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a)\(\dfrac{3.7.13.37.39-10101}{505050-70707}\)=\(\dfrac{10101.39-10101}{10101.50-10101.7}\)=\(\dfrac{10101.\left(39-1\right)}{10101.\left(50-7\right)}\)=\(\dfrac{39-1}{50-7}\)=\(\dfrac{38}{43}\)
b)\(\dfrac{18.34+\left(-18\right).124}{-36.17+9.\left(-52\right)}\)=\(\dfrac{36.17+36.\left(-62\right)}{36.\left(-17\right)+36.\left(-13\right)}\)=
\(\dfrac{36.\left[17+\left(-62\right)\right]}{36.\left[\left(-17\right)+\left(-13\right)\right]}\)=\(\dfrac{36.\left(-45\right)}{36.\left(-20\right)}\)=\(\dfrac{45}{20}\)=\(\dfrac{9}{4}\)=2\(\dfrac{1}{4}\)
b) Ta có:
\(B=\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{1}{2016}\)
\(\Rightarrow B=\left(\frac{2015}{2}+1\right)+\left(\frac{2014}{3}+1\right)+...+\left(\frac{1}{2016}+1\right)+1\)
\(\Rightarrow B=\frac{2017}{2}+\frac{2017}{3}+...+\frac{2017}{2016}+\frac{2017}{2017}\)
\(\Rightarrow B=2017\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}+\frac{1}{2017}\right)\)
\(\Rightarrow\frac{A}{B}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017}}{2017\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2017}\right)}=\frac{1}{2017}\)
Vậy \(\frac{A}{B}=\frac{1}{2017}\)
a, Ta có: \(\dfrac{32}{37}>\dfrac{32}{54}>\dfrac{19}{54}\Rightarrow\dfrac{32}{37}>\dfrac{19}{54}\)
b, Ta có: \(\dfrac{18}{53}>\dfrac{18}{54}=\dfrac{1}{3}\Rightarrow\dfrac{18}{53}>\dfrac{1}{3}\left(1\right)\)
\(\dfrac{26}{78}=\dfrac{1}{3}\left(2\right)\)
Từ (1) và (2) ta suy ra \(\dfrac{18}{53}>\dfrac{26}{78}\)
c, Ta thấy: \(\dfrac{25}{103}< \dfrac{25}{100}=\dfrac{1}{4}\left(1\right)\)
\(\dfrac{74}{295}>\dfrac{74}{296}=\dfrac{1}{4}\left(2\right)\)
Từ (1) và (2) ta suy ra \(\dfrac{25}{103}< \dfrac{74}{295}\)
a) \(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}=\dfrac{2.3\left(1+2.2+7.7\right)}{3.5\left(1+2.2+7.7\right)}=\dfrac{2}{5}\)
b) \(\dfrac{-1997.1996+1}{\left(-1995\right)\left(-1997\right)+1996}=\dfrac{-1997\left(1995+1\right)+1}{1995.1997+1996}=\dfrac{-1997.1995+\left(-1997\right)+1}{1995.1997+1996}=\dfrac{-1997.1995+\left(-1996\right)}{1995.1997+1996}=-1\)
3/ Chu vi hình chữ nhật:
\(\left(\dfrac{1}{4}+\dfrac{3}{10}\right)\cdot2=\dfrac{11}{10}\) (chưa biết đơn vị)
Diện tích hình chữ nhật:
\(\dfrac{1}{4}\cdot\dfrac{3}{10}=\dfrac{11}{20}\) (chưa biết đơn vị)
a) \(\dfrac{18.34-18.124}{-36.17+9.\left(-4\right).13}=\dfrac{18.\left(34-124\right)}{-36.\left(17+13\right)}=\dfrac{18.\left(-90\right)}{36.\left(-30\right)}=\dfrac{1.\left(-3\right)}{2.\cdot\left(-1\right)}=\dfrac{3}{2}\)
b) \(\dfrac{393939-10101}{505050-70707}=\dfrac{10101.39-10101}{10101.50-10101.7}=\dfrac{10101.\left(39-1\right)}{10101.\left(50-7\right)}=\dfrac{38}{43}\)
a) \(\dfrac{18.34+\left(-18\right).124}{-36.17+9.\left(-52\right)}=\dfrac{36.17+36.\left(-62\right)}{36.\left(-17\right)+35.\left(-13\right)}=\dfrac{36\left[17+\left(-62\right)\right]}{36\left[\left(-17\right)+\left(-13\right)\right]}=\dfrac{45}{20}=\dfrac{9}{4}\)
b) \(\dfrac{3.7.13.37.39-10101}{505050-70707}=\dfrac{10101.39-10101}{10101.50-10101.7}=\dfrac{10101\left(39-1\right)}{10101\left(50-7\right)}=\dfrac{38}{43}\)