【321218】六年级数学上册第三单元分数除法简便计算典型例题（学生版）

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六年级数学上册第三单元分数除法简便计算

典型例题

整数、小数、分数的简便计算运算定律、运算性质：

运算定律	运算性质
加法交换律：a+b=b+a	减法运算性质： a-b-c=a-(b+c) a-(b-c)=a-b+c
加法结合律：a+b+c=a+(b+c)	减法运算性质： a-b-c=a-(b+c) a-(b-c)=a-b+c
乘法交换律：a×b=b×a	除法运算性质： a÷b÷c=a÷(b×c) a÷(b÷c)=a÷b×c (a+b)÷c=a÷c+b÷c (a-b)÷c=a÷c-b÷c
乘法结合律：a×b×c=a×(b×c)
乘法分配律： (a+b)×c=a×c+b×c (a-b)×c=a×c-b×c

1.简便计算类型一：“分数除法化成分数乘法，再简便计算”。

【例题1】÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> ÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a>

【对应练习】

【例题2】 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a>

【对应练习】

【例题3】 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a>

【对应练习】

2. 简便计算类型二：“带分数化成假分数，再简便计算”。

【例题】2020÷2020 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a>

【对应练习】

22÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a>

2021÷2021 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a>

3. 简便计算类型三：“带分数化加式，再简便计算”。

【例题】2020 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> ÷2020

【对应练习】

32÷32 16 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> ÷8 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> ÷3

4. 简便计算类型四：“提取分数单位，再整体约分”。

【例题】 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> ÷ <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a>

【对应练习】

5. 简便计算类型五：“带分数化加式，再凑分数约分”。

【例题】60 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> ÷29

【对应练习】

84 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> ÷41 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a> 2010 <a href="/tags/1/" title="单元" class="c1" target="_blank">单元</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/96/" title="典型" class="c1" target="_blank">典型</a> <a href="/tags/98/" title="例题" class="c1" target="_blank">例题</a> <a href="/tags/144/" title="分数" class="c1" target="_blank">分数</a> <a href="/tags/194/" title="除法" class="c1" target="_blank">除法</a>

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单元数学典型例题分数除法