除法心算(分數變小數)

分數變小數

1. $\frac{1}{2}=0.50$

2. $\frac{1}{3}=0.333\dots$, $\frac{2}{3}=0.666\dots$

3. $\frac{1}{4}=0.25$, $\frac{2}{4}=\frac{1}{2}=0.50$, $\frac{3}{4}=0.75$

4. $\frac{1}{5}=0.20$, $\frac{2}{5}=0.40$,$\frac{3}{5}=0.60$, $\frac{4}{5}=0.80$

5. $\frac{1}{6}=0.1666\dots$, $\frac{2}{6}=\frac{1}{3}=0.333\dots$,
    $\frac{3} {6}=\frac{1}{2}=0.50$, $\frac{4}{6}=\frac{2}{3}=0.666\dots$,
    $\frac{5}{6}=0.8333\dots$

6. $\frac{1}{8}=0.125$, $\frac{2}{8}=\frac{1}{4}=0.25$, $\frac{3}{8}=0.375$
    $\left (3\times\frac{1}{8}=3\times0.125=0.375 \right )$, $\frac{4}{8}=\frac{1}{2}=0.50$,
    $\frac{5}{8}=0.625$ $\left (5\times\frac{1}{8}=5\times0.125=0.625 \right )$,
    $\frac{6}{8}=\frac{3}{4}=0.75$, $\frac{7}{8}=0.875$
    $\left (7\times\frac{1}{8}=7\times0.125=0.875 \right )$

7. $\frac{1}{9}=0.\overline{1}$, $\frac{2}{9}=0 .\overline{2}$,
    $\frac{3}{9}=\frac{1}{3}=0.\overline{3}$, $\frac{4}{9}=0.\overline{4}$,
    $\frac{5}{9}=0.\overline{5}$, $\frac{6}{9}=\frac{2}{3}=0.\overline{6}$,
    $\frac{7}{9}=0.\overline{7}$, $\frac{8}{9}=0.\overline{8}$

8. $\frac{1}{10}=0.10$, $\frac{2}{10}=\frac{1}{5}=0.20$, $\frac{3}{10}=0.30$,
    $\frac{4}{10}=\frac{2}{5}=0.40$, $\frac{5}{10}=\frac{1}{2}=0.50$,
    $\frac{6}{10}=\frac{3}{5}=0.60$, $\frac{7}{10}=0.70$, $\frac{8}{10}=\frac{4}{5}=0.80$,
    $\frac{9}{10}=0.90$

9. $\frac{1}{11}=0.\overline{09}=0.0909\dots$, $\frac{2}{11}=0.\overline{18}$
    $\left ( 2\times0.0909\dots \right )$,
    $\frac{3}{11}=0.\overline{27}$ $\left (3\times0.0909\dots \right )$,
    $\frac{4}{11}=0.\overline{36}$ $\left (4\times0.0909\dots \right )$,
    $\frac{5}{11}=0.\overline{45}$ $\left (5\times0.0909\dots \right )$,
    $\frac{6}{11}=0.\overline{54}$ $\left (6\times0.0909\dots \right )$,
    $\frac{7}{11}=0.\overline{63}$ $\left (7\times0.0909\dots \right )$,
    $\frac{8}{11}=0.\overline{72}$ $\left (8\times0.0909\dots \right )$,
    $\frac{9}{11}=0.\overline{81}$ $\left (9\times0.0909\dots \right )$,
    $\frac{10}{11}=0.\overline{90}$ $\left (10\times0.0909\dots \right )$,

10. $\frac{1}{7}=0.\overline{142857}$, $\frac{2}{7}=0.\overline{285714}$
         $\left (2\times\frac{1}{7}=2\times0.\overline{142857} \right )$,
      $\frac{3}{7}=0.\overline{428571}$  $\left (3\times\frac{1}{7}=3\times0.\overline{142857} \right )$,
      $\frac{4}{7}=0.\overline{571428}$  $\left (4\times\frac{1}{7}=4\times0.\overline{142857} \right )$,
      $\frac{5}{7}=0.\overline{714285}$  $\left (5\times\frac{1}{7}=5\times0.\overline{142857} \right )$,
       $\frac{6}{7}=0.\overline{857142}$  $\left (6\times\frac{1}{7}=6\times0.\overline{142857} \right )$,

11. $\frac{18}{34}=\frac{9}{14}=\frac{4.5}{7}=0.6\overline{428571}$

12. $\frac{29}{45}=\frac{29\times2}{45\times2}=\frac{58}{90}=\frac{58\div10}{90\div10}$
      $=\frac{5.8}{9}=0.6\overline{4}$

13. $\frac{31}{25}=\frac{31\times4}{25\times4}=\frac{124}{100}=1.24$

14. $\frac{62}{75}=\frac{62\times4}{75\times4}==\frac{248\div100}{300\div100}$
      $=\frac{2.48}{3}=0.82\overline{6}$

15. $\frac{3}{16}=0.1\dots 1.4$, $\frac{1.4}{16}=\frac{0.7}{8}=0.0875$,
      $\frac{3}{16}=0.1875$


練習

1. $\frac{2}{5}=$
2. $\frac{4}{7}=$
3. $\frac{3}{8}=$
4. $\frac{9}{12}=$
5. $\frac{5}{12}=$
6. $\frac{6}{11}=$
7. $\frac{14}{24}=$
8. $\frac{13}{27}=$
9. $\frac{18}{48}=$
10. $\frac{10}{14}=$
11. $\frac{6}{32}=$
12. $\frac{19}{45}=$

參考文章
Arthur Benjamin, Michael Shermer，《數學速算魔法》，稻田，新北市，民100.08。p.116~121