9. 计算:
(1)$(-\dfrac{1}{3})+(+\dfrac{2}{5})+(+\dfrac{3}{5})+(-1\dfrac{2}{3})$;
(2)$0-6+3.54-4.72+16.46-5.28$;
(3)$(-1.5)-(-3\dfrac{1}{4})+(+3.75)+(-4\dfrac{1}{2})$;
(4)$0-21\dfrac{2}{3}+(+3\dfrac{1}{4})-(-\dfrac{2}{3})-(+\dfrac{1}{4}).$
(1)$(-\dfrac{1}{3})+(+\dfrac{2}{5})+(+\dfrac{3}{5})+(-1\dfrac{2}{3})$;
(2)$0-6+3.54-4.72+16.46-5.28$;
(3)$(-1.5)-(-3\dfrac{1}{4})+(+3.75)+(-4\dfrac{1}{2})$;
(4)$0-21\dfrac{2}{3}+(+3\dfrac{1}{4})-(-\dfrac{2}{3})-(+\dfrac{1}{4}).$
答案
9.解:(1)原式$=-(\dfrac{1}{3}+1\dfrac{2}{3})+(\dfrac{2}{5}+\dfrac{3}{5})=-2+1=-1$.
(2)原式$=-6+(3.54+16.46)-(4.72+5.28)=-6+20-10=4$.
(3)原式$=-(1.5+4.5)+(3.25+3.75)=-6+7=1$.
(4)原式$=-(21\dfrac{2}{3}-\dfrac{2}{3})+(3\dfrac{1}{4}-\dfrac{1}{4})=-21+3=-18$.
(2)原式$=-6+(3.54+16.46)-(4.72+5.28)=-6+20-10=4$.
(3)原式$=-(1.5+4.5)+(3.25+3.75)=-6+7=1$.
(4)原式$=-(21\dfrac{2}{3}-\dfrac{2}{3})+(3\dfrac{1}{4}-\dfrac{1}{4})=-21+3=-18$.
10. 已知 $a,b$ 互为相反数,$c,d$ 互为倒数,$x$ 的绝对值为 5,求 $2a+2b-3cd-x+1$ 的值.
答案
10.解:由题意,得$a+b=0$,$cd=1$,$|x|=5$,所以$x=\pm5$.
当$x=5$时,原式$=2×0-3×1-5+1=0-3-5+1=-7$;
当$x=-5$时,原式$=2×0-3×1-(-5)+1=0-3+5+1=3$.
当$x=5$时,原式$=2×0-3×1-5+1=0-3-5+1=-7$;
当$x=-5$时,原式$=2×0-3×1-(-5)+1=0-3+5+1=3$.
11. 某路公交车从起点经过 A,B,C,D 站到达终点,各站上下车乘客的人数如下(上车为正,下车为负):起点$(15,0),A(17,-4),B(12,-9),C(6,-15),D(4,-7)$,终点$(0,$
(1)横线上应填写的数是
(2)若乘坐该车的票价为每人 2 元,则这一趟公交车能收入多少元钱?
-19
$)$.(1)横线上应填写的数是
-19
,该数的实际意义是终点有19人下车
;(2)若乘坐该车的票价为每人 2 元,则这一趟公交车能收入多少元钱?
答案
11.(1)$-19$ 终点有19人下车
(2)解:$(15+17+12+6+4)×2=54×2=108$(元).
答:这一趟公交车能收入108元.
(2)解:$(15+17+12+6+4)×2=54×2=108$(元).
答:这一趟公交车能收入108元.
12. 设$[a]$表示不超过$a$的最大整数,例如:$[2.3]=2,[-4\dfrac{1}{3}]=-5,[5]=5.$
(1)求$[2\dfrac{1}{5}]+[-3.6]-[-7]$的值;
(2)令$\{a\}=a-[a]$,求$\{2\dfrac{3}{4}\}-[-2.4]+\{-6\dfrac{1}{4}\}$的值.
(1)求$[2\dfrac{1}{5}]+[-3.6]-[-7]$的值;
(2)令$\{a\}=a-[a]$,求$\{2\dfrac{3}{4}\}-[-2.4]+\{-6\dfrac{1}{4}\}$的值.
答案
12.解:(1)$[2\dfrac{1}{5}]+[-3.6]-[-7]$
$=2+(-4)-(-7)$
$=2-4+7$
$=5$.
(2)$\{2\dfrac{3}{4}\}-[-2.4]+\{-6\dfrac{1}{4}\}$
$=2\dfrac{3}{4}-[2\dfrac{3}{4}]-[-2.4]+(-6\dfrac{1}{4})-[-6\dfrac{1}{4}]$
$=\dfrac{11}{4}-2+3-\dfrac{25}{4}+7$
$=8-\dfrac{7}{2}$
$=8-3.5$
$=4.5$.
$=2+(-4)-(-7)$
$=2-4+7$
$=5$.
(2)$\{2\dfrac{3}{4}\}-[-2.4]+\{-6\dfrac{1}{4}\}$
$=2\dfrac{3}{4}-[2\dfrac{3}{4}]-[-2.4]+(-6\dfrac{1}{4})-[-6\dfrac{1}{4}]$
$=\dfrac{11}{4}-2+3-\dfrac{25}{4}+7$
$=8-\dfrac{7}{2}$
$=8-3.5$
$=4.5$.
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