a) \(\frac{1}{4}+\frac{2}{5}+\frac{6}{8}+\frac{9}{15}+\frac{8}{1}\)
\(=\left(\frac{1}{4}+\frac{6}{8}\right)+\left(\frac{2}{5}+\frac{9}{15}\right)+\frac{8}{1}\)
\(=\left(\frac{1}{4}+\frac{3}{4}\right)+\left(\frac{2}{5}+\frac{3}{5}\right)+\frac{8}{1}\)
\(=\frac{4}{4}+\frac{5}{5}+\frac{8}{1}\)
\(=1+1+8\)
\(=10\)
b) \(\frac{15}{31}\cdot\frac{16}{43}+\frac{15}{31}\cdot\frac{27}{43}\)
\(=\frac{15}{31}\cdot\left(\frac{16}{43}+\frac{27}{43}\right)\)
\(=\frac{15}{31}\cdot\frac{43}{43}\)
\(=\frac{15}{31}\cdot1=\frac{15}{31}\)
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