Question

9．在算式1+$\frac{1}{2}$$+\frac{1}{4}$$+\frac{1}{6}$$+\frac{1}{8}$=□×$\frac{1}{2}$×$\frac{1}{4}$×$\frac{1}{6}$×$\frac{1}{8}$中，“□”中應(yīng)該填入的數(shù)是784．

Answer 1

分析 先求出等式左邊和右邊$\frac{1}{2}$×$\frac{1}{4}$×$\frac{1}{6}$×$\frac{1}{8}$的結(jié)果，左邊的分數(shù)把$\frac{1}{2}$、$\frac{1}{4}$和$\frac{1}{8}$進行拆分，通過加減相互抵消，求出結(jié)果；然后用左邊的結(jié)果除以右邊$\frac{1}{2}$×$\frac{1}{4}$×$\frac{1}{6}$×$\frac{1}{8}$的結(jié)果，即可得出．

解答 解：1+$\frac{1}{2}$$+\frac{1}{4}$$+\frac{1}{6}$$+\frac{1}{8}$
=1+1-$\frac{1}{2}$+$\frac{1}{2}$-$\frac{1}{4}$+$\frac{1}{6}$+$\frac{1}{4}$-$\frac{1}{8}$
=2+$\frac{1}{6}$-$\frac{1}{8}$
=$\frac{49}{24}$
$\frac{1}{2}$×$\frac{1}{4}$×$\frac{1}{6}$×$\frac{1}{8}$=$\frac{1}{384}$
$\frac{49}{24}$÷$\frac{1}{384}$
=$\frac{49}{24}$×384
=784
答：“□”中應(yīng)該填入的數(shù)是784．
故答案為：784．

點評 此題解答的關(guān)鍵在于通過分數(shù)的拆分求出等式左邊的結(jié)果，進而計算得出答案．