怎么计算整数除以分数

用整数除以分数就是要找出整数中包含多少个分数。计算整数除以分数的标准方法就是用整数乘以分数的倒数。你也可以画一张图来直观地显示计算过程。

步骤

乘以倒数

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/8\/82\/Divide-a-Whole-Number-With-a-Fraction-Step-1-Version-2.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-1-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/8\/82\/Divide-a-Whole-Number-With-a-Fraction-Step-1-Version-2.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 把整数转换成分数。转换时，把整数作为分数的分子，分母为1。^[1]
   • 例如，假设你要计算${\displaystyle 7÷\frac{3}{4}}$，需要先把${\displaystyle 7}$转换成${\displaystyle \frac{7}{1}}$。
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/8\/81\/Divide-a-Whole-Number-With-a-Fraction-Step-2-Version-2.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-2-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/8\/81\/Divide-a-Whole-Number-With-a-Fraction-Step-2-Version-2.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-2-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 求除数的倒数。数字的倒数就是把数字倒过来。求分数的倒数就是调换分子和分母的位置。^[2]
   • 例如，${\displaystyle \frac{3}{4}}$的倒数就是${\displaystyle \frac{4}{3}}$。
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/8\/8f\/Divide-a-Whole-Number-With-a-Fraction-Step-3-Version-2.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-3-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/8\/8f\/Divide-a-Whole-Number-With-a-Fraction-Step-3-Version-2.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-3-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 将两个分数相乘。分数相乘时，先将分子相乘，然后将分母相乘。两个分数的乘积就等于原先除法问题的商。^[3]
   • 例如，${\displaystyle \frac{7}{1}\times \frac{4}{3}=\frac{28}{3}}$
4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/db\/Divide-a-Whole-Number-by-a-Fraction-Step-4-Version-2.jpg\/v4-460px-Divide-a-Whole-Number-by-a-Fraction-Step-4-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/db\/Divide-a-Whole-Number-by-a-Fraction-Step-4-Version-2.jpg\/v4-728px-Divide-a-Whole-Number-by-a-Fraction-Step-4-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 如有必要可以进行简化。如果你得出的是假分数（即分子大于分母的分数），老师会要求你将其转换成带分数。一般老师会要求你把分数约分至最简分数。
   • 例如，${\displaystyle \frac{28}{3}}$ 简化成带分数${\displaystyle 9\frac{1}{3}}$。

画图

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/1\/19\/Divide-a-Whole-Number-With-a-Fraction-Step-5.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-5.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/1\/19\/Divide-a-Whole-Number-With-a-Fraction-Step-5.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-5.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 画出代表整数的图形。这些图形要能分成相等的几个部分，比如正方形或圆形。图形要画得足够大，能把它们分成小块。
   • 例如，假设你要计算${\displaystyle 5÷\frac{3}{4}}$，就要画5个圆形。
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/5\/56\/Divide-a-Whole-Number-With-a-Fraction-Step-6.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-6.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/5\/56\/Divide-a-Whole-Number-With-a-Fraction-Step-6.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-6.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 根据分数的分母划分每个整数图形。分数的分母告诉你整数被分成了多少份。把每个整数图形分成若干部分。^[4]
   • 例如，假设除数是${\displaystyle \frac{3}{4}}$，分母4就是告诉你要把每个整数图形分成四份。
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/4\/48\/Divide-a-Whole-Number-With-a-Fraction-Step-7.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-7.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/4\/48\/Divide-a-Whole-Number-With-a-Fraction-Step-7.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-7.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 每组中的着色部分表示分数。用整数除以分数也就是要计算出整数中有几组分数。^[5] 因此要先创建组别。由于有些组别中会有分属于两个不同整数的部分，因此最好能给每个组涂上不同的颜色。剩下的部分不用涂色。
   • 例如，假设你要计算5除以${\displaystyle \frac{3}{4}}$，需要将每组4个部分中的3个部分涂色，每组的颜色不同。要注意，很多组别中有2个四分之一部分属于其中一个整数，还有1个四分之一部分属于另一个整数。
4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/6\/6d\/Divide-a-Whole-Number-With-a-Fraction-Step-8.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-8.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/6\/6d\/Divide-a-Whole-Number-With-a-Fraction-Step-8.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-8.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 计算完整组别的数目。这个数目就是答案的整数部分。
   • 例如，在5个圆中应该有6组${\displaystyle \frac{3}{4}}$。
5. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/a8\/Divide-a-Whole-Number-With-a-Fraction-Step-9.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-9.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/a8\/Divide-a-Whole-Number-With-a-Fraction-Step-9.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-9.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 5 解释剩下的部分。将剩下部分的数目与完整组别进行比较。剩余部分与完整组别的比值就是答案的分数。不要将剩余部分与整个图形进行比较，这样计算出来的分数是错误的。
   • 例如，把5个图形分成几组${\displaystyle \frac{3}{4}}$，就剩余了2个四分之一，也就是${\displaystyle \frac{2}{4}}$。由于完整组别是3部分，而你有2部分，所以分数就是${\displaystyle \frac{2}{3}}$。
6. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/2\/2e\/Divide-a-Whole-Number-With-a-Fraction-Step-10.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-10.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/2\/2e\/Divide-a-Whole-Number-With-a-Fraction-Step-10.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-10.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 6 写下答案。将整数和分数结合起来就是最开始除法问题的商。
   • 例如，${\displaystyle 5÷\frac{3}{4}=6\frac{2}{3}}$。

求解示例问题

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/f2\/Divide-a-Whole-Number-With-a-Fraction-Step-11.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-11.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/f2\/Divide-a-Whole-Number-With-a-Fraction-Step-11.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-11.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 求解这个数学问题：$$8{\displaystyle 8}里面有多少组$$12{\displaystyle {\frac {1}{2}}}？
   • 由于问题是在8里有多少组${\displaystyle \frac{1}{2}}$，所以是除法。
   • 给8增加一个分母1使其变为分数：${\displaystyle 8=\frac{8}{1}}$。
   • 通过调换分子和分母的位置找出分数的倒数：${\displaystyle \frac{1}{2}}$变成${\displaystyle \frac{2}{1}}$。
   • 将两个分数相乘：${\displaystyle \frac{8}{1}\times \frac{2}{1}=\frac{16}{1}}$。
   • 如有必要就进行简化：${\displaystyle \frac{16}{1}=16}$。
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/0\/08\/Divide-a-Whole-Number-With-a-Fraction-Step-12.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-12.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/0\/08\/Divide-a-Whole-Number-With-a-Fraction-Step-12.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-12.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 求解下面这个问题：$$16÷58{\displaystyle 16\div {\frac {5}{8}}}。
   • 给16添加分母1将其变为分数：${\displaystyle 16=\frac{16}{1}}$。
   • 通过调换分子和分母的位置找出分数的倒数：${\displaystyle \frac{5}{8}}$ becomes ${\displaystyle \frac{8}{5}}$。
   • 将两个分数相乘：${\displaystyle \frac{16}{1}\times \frac{8}{5}=\frac{128}{5}}$。
   • 如有必要就进行简化：${\displaystyle \frac{128}{5}=25\frac{3}{5}}$。
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/6\/6f\/Divide-a-Whole-Number-With-a-Fraction-Step-13.jpg\/v4-460px-Divide-a-Whole-Number-With-a-Fraction-Step-13.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/6\/6f\/Divide-a-Whole-Number-With-a-Fraction-Step-13.jpg\/v4-728px-Divide-a-Whole-Number-With-a-Fraction-Step-13.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 用画图的方法来求解下面这个问题。小红有9罐食物，她每天吃${\displaystyle \frac{2}{3}}$罐。请问她的食物能吃几天？
   • 画9个圆圈代表9个罐头。
   • 由于她每次吃${\displaystyle \frac{2}{3}}$个罐头，把每个圆圈分成三份。
   • 给各组${\displaystyle \frac{2}{3}}$涂色。
   • 计算完整组别的数目，应该是13。
   • 解释剩下的部分。还剩下1份，也就是${\displaystyle \frac{1}{3}}$。因为完整的组是${\displaystyle \frac{2}{3}}$，还剩下组的一半。所以分数就是${\displaystyle \frac{1}{2}}$。
   • 把整数组的数字和分数组的加起来就是最终答案：${\displaystyle 9÷\frac{2}{3}=13\frac{1}{2}}$。