{2^{1007}\cdot35^{1004}}\) c) \(\left|-2,5\right|+\left|\frac{1}{3}\right|\cdot\left|6\right|-\left|\frac{2}{3}\right|\)
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\(A=-\frac{550}{9}\)\(\Rightarrow\)12.5% của A là \(\frac{-275}{36}\)
\(B=\frac{2}{5}\Rightarrow\)5% của B là \(\frac{1}{8}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có: \(\frac{16}{15}\cdot\frac{-5}{14}\cdot\frac{54}{24}\cdot\frac{56}{21}\)
\(=\frac{16}{15}\cdot\frac{-5}{14}\cdot\frac{9}{4}\cdot\frac{8}{3}\)
\(=4\cdot\frac{-1}{3}\cdot\frac{4}{7}\cdot3\)
\(=12\cdot\frac{-4}{21}=\frac{-48}{21}=\frac{-16}{7}\)
b) Ta có: \(5\cdot\frac{7}{5}=\frac{35}{5}=7\)
c) Ta có: \(\frac{1}{7}\cdot\frac{5}{9}+\frac{5}{9}\cdot\frac{1}{7}+\frac{5}{9}\cdot\frac{3}{7}\)
\(=\frac{5}{9}\left(\frac{1}{7}+\frac{1}{7}+\frac{3}{7}\right)\)
\(=\frac{5}{9}\cdot\frac{5}{7}=\frac{25}{63}\)
d) Ta có: \(4\cdot11\cdot\frac{3}{4}\cdot\frac{9}{121}\)
\(=\frac{4\cdot11\cdot3\cdot9}{4\cdot121}=\frac{27}{11}\)
e) Ta có: \(\frac{3}{4}\cdot\frac{16}{9}-\frac{7}{5}:\frac{-21}{20}\)
\(=\frac{4}{3}+\frac{4}{3}=\frac{8}{3}\)
g) Ta có: \(2\frac{1}{3}-\frac{1}{3}\cdot\left[\frac{-3}{2}+\left(\frac{2}{3}+0,4\cdot5\right)\right]\)
\(=\frac{7}{3}-\frac{1}{3}\cdot\left[\frac{-3}{2}+\frac{2}{3}+2\right]\)
\(=\frac{7}{3}-\frac{1}{3}\cdot\frac{7}{6}\)
\(=\frac{7}{3}-\frac{7}{18}=\frac{42}{18}-\frac{7}{18}=\frac{35}{18}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)\(\frac{5}{12}+1-\frac{3}{7}+\frac{2}{24}-\frac{8}{14}\)
\(=\frac{5}{12}+1-\frac{3}{7}+\frac{1}{12}-\frac{4}{7}\)
\(=\left(\frac{5}{12}+\frac{1}{12}\right)+1-\left(\frac{3}{7}+\frac{4}{7}\right)\)
\(=\frac{1}{2}+1-1=\frac{1}{2}\)
b)\(-\frac{23}{4}+\frac{1}{2}+\frac{21}{4}-2\)
\(=\left(-\frac{23}{4}+\frac{21}{4}+\frac{2}{4}\right)-2\)
\(=-2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Mình sửa lại đề xíu.
a) \(\frac{75}{100}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}=\frac{3}{4}+\frac{1}{4}+\frac{18}{21}+\frac{3}{21}+\frac{19}{32}+\frac{13}{32}=1+1+1=3\)
b) \(4\frac{2}{5}+5\frac{6}{9}+2\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}=4+\frac{2}{5}+\frac{3}{5}+5+\frac{2}{3}+\frac{1}{3}+2+\frac{3}{4}+\frac{1}{4}\)
\(=4+1+5+1+2+1=14.\)
c) \(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{41\cdot43}=\frac{5-3}{3\cdot5}+\frac{7-5}{5\cdot7}+\frac{9-7}{7\cdot9}+...+\frac{43-41}{41\cdot43}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{41}-\frac{1}{43}=\frac{1}{3}-\frac{1}{43}=\frac{43-3}{3\cdot43}=\frac{40}{129}.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{8\frac{3}{9}\cdot5\frac{1}{4}+3\frac{16}{19}\cdot5\frac{1}{4}}{\left(2\frac{14}{17}-2\frac{1}{34}\right)\cdot34}:\frac{7}{24}\)
\(A=\frac{\left(8\frac{3}{9}+3\frac{16}{19}\right)\cdot5\frac{1}{4}}{\left(2\frac{14}{17}-2\frac{1}{34}\right)\cdot34}\cdot\frac{24}{7}\)
\(A=\frac{\left(\frac{25}{3}+\frac{73}{19}\right)\cdot\frac{21}{4}}{\left(\frac{48}{17}-\frac{69}{34}\right)\cdot34}\cdot\frac{24}{7}\)
\(A=\frac{\frac{694}{57}\cdot\frac{21}{4}}{\frac{27}{34}\cdot34}\cdot\frac{24}{7}=\frac{\left(\frac{2429}{38}\right)}{27}\cdot\frac{24}{7}=\frac{1388}{171}\)
P/S : Số lớn quá
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(1\frac{3}{19}+\frac{8}{21}-\frac{3}{19}+0.5+\frac{13}{21}\)
\(=\left(1\frac{3}{19}-\frac{3}{19}\right)+\left(\frac{8}{21}+\frac{13}{21}\right)+0.5\)
\(=1+1+0.5=2.5\)
b) \(\left(-\frac{3}{4}+\frac{2}{7}\right):\frac{3}{7}+\left(\frac{5}{7}+\frac{-1}{4}\right):\frac{3}{7}\)
\(=\left(\frac{-3}{4}+\frac{2}{7}+\frac{5}{7}+\frac{-1}{4}\right):\frac{3}{7}\)
\(=0:\frac{3}{7}=0\)
a. \(\frac{2}{7}+\frac{5}{7}:\frac{2}{21}+\frac{19}{21}=\frac{6}{21}+\frac{5}{7}.\frac{21}{2}+\frac{19}{21}=\frac{25}{21}+\frac{15}{2}=\frac{365}{42}\)
b. \(\frac{14^{1005}.5^{1006}}{2^{1007}.35^{1004}}=\frac{14^{1005}.5^{1005}.5}{2^{1004}.2^3.35^{1004}}=\frac{70^{1005}.5}{70^{1004}.8}=\frac{70.5}{8}=\frac{350}{8}=\frac{175}{4}\)
c. \(\left|-2,5\right|+\left|\frac{1}{3}\right|.\left|6\right|-\left|\frac{2}{3}\right|=2,5+\frac{1}{3}.6-\frac{2}{3}=\frac{5}{2}+2-\frac{2}{3}=\frac{23}{6}\)