初中数学人教版七年级上册1.2.3 相反数课前预习课件ppt

这是一份初中数学人教版七年级上册1.2.3 相反数课前预习课件ppt，共26页。PPT课件主要包含了结合数轴考虑等内容，欢迎下载使用。

1.借助数轴理解相反数的意义，懂得数轴上表示相反数的两个点关于原点对称.（难点）Understand the meaning f ppsite numbers with the help f the number line, and understand that the tw pints representing ppsite numbers n the number line are symmetrical abut the rigin.2.会求有理数的相反数.(重点）Be able t find the ppsite f a ratinal number.
成语故事《南辕北辙》讲了一个人…… Idim stry "different directins" tells a man...
如果点O表示魏国的位置，点A表示楚国的位置，假设楚国与魏国相距30 km，以魏国为原点0，我们规定向南为正方向，而此人从魏国出发向北到了点B也走了30 km，请同学们把这3个点在数轴上表示出来． If pint O represents the psitin f the state f Wei and pint A represents the psitin f the state f Chu, assuming that the state f Chu is 30 km away frm the state f Wei and takes the state f Wei as the rigin 0, we stipulate that the suth is the psitive directin, and this persn starts frm the state f Wei and ges nrth t pint B fr 30 km. Please shw these three pints n the number line.
两位同学背靠背，规定向前为正The tw students are back-t-back, and we stipulate that frward directin is psitive directin
一人向前走3步Walk three steps frward: ,一人向后走3步Walk three steps backward: .
对照数轴,说出-3与+3两数的相同点和不同点.What's the similarities and differences between - 3 and + 3
活动1：观察下列一组数＋1和－1，＋2.5和－2.5，＋4和－4，并把它们在数轴上表示出来.Activity 1: Observe the fllwing grups f numbers + 1 and - 1, + 2.5 and - 2.5,+ 4 and - 4 and express them n the number line. 1）上述各组数之间有什么特点？ What are the characteristics f the abve numbers? 2）你能得出相反数的概念吗？ Can yu cme up with the cncept f ppsite numbers? 3）表示各对数的点在数轴上有什么位置关系？ What is the psitinal relatinship between the pints in each grup ?
探究一 相反数的概念
活动2：请观察这两个数，它们有什么异同点？你还能列举两个这样的数吗？Activity 2: please bserve these tw numbers. What are their similarities and differences? Can yu list tw such numbers?
数字相同 Same number
符号不同 Different signs
1.定义：只有符号不同的两个数叫做互为相反数.Only tw numbers with different symbls are called ppsite numbers.
2.一般地，a和-a互为相反数.In general, a and - a are ppsite numbers.
（1）－5是5的相反数 - 5 is the ppsite number f 5;（ ） （2）－5是相反数 - 5 is the ppsite number; （ ） （3） 与 互为相反数. are ppsite numbers;（ ） （4）－5和5互为相反数 －5 and 5 are ppsite numbers； （ ）
（5） 相反数等于它本身的数只有0 The ppsite number f 0 is itself﹙ ﹚ （6） 符号不同的两个数互为相反数Tw numbers with different symbls are ppsite numbers. ﹙ ﹚
0的相反数是_____. The ppsite number f 0 is itself.
一个正数的相反数是一个　　　．The ppsite f a psitive number is a negative number
一个负数的相反数是一个　　　．The ppsite f a negative number is a psitive number
一个数的相反数是它本身的数是 ______．The ppsite number f 0 is itself.　　
思考：在数轴上，画出几组表示相反数的点，并观察这两个点具有怎样的特征？On the number line, draw several grups f pints representing ppsite numbers, and bserve what characteristics these tw pints have?
位于原点两侧，且与原点的距离相等.It is lcated n bth sides f the rigin and the distance frm the rigin is equal.
探究二 相反数的几何意义 Gemetric meaning f ppsite numbers
数轴上到原点的距离相等的点所表示的数有什么特点？借助数轴填一填：What are the characteristics f the number represented by a pint with equal distance frm the number line t the rigin?1.数轴上与原点距离是2的点有____个，这些点表示的数是________；There are_____ pints n the number line whse distance frm the rigin is 2 .The number represented by these pints is________2.与原点的距离是5的点有____个，这些点表示的数是________.There are_____ pints n the number line whse distance frm the rigin is 5 .The number represented by these pints is________
1.互为相反数的两个数分别位于原点的两侧（0除外）Tw ppsite numbers are lcated n bth sides f the rigin (except 0)；2.互为相反数的两个数到原点的距离相等.Tw ppsite numbers are equal in distance t the rigin.
1. 一般地，设a是一个正数，数轴上与原点的距离是a的点有_____个，它们分别在原点的______，表示_______，我们说这两点________________.In general, let a be a psitive number. There are tw pints n the number line whse distance frm the rigin is a. They are n the left and right f the rigin, representing - a and a. We say that these tw pints are symmetrical abut the rigin.
问题1：a的相反数是什么？Questin 1: what is the ppsite number f a?
在这个数前加一个“－”号．Put a "-" befre this number
问题2：如何求一个数的相反数？Questin 2: hw t find the ppsite number f a number?
a 的相反数是－a ， a可表示任意有理数.The ppsite number f a is - a, and a can represent any ratinal number.
－（＋1.1）表示什么？－（－7）呢？－（－9.8）呢？它们的结果应是多少？
问题3：若把 a分别换成＋5，－7，0时，这些数的相反数怎样表示？Questin 3: If a is replaced by + 5, - 7 and 0 respectively, hw t express the ppsite numbers?
a = +5， - a = -（+5）a = -7， - a = -（-7）a = 0， - a = 0
(1) 是____的相反数， (2) 是______的相反数， =______ ． (3) 是_______的相反数， ． (4) 是_______的相反数， ．
思考：如果在一个数前面加上“＋”号所得得到的结果是什么呢？If yu add a "+" sign t a number, what result will yu get ?
在一个数前面加上“－”号表示求这个数的相反数.Adding a "-" sign befre a number means finding the ppsite number.
化简下列各数（先读后写）Simplify the fllwing numbers (1)-(+10) (2)+(-0.15) (3)+(+3) (4)-(-12) (5)+[-(-1.1)] (6)-[+(-7)]
(6) -[+(-7)]=-(-7)=7.
方法总结：化简多重符号时，只需数一下数字前面有多少个负号，若有偶数个，则结果为正；若有奇数个，则结果为负.Just cunt the number f minus signs in frnt f the number. If there are even numbers, the result is psitive; If there are dd numbers, the result is negative.
解：(1) -(+10)=-10；
(2) +(-0.15)=-0.15；
(3) +(+3)=3；
(4) -(-12)=12；
(5) +[-(-1.1)]=+(+1.1)=1.1；
技巧：（一查二定）1.式子中含偶数个“－”号时，结果正；If there are even numbers, the result is psitive;含奇数个“－”号时，结果为负 If there are dd numbers, the result is negative.2.凡是“+”都去掉。
1．-1.6是____的相反数，____的相反数是0.3．2．下列几对数中互为相反数的一对为（ ）． A． 和 B． 与 C． 与3．5的相反数是____；a的相反数是___；
4．若a=-13，则-a=____;若-a=-6，则a=___ ．5．若a是负数，则-a是_____数；若-a是负数，则 　 a是_____数．6. 的相反数是_____，-3x的相反数是___.
7.（1）若a=3.2，则-a= ; (2)若-a= 2,则a= ; (3)若-（-a）=3，则-a= ; (4)-（a-b）= . 
8.若2x+1是-9的相反数，求x的值.If 2x + 1 and - 9 are ppsite numbers , find the value f x.
解：由相反数的定义，得Accrding t the definitin f ppsite number,we can get 2x+1=9 2x=8 x=4
拓展思考：已知两个有理数x、y，且x+y=0, 那么这两个有理数有什么关系？Extend: Given tw ratinal numbers x and y, and x + y = 0, what is the relatinship between these tw ratinal numbers?
1.相反数的概念:只有符号不同的两个数互为相反数；特别地，0的相反数是0.The cncept f ppsite numbers: nly tw numbers with different symbls are called ppsite numbers; In particular, the ppsite f 0 is 0.2． 表示 的相反数.-a is the ppsite f a.