Đáp án đúng:
Phương pháp giải:
Sử dụng phương pháp tách, tính chất kết hợp phân phối của phép nhân và phép cộng.Giải chi tiết:a) \(\begin{array}{l}A = \frac{{1.5.6 + 2.10.12 + 4.20.24 + 9.45.54}}{{1.3.5 + 2.6.10 + 4.12.20 + 9.27.45}}\\\,\,\,\,\, = \frac{{1.5.2.3 + 2.10.2.5 + 4.20.24 + 9.2.27.54}}{{1.3.5 + 2.6.10 + 4.12.20 + 9.27.45}}\\\,\,\,\,\, = \frac{{2.\left( {1.3.5 + 2.6.10 + 4.12.20 + 9.27.45} \right)}}{{1.3.5 + 2.6.10 + 4.12.20 + 9.27.45}}\\\,\,\,\,\, = 2\end{array}\)b) \(\begin{array}{l}B = \frac{{636363.37 - 373737.63}}{{1 + 2 + 3 + \ldots + 2006}}\\\,\,\,\,\, = \frac{{63.10101.37 - 37.10101.63}}{{1 + 2 + 3 + \ldots + 2020 + 2021}}\\\,\,\,\,\, = \frac{0}{2} = 0\end{array}\)c) \(\begin{array}{l}C = \frac{{1978.1979 + 1980.21 + 1958}}{{1980.1979 - 1978.1979}}\\\,\,\,\,\, = \frac{{1978.1979 + 1979.21 + 21 + 1958}}{{1979.\left( {1980 - 1978} \right)}}\\\,\,\,\,\, = \frac{{1979.\left( {1978 + 21} \right) + 1979}}{{1979.2}}\\\,\,\,\,\, = \frac{{1979.1999 + 1979}}{{1979.2}}\\\,\,\,\,\, = \frac{{1979.\left( {1999 + 1} \right)}}{{1979.2}}\\\,\,\,\,\, = \frac{{1979.2000}}{{1979.2}}\\\,\,\,\,\, = 1000\end{array}\)d) \(\begin{array}{l}D = \frac{{2181.729 + 243.81.27}}{{9.81.243 + 18.54.162.9 + 723.729}}\\\,\,\,\,\, = \frac{{2181.729 + 243.81.9.3}}{{9.81.243 + 18.54.162.9 + 723.729}}\\\,\,\,\,\, = \frac{{2181.729 + 729.729}}{{729.243 + 1944.729 + 723.729}}\\\,\,\,\,\, = \frac{{729.\left( {2181 + 729} \right)}}{{729.\left( {243 + 1944 + 723} \right)}}\\\,\,\,\,\, = \frac{{729.2910}}{{729.2910}}\\\,\,\,\,\, = 1\end{array}\)
