Bài 1:
a: \(\left(31\frac{6}{13}+5\frac{9}{41}\right)-36\frac{6}{13}\)
\(=31+\frac{6}{13}+5+\frac{9}{41}-36-\frac{6}{13}=\frac{9}{41}\)
b: \(\frac53+\left(-\frac27\right)-\left(-1,2\right)\)
\(=\frac53-\frac27+\frac65\)
\(=\frac{175}{105}-\frac{30}{105}+\frac{126}{105}=\frac{271}{105}\)
c: \(0,25+\frac35-\left(\frac18-\frac25+1\frac14\right)\)
\(=\frac14+\frac35-\frac18+\frac25-\frac54\)
\(=\left(\frac35+\frac25\right)+\left(\frac14-\frac54\right)-\frac18=-\frac18\)
d: \(\left(8-\frac94+\frac27\right)-\left(-6-\frac37+\frac54\right)-\left(3+\frac24-\frac97\right)\)
\(=8-\frac94+\frac27+6+\frac37-\frac54-3-\frac24+\frac97\)
\(=\left(8+6-3\right)+\left(-\frac94-\frac54-\frac24\right)+\left(\frac27+\frac37+\frac97\right)\)
=11-4+2
=11-2
=9
e: \(\frac13-\frac35+\frac57-\frac79+\frac{9}{11}-\frac{11}{13}+\frac{13}{15}+\frac{11}{13}-\frac{9}{11}+\frac79-\frac57+\frac35-\frac13\)
\(=\frac{13}{15}+\left(\frac13-\frac13\right)+\left(\frac35-\frac35\right)+\left(\frac57-\frac57\right)+\left(\frac79-\frac79\right)+\left(\frac{9}{11}-\frac{9}{11}\right)+\left(\frac{11}{13}-\frac{11}{13}\right)\)
=13/15
f: \(\frac{1}{2014}-\frac{1}{2014\cdot2013}-\frac{1}{2013\cdot2012}-\cdots-\frac{1}{2\cdot1}\)
\(=\frac{1}{2014}-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\cdots+\frac{1}{2013\cdot2014}\right)\)
\(=\frac{1}{2014}-\left(1-\frac12+\frac12-\frac13+\cdots+\frac{1}{2013}-\frac{1}{2014}\right)\)
\(=\frac{1}{2014}-\left(1-\frac{1}{2014}\right)=\frac{2}{2014}-1=-\frac{2012}{2014}=-\frac{1006}{1007}\)
BÀi 3:
\(\frac12-\left(\frac13+\frac34\right)\le x\le\frac{1}{24}-\left(\frac18-\frac13\right)\)
=>\(\frac12-\frac13-\frac34\le x\le\frac{1}{24}+\frac13-\frac18\)
=>\(\frac{6}{12}-\frac{4}{12}-\frac{9}{12}\le x\le\frac{1}{24}+\frac{8}{24}-\frac{3}{24}\)
=>\(-\frac{7}{12}\le x\le\frac{6}{24}\)
mà x nguyên
nên x=0
