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\(=\frac{47}{53}.\frac{17}{3}-\frac{47}{53}.\frac{53}{47}+\frac{17}{3}.\frac{6}{17}-\frac{17}{3}.\frac{47}{53}\)
\(=\left(\frac{47}{53}.\frac{17}{3}-\frac{17}{3}.\frac{47}{53}\right)+\left(\frac{47}{53}.\frac{53}{47}-\frac{17}{3}.\frac{6}{17}\right)\)
\(=0+\left(-1\right)\)
\(=-1\).
\(\dfrac{47}{53}\left(\dfrac{17}{3}-\dfrac{53}{47}\right)+\dfrac{17}{3}\left(\dfrac{6}{17}-\dfrac{47}{53}\right)\)
\(=\dfrac{47}{53}.\dfrac{17}{3}-\dfrac{45}{53}.\dfrac{53}{47}+\dfrac{17}{3}.\dfrac{6}{17}-\dfrac{17}{3}.\dfrac{47}{53}\)
\(=-1+\dfrac{6}{3}=-1+2=1\)
1: \(=\dfrac{15}{37}\cdot\dfrac{38}{41}-\dfrac{15}{37}\cdot\dfrac{74}{45}-\dfrac{38}{41}\cdot\dfrac{15}{37}-\dfrac{38}{41}\cdot\dfrac{82}{76}\)
\(=\dfrac{-2}{3}-1=-\dfrac{5}{3}\)
2: \(=\dfrac{47}{53}\cdot\dfrac{17}{3}-\dfrac{47}{53}\cdot\dfrac{53}{47}+\dfrac{17}{3}\cdot\dfrac{6}{17}-\dfrac{17}{3}\cdot\dfrac{47}{53}\)
\(=-1+2=1\)
47 x 83 + 21 x 53 + 47 x 17 - 79 x 53
= 47 x (83 + 17) + 53 x (21 - 79)
= 47 x 100 + 53 x (-58)
= 4700 - 3074
= 1626
\(47.83+21.53+47.17-79.53\)
\(=47.\left(83+17\right)+53.\left(79+21\right)\)
\(=47.100+53.100\)
\(=4700+5300\)
\(=10000\)
`47/53*(17/3-53/47)+17/3*(6/17-47/53)`
`=47/53*17/3-1+6/3-17/3*47/53`
`=2-1+17/3*47/53-17/3*47/53`
`=1`
\(\dfrac{47}{53}.\left(\dfrac{17}{3}-\dfrac{53}{47}\right)+\dfrac{17}{3}.\left(\dfrac{6}{17}-\dfrac{47}{53}\right)\)
\(=\dfrac{47}{53}.\dfrac{17}{3}-\dfrac{47}{53}.\dfrac{53}{47}+\dfrac{17}{3}.\dfrac{6}{17}-\dfrac{17}{3}.\dfrac{47}{53}\)
\(=\left(\dfrac{47}{53}.\dfrac{17}{3}-\dfrac{17}{3}.\dfrac{47}{53}\right)+\left(\dfrac{-47}{53}.\dfrac{53}{47}+\dfrac{17}{3}.\dfrac{6}{17}\right)\)
\(=\left(1-1\right)+\left(-1+2\right)\)
\(=0+1\)
\(=1\)