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a, \(\frac{15}{7}=2\frac{1}{7}\); \(\frac{-18}{4}=-4\frac{2}{4}\) ; \(\frac{-21}{8}=-2\frac{5}{8}\)
b, \(1\frac{1}{4}=\frac{5}{4};-3\frac{2}{5}=\frac{-17}{5};-7\frac{1}{2}=-\frac{15}{2}\)

a) Chuyển các phân số sau về dạng hỗn số:
\(\frac{15}{7}\)=2\(\frac{1}{7}\)
\(\frac{-18}{4}\)=- 4\(\frac{2}{4}\)
-\(\frac{21}{8}\)=- 2\(\frac{5}{8}\)
b) Chuyển các hỗn số sau về dạng phân số:
1\(\frac{1}{4}\)=\(\frac{5}{4}\)
-3\(\frac{2}{5}\)=-\(\frac{17}{5}\)
-7\(\frac{1}{2}\)=-\(\frac{15}{2}\)

a) \(\frac{-8}{3}+\frac{7}{5}+\frac{-71}{15}\)< \(x\) < \(\frac{-13}{7}+\frac{19}{14}+\frac{-7}{2}\)
Ta có: \(\frac{-8}{3}+\frac{7}{5}+\frac{-71}{15}\)
=\(\frac{-40}{15}+\frac{21}{15}+\frac{-71}{15}\)
=\(\frac{-90}{15}\)
=\(-6\)
Ta có: \(\frac{-13}{7}+\frac{19}{14}+\frac{-7}{2}\)
=\(\frac{-26}{14}+\frac{19}{14}+\frac{-49}{14}\)
=\(\frac{-56}{14}\)
=\(-4\)
=> \(-6\)< \(x\)<\(-4\)
=> \(x=-5\)
b)\(\frac{5}{17}+\frac{-4}{9}+\frac{-20}{31}+\frac{12}{17}+\frac{-11}{31}\)< \(\frac{x}{9}\)<\(\frac{-3}{7}+\frac{7}{15}+\frac{4}{-7}+\frac{8}{15}+\frac{2}{3}\)
Ta có: \(\frac{5}{17}+\frac{-4}{9}+\frac{-20}{31}+\frac{12}{17}+\frac{-11}{31}\)
=\(\left(\frac{5}{17}+\frac{12}{17}\right)+\left(\frac{-20}{31}+\frac{-11}{31}\right)+\frac{-4}{9}\)
=\(1+\left(-1\right)+\frac{-4}{9}\)
=\(0+\frac{-4}{9}\)
=\(\frac{-4}{9}\)
Ta có: \(\frac{-3}{7}+\frac{7}{15}+\frac{4}{-7}+\frac{8}{15}+\frac{2}{3}\)
=\(\frac{-3}{7}+\frac{7}{15}+\frac{-4}{7}+\frac{8}{15}+\frac{2}{3}\)
=\(\left(\frac{-3}{7}+\frac{-4}{7}\right)+\left(\frac{7}{15}+\frac{8}{15}\right)+\frac{2}{3}\)
=\(\left(-1\right)+1+\frac{2}{3}\)
=\(0+\frac{2}{3}\)
=\(\frac{2}{3}\)
=> \(\frac{-4}{9}\)< \(\frac{x}{9}\)<\(\frac{2}{3}\)
=
=> \(\frac{-4}{9}\)<\(\frac{x}{9}\)<\(\frac{6}{9}\)
=> \(-4\)< \(x\)<\(6\)
=>\(x\in\left\{-3;-2;-1;0;1;2;3;4;5\right\}\)
a) \(\frac{-19}{100}+\frac{-17}{-150}-\frac{13}{-200}\)\(=\frac{-114}{600}+\frac{68}{600}+\frac{39}{600}\)\(=\frac{-46}{600}+\frac{39}{600}\)\(=\frac{23}{600}\)
b)
=\(\frac{-2130-858-1364}{6600}\)
=\(\frac{4352}{6600}\)
=\(\frac{544}{825}\)