2323/202+2323/606+2323/1212+2323/2020+2323/3030+2323/4242+2323/5656+2323/7272+2323/9090.=

\(\frac{23\times101}{2\times101}+\frac{23\times101}{6\times101}+\frac{23\times101}{12\times101}+....+\frac{23\times101}{72\times101}+\frac{23\times101}{90\times101} \)

=\(\frac{23}{2}+\frac{23}{6}+..........+\frac{23}{72}+\frac{23}{90}\)

=\(23\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+.....+\frac{1}{9\times10}\right)\)

=\(23\times\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}_{ }\right)\)

=\(23\left(1-\frac{1}{10}\right)_{ }\)

=\(23\times\frac{9}{10}\)

==\(\frac{207}{10}\)           

chúc học giỏi nha bn

\(\frac{42}{46}+\frac{250}{186}+\left(\frac{-2121}{2323}\right)+\left(\frac{-125125}{143143}\right)\)

\(=\frac{21}{23}+\frac{125}{93}+\left(\frac{-21}{23}\right)+\left(\frac{-125}{143}\right)\)

Đến chỗ này bạn xem lại đề nhé 

THANKS BẠN

UWCLN(1054;69690)=1

UCLN(1054,6969)=1

a) \(\frac{17}{23}.\frac{18}{16}.\frac{23}{17}-\left(-80\right)-\frac{3}{4}\)

= \(\frac{17.18.23}{23.16.17}+80-\frac{3}{4}\)

= \(\frac{9}{8}+80-\frac{3}{4}\)

= \(\frac{3}{8}+80=\frac{643}{8}\)

b) \(\frac{5}{11}.\frac{18}{29}-\frac{5}{11}.\frac{8}{29}+\frac{5}{11}.\frac{19}{29}\)

= \(\frac{5}{11}.\left(\frac{18}{29}-\frac{8}{29}+\frac{19}{29}\right)\)

= \(\frac{5}{11}.1=\frac{5}{11}\)

c) \(\left(\frac{13}{23}+\frac{1313}{2323}-\frac{131313}{232323}\right).\left(\frac{1}{3}+\frac{1}{4}-\frac{7}{12}\right)\)

= \(\left(\frac{13}{23}+\frac{1313}{2323}-\frac{131313}{232323}\right).0\)

= \(0\)

\(\frac{1717}{6969}=\frac{17}{69};\frac{2525}{9999}=\frac{25}{99}\)

Ta có : khoảng cách ở tử và mẫu càng bé thì phân số càng lớn

 69 - 17 = 52

 99 - 25 = 74

Vì 52 < 74 

\(\Rightarrow\frac{1717}{6969}>\frac{2525}{9999}\)

\(\dfrac{42}{46}+\dfrac{250}{186}+\dfrac{-2121}{2323}+\dfrac{-125125}{143143}\)

\(=\dfrac{21}{23}+\dfrac{125}{143}+\left(\dfrac{-21}{23}\right)+\left(\dfrac{-125}{143}\right)\)

\(=\dfrac{21}{23}+\dfrac{125}{143}-\dfrac{21}{23}-\dfrac{125}{143}\)

\(=0\)

\(\dfrac{42}{46}+\dfrac{250}{186}+\dfrac{-2121}{2323}+\dfrac{-125125}{143143}\)

\(=\dfrac{21}{23}+\dfrac{125}{93}+\dfrac{-21}{23}+\dfrac{-125}{143}\)

\(=125\left(\dfrac{1}{93}-\dfrac{1}{143}\right)\)

\(=\dfrac{6250}{13299}\)

a: =-11/23(6/7+8/7)-1/23

=-22/23-1/23

=-1

b: =21/23-21/23+125/143-125/143

=0

\(A=\frac{17}{23}\cdot\frac{8}{16}\cdot\frac{23}{17}\cdot\left(-80\right)\cdot\frac{3}{4}\)\(=\frac{17\cdot4\cdot2\cdot23\cdot16\cdot\left(-5\right)\cdot3}{23\cdot16\cdot17\cdot4}\)

=> \(A=\frac{2\cdot\left(-5\right)\cdot3}{1}=-30\)

\(B=\left(\frac{13}{23}+\frac{1313}{2323}-\frac{131313}{232323}\right)\left(\frac{1}{3}+\frac{1}{4}-\frac{7}{12}\right)\)

=> \(B=\left(\frac{13}{23}+\frac{1313}{2323}-\frac{131313}{232323}\right)\left(\frac{7}{12}-\frac{7}{12}\right)\)

=> \(B=\left(\frac{13}{23}+\frac{1313}{2323}-\frac{131313}{232323}\right)\cdot0=0\)