Câu 1:

a: \(\frac37+\left(-\frac52\right)+\frac35\)

\(=\frac37-\frac52+\frac35\)

\(=\frac{30}{70}-\frac{175}{70}+\frac{42}{70}=\frac{30+42-175}{70}=-\frac{103}{70}\)

b: \(0,8-\left(-\frac27\right)-\frac{7}{10}=\frac45+\frac27-\frac{7}{10}\)

\(=\frac{56}{70}+\frac{20}{70}-\frac{49}{70}=\frac{56+20-49}{70}=\frac{56-29}{70}=\frac{27}{70}\)

c: \(\frac34-\left\lbrack\left(-\frac53\right)-\left(\frac{1}{12}+\frac29\right)\right\rbrack\)

\(=\frac34+\frac53+\frac{1}{12}+\frac29\)

\(=\frac{27}{36}+\frac{60}{36}+\frac{3}{36}+\frac{8}{36}=\frac{98}{36}=\frac{49}{18}\)

d: \(19\frac13\cdot\frac45-\frac45\cdot15\frac13\)

\(=\frac45\left(19+\frac13-15-\frac13\right)\)

\(=\frac45\cdot4=\frac{16}{5}\)

e: \(\frac38\cdot\left(-\frac{3}{11}\right)+\frac38\cdot\left(-\frac{8}{11}\right)+2\frac57\)

\(=\frac38\left(-\frac{3}{11}-\frac{8}{11}\right)+2+\frac57\)

\(=-\frac38+2+\frac57=\frac{13}{8}+\frac57=\frac{91}{56}+\frac{40}{56}=\frac{131}{56}\)

f: \(\left(-\frac{5}{11}:\frac{13}{8}-\frac{5}{11}:\frac{13}{3}\right)-\left|-\frac{1}{33}\right|\)

\(=-\frac{5}{11}\cdot\frac{8}{13}-\frac{5}{11}\cdot\frac{3}{13}-\frac{1}{33}\)

\(=-\frac{5}{11}\cdot\frac{11}{13}-\frac{1}{33}=-\frac{5}{13}-\frac{1}{33}=\frac{-165-13}{13\cdot33}=\frac{-178}{429}\)

g: \(\frac{4}{23}+\frac{5}{21}+\frac12-\frac{4}{23}+\frac{16}{21}\)

\(=\left(\frac{4}{23}-\frac{4}{23}\right)+\left(\frac{5}{21}+\frac{16}{21}\right)+\frac12\)

\(=1+\frac12=\frac32\)

h: \(\frac{13}{25}+\frac{6}{41}+\frac{-38}{25}+\frac{35}{41}-0,5\)

\(=\left(\frac{13}{25}-\frac{38}{25}\right)+\left(\frac{6}{41}+\frac{35}{41}\right)-0,5\)

\(=-\frac{25}{25}+\frac{41}{41}-0,5=-0,5\)

i: \(\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-1\frac{15}{17}+\frac23\)

\(=\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac13+\frac23\right)-1-\frac{15}{17}\)

\(=1+1-1-\frac{15}{17}=1-\frac{15}{17}=\frac{2}{17}\)

j: \(\left(\frac{2022}{2023}\right)^0-\left(-3\right)_{}^3+\frac12:\left(-\frac12\right)^3\)

\(=1-\left(-27\right)+\frac12:\frac{-1}{8}\)

=28-4

=24

k: \(\left(-2\right)^3+\frac12:\frac{-1}{4}-\left|15\right|\)

\(=-8+\frac12\cdot\left(-4\right)-15\)

=-8-2-15

=-25

l: \(3:\left(-\frac32\right)^2+\frac19\cdot\sqrt{36}\)

\(=3:\frac94+\frac19\cdot6=3\cdot\frac49+\frac69=\frac{12}{9}+\frac69=\frac{18}{9}\)

=2

m: \(\sqrt{81}\cdot\frac13-\left(-3\right)^3=9\cdot\frac13-\left(-27\right)\)

=3+27

=30

n: \(\sqrt{\frac{16}{25}}\cdot\sqrt{\frac{121}{64}}-1\frac{3}{10}\)

\(=\frac45\cdot\frac{11}{8}-\frac{13}{10}\)

\(=\frac{11}{10}-\frac{13}{10}=-\frac{2}{10}=-\frac15\)

o: \(\frac{3^2}{2^3}\cdot\sqrt{144}-50\%\)

\(=\frac98\cdot12-\frac12=9\cdot\frac32-\frac12=\frac{27}{2}-\frac12=\frac{26}{2}\)

=13

p: \(\frac{6^2+3\cdot6^2+3^2}{-13}\)

\(=\frac{36+3\cdot108+9}{-13}=\frac{45+324}{-13}=\frac{369}{-13}=-\frac{369}{13}\)

q: \(\frac{5^4\cdot20^4}{25^5\cdot4^5}=\frac{\left(5\cdot20\right)^4}{\left(25\cdot4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)

r: \(\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)

\(=\frac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)

\(=\frac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=\frac{2^{12}\cdot3^{10}\left(1+5\right)}{2^{11}\cdot3^{11}\cdot5}=\frac23\cdot\frac65=\frac{12}{15}=\frac45\)