Tính một cách hợp lí giá trị của biểu thức
A = (-25).8.2.5.(-4).13
B = 13.(-7)+(-13).57+13.(-36)
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Lời giải:
$25\frac{2}{13}-(\frac{15}{17}+15\frac{2}{13)$
$=25+\frac{2}{13}-\frac{15}{17}-15-\frac{2}{13}$
$=(25-15)+(\frac{2}{13}-\frac{2}{13})-\frac{15}{17}$
$=10-\frac{15}{17}=\frac{155}{17}$
\(\begin{array}{l}B = \left( {\frac{{ - 3}}{{13}}} \right) + \frac{{16}}{{23}} + \left( {\frac{{ - 10}}{{13}}} \right) + \frac{5}{{11}} + \frac{7}{{23}}\\ = \left[ {\left( {\frac{{ - 3}}{{13}}} \right) + \left( {\frac{{ - 10}}{{13}}} \right)} \right] + \left[ {\frac{{16}}{{23}} + \frac{7}{{23}}} \right] + \frac{5}{{11}}\\ = - 1 + 1 + \frac{5}{{11}}\\ = \frac{5}{{11}}\end{array}\)
\(A=\dfrac{5}{11}.\dfrac{5}{7}+\dfrac{5}{11}.\dfrac{2}{7}+\dfrac{6}{11}=\dfrac{5}{11}\left(\dfrac{5}{7}+\dfrac{2}{7}\right)+\dfrac{6}{11}=\dfrac{5}{11}.1+\dfrac{6}{11}=\dfrac{5}{11}+\dfrac{6}{11}=\dfrac{11}{11}=1\)
\(B=\dfrac{3}{13}.\dfrac{6}{11}+\dfrac{3}{13}.\dfrac{9}{11}-\dfrac{3}{13}.\dfrac{4}{11}=\dfrac{3}{13}\left(\dfrac{6}{11}+\dfrac{9}{11}-\dfrac{4}{11}\right)=\dfrac{3}{13}.1=\dfrac{3}{13}\)
\(C=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{3}{6}-\dfrac{2}{6}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right).0=0\)
A=\(\frac{6}{19}\). \(\frac{-7}{11}\)+\(\frac{6}{19}\).\(\frac{-4}{11}\)+\(\frac{-13}{19}\)
=\(\frac{6}{19}\).(\(\frac{-7}{11}\)+\(\frac{-4}{11}\))+\(\frac{-13}{19}\)
=\(\frac{6}{19}\).\(\frac{-11}{11}\)+\(\frac{-13}{19}\)
=\(\frac{6}{19}\).-1 +\(\frac{-13}{19}\)
=\(\frac{-6}{19}\)+\(\frac{-13}{19}\)
=\(\frac{-19}{19}\)
+1
A = (-25).8.2.5.(-4).13 = [(-25).(-4)].8.2.5.13 = 100.8.10.13 = 10400
B = 13.(-7) + (-13).57 + 13.(-36) = 13.(-7) - 13.57 + 13.(-36)
= 13.[(-7) + (-57) + (-36)]
= 13. (-100)
= -1300
Ta có: \(A=\left(-25\right)\cdot8\cdot2\cdot5\cdot\left(-4\right)\cdot13\)
\(=\left[\left(-25\right)\cdot\left(-4\right)\right]\cdot\left(2\cdot5\right)\cdot\left(8\cdot13\right)\)
\(=104000\)
Ta có: \(B=13\cdot\left(-7\right)+\left(-13\right)\cdot57+13\cdot\left(-36\right)\)
\(=13\cdot\left(-7\right)-13\cdot57-13\cdot36\)
\(=13\left(-7-57-36\right)\)
\(=13\cdot\left(-100\right)=-1300\)