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a)\(1\frac{4}{23}+\frac{5}{21}-\frac{4}{23}+0,5+\frac{16}{21}\)
\(=\left(1\frac{4}{23}-\frac{4}{23}\right)+\left(\frac{5}{21}+\frac{16}{21}\right)+0,5\)
\(=1+1+0,5\)
\(=2,5\)
b)\(\frac{3}{7}.19\frac{1}{3}-\frac{3}{7}.33\frac{1}{3}\)
\(=\frac{3}{7}.\left(19\frac{1}{3}-33\frac{1}{3}\right)\)
\(=\frac{3}{7}.\left(-14\right)\)
\(=-6\)
c)\(9.\left(-\frac{1}{3}\right)^3+\frac{1}{3}\)
\(=9.\left(-\frac{1}{3}\right)^3+9.\frac{1}{27}\)
\(=9.\left[\left(-\frac{1}{3}\right)^3+\frac{1}{27}\right]\)
\(=9.0=0\)
d)\(15\frac{1}{4}:\left(-\frac{5}{7}\right)-25\frac{1}{4}:\left(-\frac{5}{7}\right)\)
\(=\left(15\frac{1}{4}-25\frac{1}{4}\right):\left(-\frac{5}{7}\right)\)
\(=\left(-10\right):\left(-\frac{5}{7}\right)\)
\(=14\)
a) \(\frac{6}{5}.{\left( {1,2} \right)^8} = 1,2.{(1,2)^8} = {(1,2)^{1 + 8}} = {(1,2)^9}\)
b) \({\left( {\frac{{ - 4}}{9}} \right)^7}:\frac{{16}}{{81}} = {\left( {\frac{{ - 4}}{9}} \right)^7}:{\left( {\frac{{ - 4}}{9}} \right)^2} = {\left( {\frac{{ - 4}}{9}} \right)^{7 - 2}} = {\left( {\frac{{ - 4}}{9}} \right)^5}\)
\(\frac{3}{2^2}.\frac{2^3}{3^2}.\frac{5.3}{4^2}.......\frac{3.3333}{100^2}\)
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Câu 1;
\(\frac{\frac{1}{3}-\frac{1}{7}-\frac{1}{13}}{\frac{2}{3}-\frac{2}{7}-\frac{2}{13}}\cdot\frac{\frac{3}{4}-\frac{3}{16}-\frac{3}{64}-\frac{3}{256}}{1-\frac{1}{4}-\frac{1}{16}-\frac{1}{64}}+\frac{5}{8}\)
\(=\frac{\frac{1}{3}-\frac{1}{7}-\frac{1}{13}}{2\left(\frac{1}{3}-\frac{1}{7}-\frac{1}{13}\right)}\cdot\frac{3\left(\frac{1}{4}-\frac{1}{16}-\frac{1}{64}-\frac{1}{256}\right)}{4\left(\frac{1}{4}-\frac{1}{16}-\frac{1}{64}-\frac{1}{256}\right)}+\frac{5}{8}\)
\(=\frac{1}{2}\cdot\frac{3}{4}+\frac{5}{8}=\frac{3}{8}+\frac{5}{8}=1\)
Câu 2:
\(\frac{0,75-0,6+\frac{3}{7}+\frac{3}{13}}{2,75-2,2+\frac{11}{7}+\frac{11}{3}}=\frac{\frac{3}{4}-\frac{3}{5}+\frac{3}{7}+\frac{3}{13}}{\frac{11}{4}-\frac{11}{5}+\frac{11}{7}+\frac{11}{3}}=\frac{3\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{13}\right)}{11\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{13}\right)}=\frac{3}{11}\)
Câu 1;
13 −17 −113 23 −27 −213 ·34 −316 −364 −3256 1−14 −116 −164 +58
=13 −17 −113 2(13 −17 −113 ) ·3(14 −116 −164 −1256 )4(14 −116 −164 −1256 ) +58
=12 ·34 +58 =38 +58 =1
Câu 2:
\(\begin{array}{l}B = \left( {\frac{{ - 3}}{{13}}} \right) + \frac{{16}}{{23}} + \left( {\frac{{ - 10}}{{13}}} \right) + \frac{5}{{11}} + \frac{7}{{23}}\\ = \left[ {\left( {\frac{{ - 3}}{{13}}} \right) + \left( {\frac{{ - 10}}{{13}}} \right)} \right] + \left[ {\frac{{16}}{{23}} + \frac{7}{{23}}} \right] + \frac{5}{{11}}\\ = - 1 + 1 + \frac{5}{{11}}\\ = \frac{5}{{11}}\end{array}\)
Ta có: \(A=\frac{\frac{3}{11}+1-\frac{3}{7}}{3+\frac{9}{11}-\frac{9}{7}}-\frac{\frac{1}{3}+0,25-\frac{1}{5}+0,125}{\frac{7}{6}+\frac{7}{8}-0,7+\frac{7}{16}}\)
\(=\frac{3\left(\frac{1}{11}+\frac{1}{3}-\frac{1}{7}\right)}{9\left(\frac{1}{3}+\frac{1}{11}-\frac{1}{7}\right)}-\frac{2\left(\frac{1}{6}+\frac{1}{8}-\frac{1}{10}+\frac{1}{16}\right)}{7\left(\frac{1}{6}+\frac{1}{8}-\frac{1}{10}+\frac{1}{16}\right)}\)
\(=\frac{3}{9}-\frac{2}{7}=\frac{1}{3}-\frac{2}{7}=\frac{7}{21}-\frac{6}{21}=\frac{1}{21}\)
Vậy \(A=\frac{1}{21}\)
\(\begin{array}{l}1,2.\frac{{15}}{4} + \frac{{16}}{7}.\frac{{ - 85}}{8} - 1,2.5\frac{3}{4} - \frac{{16}}{7}.\frac{{ - 71}}{8}\\ =(1,2.\frac{{15}}{4} - 1,2.5\frac{3}{4}) +( \frac{{16}}{7}.\frac{{ - 85}}{8}- \frac{{16}}{7}.\frac{{ - 71}}{8}) \\= \frac{{12}}{{10}}.\frac{{15}}{4} - \frac{{12}}{{10}}.\frac{{23}}{4} + \frac{{16}}{7}.\frac{{ - 85}}{8} - \frac{{16}}{7}.\frac{{ - 71}}{8}\\ = \frac{6}{5}.\frac{{15}}{4} - \frac{6}{5}.\frac{{23}}{4} + \frac{{16}}{7}.\frac{{ - 85}}{8} + \frac{{16}}{7}.\frac{{71}}{8}\\ = \frac{6}{5}.(\frac{{15}}{4} - \frac{{23}}{4}) + \frac{{16}}{7}.(\frac{{ - 85}}{8} + \frac{{71}}{8})\\ = \frac{6}{5}.\frac{{ - 8}}{4} + \frac{{16}}{7}.\frac{{ - 14}}{8}\\ = \frac{6}{5}.( - 2) + ( - 4)\\ = \frac{{ - 12}}{5} + \frac{{ - 20}}{5}\\ = \frac{{ - 32}}{5}\end{array}\)
Chú ý: Nếu phân số chưa tối giản, ta nên tối giản phân số trước để việc tính toán được thuận tiện hơn.