怎么求整数和分数的差

从整数中减去分数，并没有看上去得那么难。方法有两种：一种是将整数转化为分数，另一种是先从整数中减去1，然后将1转化成和分数分母相同的分数，再求差。只要分数的分母相同，就可以开始求差。这两种方法都很简单，如果你想了解具体的做法，就请阅读本文吧。

步骤

用整数减去分数

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/4\/48\/Subtract-Fractions-from-Whole-Numbers-Step-1-Version-3.jpg\/v4-460px-Subtract-Fractions-from-Whole-Numbers-Step-1-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/4\/48\/Subtract-Fractions-from-Whole-Numbers-Step-1-Version-3.jpg\/v4-728px-Subtract-Fractions-from-Whole-Numbers-Step-1-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 将整数转化成分数。比如，把整数的分母设为1。^[1]
   • 示例：${\displaystyle 8-\frac{4}{5}}$
   • ${\displaystyle =\frac{8}{1}-\frac{4}{5}}$
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/6\/6a\/Subtract-Fractions-from-Whole-Numbers-Step-2-Version-3.jpg\/v4-460px-Subtract-Fractions-from-Whole-Numbers-Step-2-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/6\/6a\/Subtract-Fractions-from-Whole-Numbers-Step-2-Version-3.jpg\/v4-728px-Subtract-Fractions-from-Whole-Numbers-Step-2-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 换算成分母相同的分数。原分数的分母也是这两个分数的最小公分母（LCD）。将“整数分数”的分子和分母都乘以这个数字，让分数的分母相同。^[2]
   • ${\displaystyle \frac{8}{1}-\frac{4}{5}}$
   • ${\displaystyle =\frac{8\ast 5}{1\ast 5}-\frac{4}{5}}$
   • ${\displaystyle =\frac{40}{5}-\frac{4}{5}}$
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/1\/18\/Subtract-Fractions-from-Whole-Numbers-Step-3-Version-3.jpg\/v4-460px-Subtract-Fractions-from-Whole-Numbers-Step-3-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/1\/18\/Subtract-Fractions-from-Whole-Numbers-Step-3-Version-3.jpg\/v4-728px-Subtract-Fractions-from-Whole-Numbers-Step-3-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 分子相减。现在，分数的分母相同，你可以对分子进行普通的减法计算：^[3]
   • ${\displaystyle \frac{40}{5}-\frac{4}{5}}$
   • ${\displaystyle =\frac{40-4}{5}}$
   • = ${\displaystyle \frac{36}{5}}$
4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/7\/78\/Subtract-Fractions-from-Whole-Numbers-Step-4-Version-3.jpg\/v4-460px-Subtract-Fractions-from-Whole-Numbers-Step-4-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/7\/78\/Subtract-Fractions-from-Whole-Numbers-Step-4-Version-3.jpg\/v4-728px-Subtract-Fractions-from-Whole-Numbers-Step-4-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 换算成带分数（可选）。如果答案是假分数，那可能就得把它换算成带分数：^[4]
   • 示例：把${\displaystyle \frac{36}{5}}$改写为带分数。
   • 36用5整除等于多少？5 x 7 = 35，因此整数部分是7。
   • 还剩下什么？整数部分等于${\displaystyle \frac{35}{5}}$，所以结果是${\displaystyle \frac{36}{5}}$ - ${\displaystyle \frac{35}{5}}$ = ${\displaystyle \frac{1}{5}}$
   • 把整数和分数合并起来：${\displaystyle \frac{36}{5}}$ = ${\displaystyle 7\frac{1}{5}}$

替代法

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/3b\/Subtract-Fractions-from-Whole-Numbers-Step-5-Version-2.jpg\/v4-460px-Subtract-Fractions-from-Whole-Numbers-Step-5-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/3b\/Subtract-Fractions-from-Whole-Numbers-Step-5-Version-2.jpg\/v4-728px-Subtract-Fractions-from-Whole-Numbers-Step-5-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 较大的整数可以尝试这种方法。上面学习了把整数换算成分数，然后最后再换算成带分数。而这种方法会跳过一些步骤，让分数变小一点。
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/4\/4d\/Subtract-Fractions-from-Whole-Numbers-Step-6-Version-2.jpg\/v4-460px-Subtract-Fractions-from-Whole-Numbers-Step-6-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/4\/4d\/Subtract-Fractions-from-Whole-Numbers-Step-6-Version-2.jpg\/v4-728px-Subtract-Fractions-from-Whole-Numbers-Step-6-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 把假分数换算成带分数。如果不是假分数，那就跳过这一步。（假分数的分子要比分母更大。）^[5]
   • 示例：${\displaystyle 11-\frac{4}{3}}$
   • ${\displaystyle =11-1\frac{1}{3}}$
   • ${\displaystyle =10-\frac{1}{3}}$
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/2\/28\/Subtract-Fractions-from-Whole-Numbers-Step-7-Version-2.jpg\/v4-460px-Subtract-Fractions-from-Whole-Numbers-Step-7-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/2\/28\/Subtract-Fractions-from-Whole-Numbers-Step-7-Version-2.jpg\/v4-728px-Subtract-Fractions-from-Whole-Numbers-Step-7-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 把整数分成1和另一个整数。例如，5可以改写成4 + 1，或者22可以改写成21 + 1。
   • ${\displaystyle 10-\frac{1}{3}}$
   • ${\displaystyle =9+1-\frac{1}{3}}$
4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/d3\/Subtract-Fractions-from-Whole-Numbers-Step-8-Version-2.jpg\/v4-460px-Subtract-Fractions-from-Whole-Numbers-Step-8-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/d3\/Subtract-Fractions-from-Whole-Numbers-Step-8-Version-2.jpg\/v4-728px-Subtract-Fractions-from-Whole-Numbers-Step-8-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 把1换算成分数。这时候，我们要用上面的方法来求解“1-（分数）”。其它整数在剩余的解题过程中保持不变。
   • ${\displaystyle =9+1-\frac{1}{3}}$
   • ${\displaystyle =9+\frac{1}{1}-\frac{1}{3}}$
5. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/f4\/Subtract-Fractions-from-Whole-Numbers-Step-9-Version-2.jpg\/v4-460px-Subtract-Fractions-from-Whole-Numbers-Step-9-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/f4\/Subtract-Fractions-from-Whole-Numbers-Step-9-Version-2.jpg\/v4-728px-Subtract-Fractions-from-Whole-Numbers-Step-9-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 5 做乘法，把分数变成相同的分母。如上所述，把新分数的分子和分母同时乘以一个数，让它变成和原分数的分母相同。
   • ${\displaystyle =9+\frac{1\ast 3}{1\ast 3}-\frac{1}{3}}$
   • ${\displaystyle =9+\frac{3}{3}-\frac{1}{3}}$
6. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/b\/bb\/Subtract-Fractions-from-Whole-Numbers-Step-10-Version-2.jpg\/v4-460px-Subtract-Fractions-from-Whole-Numbers-Step-10-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/b\/bb\/Subtract-Fractions-from-Whole-Numbers-Step-10-Version-2.jpg\/v4-728px-Subtract-Fractions-from-Whole-Numbers-Step-10-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 6 合并两个分数。两个分子相减，求出小数部分。
   • ${\displaystyle =9+\frac{3-1}{3}}$
   • ${\displaystyle =9+\frac{2}{3}}$
   • ${\displaystyle =9\frac{2}{3}}$

你需要准备

• 纸
• 笔

References

1. ↑ http://virtualnerd.com/algebra-1/algebra-foundations/real-number-add-subtract/real-number-subtract/subtract-whole-number-from-fraction
2. ↑ https://mathwizz.com/fractions/help/help11.htm
3. ↑ https://www.montereyinstitute.org/courses/DevelopmentalMath/TEXTGROUP-1-8_RESOURCE/U02_L3_T2_text_final.html
4. ↑ https://www.calculatorsoup.com/calculators/math/mixednumbers.php
5. ↑ https://www.mathsisfun.com/improper-fractions.html