《2025年触类旁通奥数点睛六年级数学通用版》

### 金牌例题 4
计算。
(1)$0.74\div(71\times\frac{74}{100})$
(2)$98\div98\frac{98}{99}$

答案： 1)$0.74\div(71\times\frac{74}{100}) = 0.74\div\frac{74}{100}\div71 = 1\div71 = \frac{1}{71}$

(2)$98\div98\frac{98}{99} = 1\div(98\frac{98}{99}\div98) = 1\div(98\div98 + \frac{98}{99}\div98) = 1\div(1 + \frac{1}{99}) = 1\div\frac{100}{99} = \frac{99}{100}$

计算。
$4.5\div\frac{8}{5} + 3.5\times\frac{5}{8}$
$\frac{5}{12}\div(\frac{5}{6} - \frac{1}{2}\times\frac{3}{4})$
$2021\frac{2021}{2022}\div2021$
$1\div(1.3\div1.7)\div(1.7\div7)\div(7\div2.6)$
$18.25\times11\frac{4}{5} - 17\frac{1}{4}\div(1 - \frac{54}{59})$
$(2\frac{2}{9} + 3\frac{4}{7} + 1\frac{4}{11})\div(\frac{3}{11} + \frac{5}{7} + \frac{4}{9})$
$(1\frac{1}{1007}\times3.4 + 3\frac{2}{5}\times8\frac{1006}{1007})\div2\frac{3}{7}$

答案： 原式=4.5×$\frac{5}{8}$+3.5×$\frac{5}{8}$=$\frac{5}{8}$×(4.5 + 3.5)=$\frac{5}{8}$×8 = 5
原式=$\frac{5}{12}$÷($\frac{5}{6}$−$\frac{3}{8}$)=$\frac{5}{12}$÷$\frac{11}{24}$=$\frac{10}{11}$
原式=(2021+$\frac{2021}{2022}$)×$\frac{1}{2021}$=2021×$\frac{1}{2021}$+$\frac{2021}{2022}$×$\frac{1}{2021}$=1+$\frac{1}{2022}$=1$\frac{1}{2022}$
原式=1÷1.3×1.7÷1.7×7÷7×2.6 = 1×2=2
原式=18.25×$\frac{59}{5}$−17.25÷$\frac{5}{59}$=18.25×$\frac{59}{5}$-17.25×$\frac{59}{5}$=(18.25 - 17.25)×$\frac{59}{5}$=1×$\frac{59}{5}$=$\frac{59}{5}$=11$\frac{4}{5}$
原式=5×($\frac{3}{11}$+$\frac{5}{7}$+$\frac{4}{9}$)÷($\frac{3}{11}$+$\frac{5}{7}$+$\frac{4}{9}$) = 5
原式=(1$\frac{1}{1007}$×$\frac{17}{5}$+$\frac{17}{5}$×8$\frac{1006}{1007}$)×$\frac{7}{17}$=$\frac{17}{5}$×$\frac{7}{17}$×(1$\frac{1}{1007}$+8$\frac{1006}{1007}$)=$\frac{7}{5}$×10 = 14