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【323555】2023七年级数学上册 第2章 有理数2.7有理数的减法课时练习 (新版)华东师大版

时间:2025-01-15 19:22:54 作者: 字数:3146字
简介:


有理数的减法

(30分钟 50)

一、选择题(每小题4,12)

1.(聊城中考)计算|- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> |- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 的结果是 (  )

A.- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> C.-1 D.1

2.下列计算正确的是 (  )

A <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> .(-14)-(+5)=-9 B.0-(-3)=3

C.(-3)-(-3)=-6 D.|3-5|=-(5-3)

3.-2,3,-10这三个数中任意两个数之和的最大值与最小值的差是 (  )

A.13 B.-9 C.-5 D.5

二、填空题(每小题4,12)

4.“早穿皮袄午穿纱”这句民谣形象地描绘了我国新疆奇妙的气温变化现象.乌鲁木齐市五月的某一天,最高气温是20,最低温度是-2,则当天的最大温差是________.

5.x的相反 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 数是2013,|y|=2014,x-y的值为________.

6.符号“f”表示 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 一种运算,它对一些数的运算结果如下:

(1)f(1)=0,f(2)=1,f(3)=2,f(4)=3,…

(2)f( <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> )=2,f( <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> )=3,f( <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> )=4,f( <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> )=5,…

利用以上规律计算:f(201 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 3)-f( <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> )=________.

三、解答题(26)

7.(8)根据题意列出算式并计算:

(1)一个加数是1.8,和是-0.81,求另一个加数.

(2 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> )- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 的绝对值的相反数与 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 的相反数的差.

8.(8)如图是某地区春季某天的气温随时间的变化图象.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a>

请根据图象回答:

(1)何时气温最低?最低气温为多少?

(2)当天的最高气温是多少?这一天的最大温差 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 是多少?

(3)这天晚上的天气预报说,将有一股冷空气袭击该地区,第二天气温将下降1012.请你估计第二天该地区的最高气温不会高于多少?最低气温不会低于多少?第二天的最小温差是多少?

【拓展延伸】

9.(10)a,b是两个任意有理数,比较:

(1)a+ba-b的大小.

(2)|a-b|a-b的大小.







答案解析

1.【解析】选A <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> .|- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> |- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> = <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> +(- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> )=- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> .

2.【解析】选B.只有0-(-3)=0+3=3正确.

3.【解析】选A.和的最大值为-2+3=1,最小值为-2+(-10)=-12,所以1-(-12)=1+12=13.

4.【解析】最大温差是最高气温和最低气温的差,

20-(-2)=22℃.

答案:22

5.【解析】若x的相反数是2013,x=-2013;|y|=2014,y=±2014.所以x-y=(-2013)-2014=-4027 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> x-y=(-2013)-(-2014)=1.

答案:-40271

【知识拓展】此类与绝对值有关的计算往 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 往需要分情况讨论.例如,|x|=5,|y|=3,x-y=________.

【解析】由|x|=5,|y|=3x=±5,y=±3,4种情况讨论:

(1)x=5,y=3,x-y=5-3=2.

(2)x=5,y=-3,x-y=5-(-3)=5+3=8.

(3)x=-5,y=3,

x-y=-5-3=-5+(-3)=-8.

(4)x=-5,y=-3,

x-y=-5-(-3)=-5+(+3)=-2.

答案:±2±8

6.【解析】观察(1)中的各数,我们可以得出f(2013)=2012,

观察(2)中的各数,我们可以得出f( <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> )=2013.:f(2013)-f( <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> )=

2012-2013=-1.

答案:-1

7.【解析】(1)(-0.81)-1.8=(-0.81)+(-1.8)

=-2.61.

(2)-|- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> |-(- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> )=- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> + <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> = <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> .

8.【解析】(1) <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 由图象 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 可知2 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 时气温最 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a>,-2℃.

(2)最高气温为10℃,

最大温差为10-(-2)=10+2=12(℃).

(3)第二天该地区的最高气温不会高于10-10=0(℃),

最低气温 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/52/" title="减法" class="c1" target="_blank">减法</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/852/" title="有理数" class="c1" target="_blank">有理数</a> 不会低于

-2-12=-2+(-12)=-14(℃);

最小温差是

(10-12)-(-2-10)=-2-(-12)=10(℃).

9.【解析】(1)b>0,a+b>a-b;

b=0,a+b=a-b;

b<0,a+b<a-b.

(2)a>b,|a-b|=a-b;

a=b,|a-b|=a-b;a<b,|a-b|>a-b.

|a-b|≥a-b.

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