怎么将带分数简化约分

分数代表整数的一部分。如果分数的分子大于分母，这样的分数就叫“假分数”。假分数可以约分，简化为带分数（既包含整数，又包含分数的形式）。假分数本身没有任何问题，实际上，在数学问题中假分数比带分数运算起来更方便。但在日常生活中，人们更常用到带分数，而不是假分数，^[1] 所以我们有必要学习如何将假分数约分，简化为带分数。

步骤

通过画图约分

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/5\/5f\/Simplify-an-Improper-Fraction-Step-1-Version-3.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-1-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/5\/5f\/Simplify-an-Improper-Fraction-Step-1-Version-3.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-1-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 判断某个分数是否为假分数。假分数就是分子大于分母的分数。^[2]
   • 比如，${\displaystyle \frac{10}{4}}$就是假分数，因为10大于4。
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/8\/8f\/Simplify-an-Improper-Fraction-Step-2-Version-3.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-2-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/8\/8f\/Simplify-an-Improper-Fraction-Step-2-Version-3.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-2-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 分析分母。分母就是分数线下面的数字。分母是多少，就表示一个整体被分成了多少相同的部分。
   • 比如，在分数${\displaystyle \frac{10}{4}}$中，4是分母，表明整体被分成了4个相同的部分。
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/d6\/Simplify-an-Improper-Fraction-Step-3-Version-3.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-3-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/d6\/Simplify-an-Improper-Fraction-Step-3-Version-3.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-3-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 分析分子。分子就是分数线上面的数字。分子表明多少份。
   • 比如，在分数${\displaystyle \frac{10}{4}}$里， 10是分子，表明有10份。
4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/8\/84\/Simplify-an-Improper-Fraction-Step-4-Version-3.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-4-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/8\/84\/Simplify-an-Improper-Fraction-Step-4-Version-3.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-4-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 画圆圈表示整体。根据分数的分母来划分整体。
   • 如果分母是4，将每个圆圈平分为4份。
5. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/a5\/Simplify-an-Improper-Fraction-Step-5-Version-3.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-5-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/a5\/Simplify-an-Improper-Fraction-Step-5-Version-3.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-5-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 5 根据分子将圆圈涂黑。分子是多少就将多少份涂黑。
   • 如果分数是${\displaystyle \frac{10}{4}}$，就将10份涂黑。
6. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/3e\/Simplify-an-Improper-Fraction-Step-6-Version-3.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-6-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/3e\/Simplify-an-Improper-Fraction-Step-6-Version-3.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-6-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 6 数数你涂了多少个完整的圈。为了将假分数约分，你必须将其变成由一个整数和一个分数组成的带分数。整圈的数目就是带分数中的整数。把这个数写下来。
   • 如果分数是${\displaystyle \frac{10}{4}}$，整个涂黑的圆圈应该有两个，所以带分数的整数部分就是2。
7. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/b\/b1\/Simplify-an-Improper-Fraction-Step-7-Version-3.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-7-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/b\/b1\/Simplify-an-Improper-Fraction-Step-7-Version-3.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-7-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 7 数数圆圈里被涂黑的份数是多少。剩下涂黑的部分就表示带分数的分数。把这个分数写在整数旁边就是带分数了。
   • 对于分数${\displaystyle \frac{10}{4}}$而言，一个整圈有${\displaystyle \frac{2}{4}}$被涂黑了，所以带分数的分数部分就是${\displaystyle \frac{2}{4}}$。最后，${\displaystyle \frac{10}{4}}$等同于 ${\displaystyle 2\frac{2}{4}}$。
8. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/7\/74\/Simplify-an-Improper-Fraction-Step-8-Version-3.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-8-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/7\/74\/Simplify-an-Improper-Fraction-Step-8-Version-3.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-8-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 8 如有必要，简化你的答案。有时候带分数的分数部分需要进一步约分才能得到最后答案。^[3]
   • 比如，带分数${\displaystyle 2\frac{2}{4}}$可以约分，变成${\displaystyle 2\frac{1}{2}}$。

通过除法约分

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/3b\/Simplify-an-Improper-Fraction-Step-9.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-9.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/3b\/Simplify-an-Improper-Fraction-Step-9.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-9.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 判断某个分数是否是假分数。假分数就是分子大于分母的分数。^[4]
   • 比如，${\displaystyle \frac{10}{4}}$是个假分数，因为${\displaystyle 10>4}$。
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/1\/10\/Simplify-an-Improper-Fraction-Step-10-Version-3.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-10-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/1\/10\/Simplify-an-Improper-Fraction-Step-10-Version-3.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-10-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 用分子除以分母。记住，分数线可以理解为除号。^[5] 当将假分数约分时，你必须把假分数变成带分数，也就是部分为整数，部分为分数的形式。用分子除以分母，得到的整数结果就是带分数的整数部分。把这个数写下来，再注明余数。
   • 分子无法平均分成分母代表的份数。余数将成为带分数中分数的一部分。
   • 比如将分数${\displaystyle \frac{10}{4}}$约分时，你计算出${\displaystyle 10÷4=2R2}$。所以带分数的整数部分就是${\displaystyle 2}$。
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/5\/57\/Simplify-an-Improper-Fraction-Step-11-Version-3.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-11-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/5\/57\/Simplify-an-Improper-Fraction-Step-11-Version-3.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-11-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 把余数转换为分数。具体方法就是将余数放在原来假分数的分母上，再将得到的新分数和整数结合，最后的结果就是带分数了。
   • 比如，在${\displaystyle 10÷4=2R2}$中，带分数的分数部分是${\displaystyle \frac{2}{4}}$。所以，${\displaystyle \frac{10}{4}}$等于${\displaystyle 2\frac{2}{4}}$。
4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/f6\/Simplify-an-Improper-Fraction-Step-12-Version-3.jpg\/v4-460px-Simplify-an-Improper-Fraction-Step-12-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/f6\/Simplify-an-Improper-Fraction-Step-12-Version-3.jpg\/v4-728px-Simplify-an-Improper-Fraction-Step-12-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 必要的话，将答案约分。有时带分数的分数部分还要继续约分才能得到最后，最简化的答案。^[6]
   • 比如，带分数${\displaystyle 2\frac{2}{4}}$可以约分，简化为${\displaystyle 2\frac{1}{2}}$。

小提示

• 如果要将带分数变回假分数，用整数部分乘以分母，再将结果加在分子上就可以了。
• 分母保持不变。比如，${\displaystyle 2\frac{1}{2}}$可以写成${\displaystyle \frac{5}{2}}$，因为 ${\displaystyle 2\times 2+1=5}$。
• 有些假分数也可以表示整数，比如${\displaystyle \frac{24}{3}}$。