13. 用合适的方法计算:
(1) $-\dfrac{3}{4} × (8 - \dfrac{4}{3} - \dfrac{14}{15})$;
(2) $(-5.25) × (-4.73) - 4.73 × (-19.75) - 25 × (-5.27)$;
(3) $0.7 × 1\dfrac{4}{9} + 2\dfrac{3}{4} × (-15) + 0.7 × \dfrac{5}{9} + \dfrac{1}{4} × (-15)$。
(1) $-\dfrac{3}{4} × (8 - \dfrac{4}{3} - \dfrac{14}{15})$;
(2) $(-5.25) × (-4.73) - 4.73 × (-19.75) - 25 × (-5.27)$;
(3) $0.7 × 1\dfrac{4}{9} + 2\dfrac{3}{4} × (-15) + 0.7 × \dfrac{5}{9} + \dfrac{1}{4} × (-15)$。
答案
13.(1)$-4\dfrac{3}{10}$ (2)$250$ (3)$-43.6$
14.如图,请你参考黑板中老师的讲解,利用运算律简便计算:

(1)$999×(-15)$;
(2)$999×118\frac{4}{5}+999×(-\frac{1}{5})-999×18\frac{3}{5}$;
(3)$99\frac{8}{9}×(-18)$;
(4)$99\frac{7}{8}×(-4)-(\frac{1}{2}-\frac{1}{3}-\frac{5}{6})×24$.
(1)$999×(-15)$;
(2)$999×118\frac{4}{5}+999×(-\frac{1}{5})-999×18\frac{3}{5}$;
(3)$99\frac{8}{9}×(-18)$;
(4)$99\frac{7}{8}×(-4)-(\frac{1}{2}-\frac{1}{3}-\frac{5}{6})×24$.
答案
14.(1)$-14\ 985$ (2)$99\ 900$ (3)$-1\ 798$ (4)$-383\dfrac{1}{2}$
15.【创新意识,运算能力】观察下列各式:
$\frac{1}{2}×\frac{2}{3}=\frac{1}{3}$;
$\frac{1}{2}×\frac{2}{3}×\frac{3}{4}=\frac{1}{4}$;
$\frac{1}{2}×\frac{2}{3}×\frac{3}{4}×\frac{4}{5}=\frac{1}{5}$;
……
(1)猜想:$\frac{1}{2}×\frac{2}{3}×\frac{3}{4}×…×\frac{49}{50}=$
(2)根据上面发现的规律,计算:
$(\frac{1}{100}-1)×(\frac{1}{99}-1)×(\frac{1}{98}-1)×…×(\frac{1}{2}-1)$。
$\frac{1}{2}×\frac{2}{3}=\frac{1}{3}$;
$\frac{1}{2}×\frac{2}{3}×\frac{3}{4}=\frac{1}{4}$;
$\frac{1}{2}×\frac{2}{3}×\frac{3}{4}×\frac{4}{5}=\frac{1}{5}$;
……
(1)猜想:$\frac{1}{2}×\frac{2}{3}×\frac{3}{4}×…×\frac{49}{50}=$
$\dfrac{1}{50}$
;(2)根据上面发现的规律,计算:
$(\frac{1}{100}-1)×(\frac{1}{99}-1)×(\frac{1}{98}-1)×…×(\frac{1}{2}-1)$。
答案
15.(1)$\dfrac{1}{50}$ (2)$-\dfrac{1}{100}$
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