9.(1)一个数的相反数是-0.7,则这个数的倒数是
(2)已知a是最大的负整数,b是-2的相反数,c与d互为倒数,则$a+b-c× d=$
(3)如果$a× b=-1$,那么称$a,b$互为“负倒数”,则-3的“负倒数”为
$\dfrac{10}{7}$
;(2)已知a是最大的负整数,b是-2的相反数,c与d互为倒数,则$a+b-c× d=$
0
;(3)如果$a× b=-1$,那么称$a,b$互为“负倒数”,则-3的“负倒数”为
$\dfrac{1}{3}$
。答案
9.(1)$\dfrac{10}{7}$ (2)0 (3)$\dfrac{1}{3}$
10. 用简便方法计算:
(1) $39\frac{5}{6} × (-6)$;
(2) $(-7.33) × 42.07 + (-2.07) × (-7.33)$;
(3) $[1\frac{1}{24} - (\frac{3}{8} + \frac{1}{6} - \frac{3}{4}) × 24] × (-\frac{1}{5})$;
(4) $3.59 × (-\frac{4}{7}) + 2.41 × (-\frac{4}{7}) - 6 × (-\frac{4}{7})$;
(1) $39\frac{5}{6} × (-6)$;
(2) $(-7.33) × 42.07 + (-2.07) × (-7.33)$;
(3) $[1\frac{1}{24} - (\frac{3}{8} + \frac{1}{6} - \frac{3}{4}) × 24] × (-\frac{1}{5})$;
(4) $3.59 × (-\frac{4}{7}) + 2.41 × (-\frac{4}{7}) - 6 × (-\frac{4}{7})$;
答案
10.(1)$-239$ (2)$-293.2$ (3)$-\dfrac{29}{24}$ (4)$0$
11. 我们知道:$\frac{1}{2}×\frac{2}{3}=\frac{1}{3}$,$\frac{1}{2}×\frac{2}{3}×\frac{3}{4}=\frac{1}{4}$,$\frac{1}{2}×\frac{2}{3}×\frac{3}{4}×\frac{4}{5}=\frac{1}{5}$,…,$\frac{1}{2}×\frac{2}{3}×\frac{3}{4}×…×\frac{n}{n+1}=\frac{1}{n+1}$。
试根据以上规律,解答下列问题:
(1) 计算:$(\frac{1}{2}-1)×(\frac{1}{3}-1)×(\frac{1}{4}-1)×…×(\frac{1}{100}-1)$;
(2) 将2026减去它的$\frac{1}{2}$,再减去余下的$\frac{1}{3}$,再减去余下的$\frac{1}{4}$,再减去余下的$\frac{1}{5}$……以此类推,直至减去余下的$\frac{1}{2026}$,最后的结果是多少?
试根据以上规律,解答下列问题:
(1) 计算:$(\frac{1}{2}-1)×(\frac{1}{3}-1)×(\frac{1}{4}-1)×…×(\frac{1}{100}-1)$;
(2) 将2026减去它的$\frac{1}{2}$,再减去余下的$\frac{1}{3}$,再减去余下的$\frac{1}{4}$,再减去余下的$\frac{1}{5}$……以此类推,直至减去余下的$\frac{1}{2026}$,最后的结果是多少?
答案
11.解:(1)原式$=(-\dfrac{1}{2})×(-\dfrac{2}{3})×(-\dfrac{3}{4})×…×(-\dfrac{99}{100})=-\dfrac{1}{100}.$
(2)$2026×(1-\dfrac{1}{2})×(1-\dfrac{1}{3})×…×(1-\dfrac{1}{2026})=2026×\dfrac{1}{2}×\dfrac{2}{3}×\dfrac{3}{4}×…×\dfrac{2025}{2026}=2026×\dfrac{1}{2026}=1.$
(2)$2026×(1-\dfrac{1}{2})×(1-\dfrac{1}{3})×…×(1-\dfrac{1}{2026})=2026×\dfrac{1}{2}×\dfrac{2}{3}×\dfrac{3}{4}×…×\dfrac{2025}{2026}=2026×\dfrac{1}{2026}=1.$
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