1. 直接写得数。
$0.5×0.8=$
$0.05×8=$
$0.8÷0.5=$
$0.8×\frac{3}{4}=$
$0.8÷\frac{3}{4}=$
$0.12÷0.3=$
$0.12÷0.4×0.3=$
$0.12×0.3÷0.12×0.3=$
答案：$0.5×0.8=0.4$
$0.05×8=0.4$
$0.8÷0.5=1.6$
$0.8×\frac{3}{4}=0.6$
$0.8÷\frac{3}{4}=\frac{16}{15}$
$0.12÷0.3=0.4$
$0.12÷0.4×0.3=0.09$
$0.12×0.3÷0.12×0.3=0.09$
2. 用递等式计算。
$0.25 + 0.75 ÷ 0.125$
$8 ÷ \frac{2}{5} + 8 ÷ \frac{3}{5}$
$( \frac{7}{4} - \frac{2}{5} ) ÷ 0.625$
$3.69 - 0.69 ÷ 0.75$
$\frac{10}{21} ÷ [ ( \frac{5}{6} + \frac{1}{12} ) × \frac{8}{11} ]$
$\frac{7}{20} ÷ ( 2.4 × \frac{7}{24} - \frac{2}{5} )$
答案：$0.25+0.75÷0.125$
$=0.25+6$
$=6.25$
$8÷ \frac{2}{5}+8÷ \frac{3}{5}$
$=8× \frac{5}{2}+8× \frac{5}{3}$
$=20+\frac{40}{3}$
$=\frac{100}{3}$
$(\frac{7}{4}-\frac{2}{5})÷ 0.625$
$=(\frac{35}{20}-\frac{8}{20})÷ \frac{5}{8}$
$=\frac{27}{20}× \frac{8}{5}$
$=\frac{54}{25}$
$3.69-0.69÷ 0.75$
$=3.69-0.92$
$=2.77$
$\frac{10}{21}÷ [(\frac{5}{6}+\frac{1}{12})× \frac{8}{11}]$
$=\frac{10}{21}÷ [\frac{11}{12}× \frac{8}{11}]$
$=\frac{10}{21}÷ \frac{2}{3}$
$=\frac{10}{21}× \frac{3}{2}$
$=\frac{5}{7}$
$\frac{7}{20}÷ (2.4× \frac{7}{24}-\frac{2}{5})$
$=\frac{7}{20}÷ (0.7-0.4)$
$=\frac{7}{20}÷ \frac{3}{10}$
$=\frac{7}{20}× \frac{10}{3}$
$=\frac{7}{6}$
3. 简便计算。
$(\frac{2}{9}+\frac{2}{17})×4+\frac{9}{17}$
$(\frac{11}{18}+0.75-\frac{2}{9})÷\frac{1}{36}$
$19×\frac{2025}{2026}$
$\frac{10}{13}×\frac{5}{7}+\frac{10}{13}÷\frac{13}{8}$
$\frac{10}{13}×(\frac{13}{10}+\frac{7}{9})÷\frac{7}{9}$
$2026×\frac{19}{2025}$
答案：第一题
$\begin{aligned}(\frac{2}{9}+\frac{2}{17})×4+\frac{9}{17}&=\frac{2}{9}×4+\frac{2}{17}×4+\frac{9}{17}\\&=\frac{8}{9}+\frac{8}{17}+\frac{9}{17}\\&=\frac{8}{9}+(\frac{8}{17}+\frac{9}{17})\\&=\frac{8}{9}+1\\&=1\frac{8}{9}\end{aligned}$
第二题
$\begin{aligned}(\frac{11}{18}+0.75-\frac{2}{9})÷\frac{1}{36}&=(\frac{11}{18}+\frac{3}{4}-\frac{2}{9})×36\\&=\frac{11}{18}×36+\frac{3}{4}×36-\frac{2}{9}×36\\&=22+27-8\\&=41\end{aligned}$
第三题
$\begin{aligned}19×\frac{2025}{2026}&=19×(1-\frac{1}{2026})\\&=19×1-19×\frac{1}{2026}\\&=19-\frac{19}{2026}\\&=18\frac{2007}{2026}\end{aligned}$
第四题
$\begin{aligned}\frac{10}{13}×\frac{5}{7}+\frac{10}{7}÷\frac{13}{8}&=\frac{10}{13}×\frac{5}{7}+\frac{10}{7}×\frac{8}{13}\\&=\frac{10}{13}×\frac{5}{7}+\frac{10}{13}×\frac{8}{7}\\&=\frac{10}{13}×(\frac{5}{7}+\frac{8}{7})\\&=\frac{10}{13}×\frac{13}{7}\\&=\frac{10}{7}\end{aligned}$
第五题
$\begin{aligned}\frac{10}{13}×(\frac{13}{10}+\frac{7}{9})÷\frac{7}{9}&=\frac{10}{13}×(\frac{13}{10}+\frac{7}{9})×\frac{9}{7}\\&=\frac{10}{13}×\frac{13}{10}×\frac{9}{7}+\frac{10}{13}×\frac{7}{9}×\frac{9}{7}\\&=\frac{9}{7}+\frac{10}{13}\\&=\frac{117}{91}+\frac{70}{91}\\&=\frac{187}{91}\end{aligned}$
第六题
$\begin{aligned}2026×\frac{19}{2025}&=(2025+1)×\frac{19}{2025}\\&=2025×\frac{19}{2025}+1×\frac{19}{2025}\\&=19+\frac{19}{2025}\\&=19\frac{19}{2025}\end{aligned}$
4. 先画一个正方形表示“1”，再在正方形中涂色表示出下面算式中的分数，想想怎样更快地算出结果。
$\frac{1}{3}+\frac{1}{9}+$
$+\frac{1}{81}+\frac{1}{243}$
答案：图略 $(1-\dfrac{1}{243})×\dfrac{1}{2}=\dfrac{121}{243}$
