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a) \(\dfrac{7}{30}+\dfrac{\left(-12\right)}{37}+\dfrac{23}{30}+\dfrac{\left(-25\right)}{37}=\left(\dfrac{7}{30}+\dfrac{23}{30}\right)+\left(\dfrac{-12}{37}+\dfrac{-25}{37}\right)=1+\left(-1\right)=0\)
b) \(\dfrac{5}{7}\cdot\dfrac{5}{11}+\dfrac{5}{7}\cdot\dfrac{2}{11}-\dfrac{5}{7}\cdot\dfrac{14}{11}=\dfrac{5}{7}\cdot\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}\cdot\left(-\dfrac{7}{11}\right)=-\dfrac{5}{11}\)
c) \(\dfrac{\left(-5\right)}{7}\cdot\dfrac{3}{13}-\dfrac{5}{7}\cdot\dfrac{10}{13}+1\dfrac{5}{7}=\dfrac{5}{7}\cdot\dfrac{-3}{13}-\dfrac{5}{7}\cdot\dfrac{10}{13}+\dfrac{12}{7}=\dfrac{5}{7}\cdot\left(\dfrac{-3}{13}-\dfrac{10}{13}\right)+\dfrac{12}{7}=\dfrac{5}{7}\cdot\left(-1\right)+\dfrac{12}{7}=\left(-\dfrac{5}{7}\right)+\dfrac{12}{7}=\dfrac{7}{7}=1\)
*\(\left(45-25\right).\left(-11\right)+29.\left(-3-17\right)\)
\(=20.\left(-11\right)+29.\left(-20\right)\)
\(=-220+\left(-580\right)\)
\(=-800\)
*\(\left(-37\right).\left(55-23\right)-55.\left(23-37\right)\)
\(=-37.32-55.\left(-14\right)\)
\(=-1184-\left(-770\right)\)
\(=-1184+770\)
\(=-414\)
*\(\left(-12\right).\left(-125\right).\left(-4\right)\)
\(=1500.\left(-4\right)\)
\(=-6000\)
*\(\left(-1\right).2.\left(-3\right).4.\left(-5\right)\)
\(=-2.\left(-12\right).\left(-5\right)\)
\(=24.\left(-5\right)\)
\(=-120\)
c) 37 . 143 + 37 . 57 + 1300
= (37 . 143 + 37.57) + 1300
= 37.(143+ 57) + 1300
= 37. 200 + 1300
= 7400 + 1300
8700.
a) (-124) + 24 = -100
b) 37. 78 + 37. 22
= 37 . ( 78 + 22 )
= 37 . 100
= 3700
\(=\left[37.\left(23-11\right)\right]\div37\)
\(=\left[37.12\right]\div37\)
\(=444\div37=12\)
\(\left(23\times37-37\times11\right):37\\ =\left[37\times\left(37-11\right)\right]:37\\ =37\times12:37\\ =37:37\times12=1\times12\\ =12\)