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【330004】15.1.1 从分数到分式

时间:2025-02-07 09:16:59 作者: 字数:3494字

 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

15.1.1 从分数到分式

学习目标

1、了解分式的概念以及分式与整式概念的区别与联系。

2、掌握分式有意义的条件,进一步理解用字母表示数的意义,发展符号感。

3、以描述实际问题中的数量关系为背景,体会分式是刻画现实生活中数量关系的一类代数式。

学习重点: 分式的概念和分式有意义的条件。

学教难点: 分式的特点和分式有意义的条件。

课前预习

  1. 什么是整式? ,整式中如有分母,

分母中 (含、不含)字母

  1. 下列各式中,哪些是整式?哪些不是整式?两者有什么区别?

 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 2x+y  <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>3a 5 .

  1. 阅读“引言”, “引言”中出现的式子是整式吗?

  2. 自主探究:完成p127的“思考”,通过探究发现, <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 与分数一样,都是 的形式,分数的分子A与分母B都是 ,并且B中都含有

  3. 归纳:分式的意义:

代数式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 都是 。分数有意义的条件是 。那么分式有意义的条件是

课内探究

1、什么是分式?



2、分式中分母应满足什么条件?



1、在下列各式中,哪些是整式?哪些是分式?

15x-7 23x2-1 3 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>4 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

5)—5 6 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>7 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>8 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>





2p128的“例1”填空:

1)当x 时,分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 有意义 (2)当x 时,分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 有意义

3)当b 时,分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 有意义

4)当xy满足关系 时,分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 有意义

3x为何值时,下列分式有意义?

1 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>2 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>3 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>



4x为何值时,下列分式的值为0

1 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>2 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>3 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>





当堂检测

1、下列各式中,(1 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>2 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>3 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>4 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>5 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

60.7 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>x+y)整式是 ,分式是 。(只填序号)

2、当x= 时,分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 没有意义。3、当x= 时,分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 的值为0

4、当x= 时,分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 的值为正,当x= 时,分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 的值为非负数。

5、甲,乙两人分别从两地同时出发,若相向而行, <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 小时相遇;若同而行则 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 小时甲追上乙,那么甲的速度是乙的速度的( )倍.

. <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>    B. <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>     C. <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>    D. <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

课后训练

1、分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> ,当 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> _______时,分式有意义;当 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> _______时,分式的值为零.

2、有理式① <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> ,② <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> ,③ <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> ,④ <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 中,是分式的有( )

A、①② B、③④ C、①③ D、①②③④

3、分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 中,当 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 时,下列结论正确的是( )

A、分式的值为零; B、分式无意义

C、若 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 时,分式的值为零; D、若 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 时,分式的值为零

4、当 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> _______时,分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 的值为正;当 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> ______时,分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 的值为负.

5、下列各式中,可能取值为零的是( )

A <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> B <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> C <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> D <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

6、使分式 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 无意义,x的取值是( )

A0 B1 C <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> D <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

13、(学科综合题)已知 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 取哪些值时:

1 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 的值是正数;

2 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 的值是负数;

3 <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 的值是零;

4)分式无意义.