9. 计算:
(1) $(-1.4) × (+1\dfrac{1}{11}) × (-1\dfrac{2}{3}) × (-5.5) × (+\dfrac{4}{7});$
(2) $\dfrac{8}{9} × [0.75 - (\dfrac{7}{16} - 0.25)].$
(1) $(-1.4) × (+1\dfrac{1}{11}) × (-1\dfrac{2}{3}) × (-5.5) × (+\dfrac{4}{7});$
(2) $\dfrac{8}{9} × [0.75 - (\dfrac{7}{16} - 0.25)].$
答案
(1) 原式$=-\frac{7}{5}×\frac{12}{11}×\frac{5}{3}×\frac{11}{2}×\frac{4}{7}=-8$
(2) 原式$=\frac{8}{9}×(0.75-\frac{7}{16}+0.25)=\frac{8}{9}×(0.75+0.25-\frac{7}{16})=\frac{8}{9}×(1-\frac{7}{16})=\frac{8}{9}×\frac{9}{16}=\frac{1}{2}$
(2) 原式$=\frac{8}{9}×(0.75-\frac{7}{16}+0.25)=\frac{8}{9}×(0.75+0.25-\frac{7}{16})=\frac{8}{9}×(1-\frac{7}{16})=\frac{8}{9}×\frac{9}{16}=\frac{1}{2}$
10. 用简便方法计算:
(1)$(-1.25)×\frac{5}{7}×(-4)×(-\frac{7}{5})$;
(2)$(-99\frac{8}{9})×18$。
(1)$(-1.25)×\frac{5}{7}×(-4)×(-\frac{7}{5})$;
(2)$(-99\frac{8}{9})×18$。
答案
(1) 原式$=[(-1.25)×(-4)]×[\frac{5}{7}×(-\frac{7}{5})]=5×(-1)=-5$
(2) 原式$=(-100+\frac{1}{9})×18=-100×18+\frac{1}{9}×18=-1\ 800+2=-1\ 798$
(2) 原式$=(-100+\frac{1}{9})×18=-100×18+\frac{1}{9}×18=-1\ 800+2=-1\ 798$
11. 阅读下面的材料:
$(1+\frac{1}{2})×(1-\frac{1}{3})=\frac{3}{2}×\frac{2}{3}=1;$
$(1+\frac{1}{2})×(1+\frac{1}{4})×(1-\frac{1}{3})×(1-\frac{1}{5})$
$=\frac{3}{2}×\frac{5}{4}×\frac{2}{3}×\frac{4}{5}$
$=(\frac{3}{2}×\frac{2}{3})×(\frac{5}{4}×\frac{4}{5})$
$=1×1$
$=1.$
根据以上方法和规律解答下列问题:
(1) 计算:$(1+\frac{1}{2})×(1+\frac{1}{4})×(1+\frac{1}{6})×(1-\frac{1}{3})×(1-\frac{1}{5})×(1-\frac{1}{7})=\_\_\_\_\_\_;$
(2) 猜想:
$(1+\frac{1}{2})×(1+\frac{1}{4})×(1+\frac{1}{6})×···×(1+\frac{1}{2026})×(1-\frac{1}{3})×(1-\frac{1}{5})×(1-\frac{1}{7})×···×(1-\frac{1}{2027})=\_\_\_\_\_\_.$
$(1+\frac{1}{2})×(1-\frac{1}{3})=\frac{3}{2}×\frac{2}{3}=1;$
$(1+\frac{1}{2})×(1+\frac{1}{4})×(1-\frac{1}{3})×(1-\frac{1}{5})$
$=\frac{3}{2}×\frac{5}{4}×\frac{2}{3}×\frac{4}{5}$
$=(\frac{3}{2}×\frac{2}{3})×(\frac{5}{4}×\frac{4}{5})$
$=1×1$
$=1.$
根据以上方法和规律解答下列问题:
(1) 计算:$(1+\frac{1}{2})×(1+\frac{1}{4})×(1+\frac{1}{6})×(1-\frac{1}{3})×(1-\frac{1}{5})×(1-\frac{1}{7})=\_\_\_\_\_\_;$
(2) 猜想:
$(1+\frac{1}{2})×(1+\frac{1}{4})×(1+\frac{1}{6})×···×(1+\frac{1}{2026})×(1-\frac{1}{3})×(1-\frac{1}{5})×(1-\frac{1}{7})×···×(1-\frac{1}{2027})=\_\_\_\_\_\_.$
答案
11. (1)1 (2)1
登录