Question

Tính nhanh:

1) \(\dfrac{2}{15}.6\dfrac{5}{11}+\dfrac{5}{11}.\dfrac{-2}{15}-\dfrac{2}{15}.2015^0\)

2)\(\dfrac{5}{2.7}+\dfrac{3}{14.11}+ \dfrac{4}{11.7}+\dfrac{1}{14.15}+\dfrac{13}{15.16}\)

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Answer 1

1) \(\dfrac{2}{15}\cdot6\dfrac{5}{11}+\dfrac{5}{11}\cdot\dfrac{-2}{15}-\dfrac{2}{15}\cdot2015^0\)

\(=\dfrac{2}{15}\cdot\dfrac{71}{11}-\dfrac{1}{11}\cdot\dfrac{2}{3}-\dfrac{2}{15}\cdot1\)

\(=\dfrac{142}{165}-\dfrac{2}{33}-\dfrac{2}{15}\)

\(=\dfrac{2}{3}\)

2) \(\dfrac{5}{2\cdot7}+\dfrac{3}{14\cdot11}+\dfrac{4}{11\cdot7}+\dfrac{1}{14\cdot15}+\dfrac{13}{15\cdot16}\)

\(=\dfrac{5}{14}+\dfrac{3}{154}+\dfrac{4}{77}+\dfrac{1}{210}+\dfrac{13}{240}\)

\(=\dfrac{39}{80}\)

Answer 2

\(\dfrac{2}{15}.6\dfrac{5}{11}+\dfrac{5}{11}.\dfrac{-2}{15}-\dfrac{2}{15}.2015^0\)

\(=\dfrac{2}{15}.\dfrac{71}{11}+\dfrac{-5}{11}.\dfrac{2}{5}-\dfrac{2}{15}.1\)

\(=\dfrac{2}{15}\left(\dfrac{71}{11}+\dfrac{-5}{11}-1\right)=\dfrac{2}{15}.5=\dfrac{2}{3}\)

\(\dfrac{5}{2.7}+\dfrac{3}{14.11}+\dfrac{4}{11.7}+\dfrac{1}{14.15}+\dfrac{13}{15.16}\)

\(=\dfrac{5}{14}+\dfrac{3}{154}+\dfrac{4}{77}+\dfrac{1}{210}+\dfrac{13}{240}\)

\(=\dfrac{39}{80}\)