如何找到最小公分母

方法 1

方法 1 的 4:最小公倍数法[2]
X
研究来源

WH.shared.addScrollLoadItem(‘85110a1f5f6ee0781f74345caad7dfd6’)

WH.performance.clearMarks(‘image1_rendered’); WH.performance.mark(‘image1_rendered’);{“smallUrl”:”https://www.wikihow.com/images_en/thumb/c/c6/Find-the-Least-Common-Denominator-Step-1-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-1-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/c/c6/Find-the-Least-Common-Denominator-Step-1-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-1-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
1
列出每个分母的整数倍数。为每个分母制作一个倍数表,里面罗列着不同分母的整数倍数。包括不同分母数字分别乘以1、2、3、4等数字后得到的结果。
例如:要计算 1/2 + 1/3 + 1/5
“2的倍数有:” 2 * 1 = 2;2 * 2 = 4;2 * 3 = 6; 2 * 4 = 8;2 * 5 = 10; 2 * 6 = 12; 2 * 7 = 14等等。
“3的倍数有:” 3 * 1 = 3; 3 * 2 = 6;3 *3 = 9; 3 * 4 = 12;3 * 5 = 15; 3 * 6 = 18; 3 * 7 = 21等等。
“5的倍数:”5 * 1 = 5;5 * 2 = 10;5 * 3 = 15;5 * 4 = 20;5 * 5 = 25;5 * 6 = 30;5 * 7 = 35等等。
WH.performance.mark(‘step1_rendered’);

WH.shared.addScrollLoadItem(‘2f0ecce8cb1fed959098e6497738f0fc’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/1/18/Find-the-Least-Common-Denominator-Step-2-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-2-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/1/18/Find-the-Least-Common-Denominator-Step-2-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-2-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
2
确定最小公倍数。浏览每个列表,标记出几个原始分母共同的倍数。找到全部公倍数后,确定最小的公倍数。然后就能确定最小公分母啦。
请注意,如果在你已写出的倍数中没有共同的倍数,你可能需要继续写,直到你最后找到一个相同的倍数。
如果分数的分母是较小的数字,用这个方法查找公分母相对简单。
在上述的例子中,最小的公分母是30: 2 * 15 = 30;3 * 10 = 30;5 * 6 = 30

最小公倍数= 30。

WH.shared.addScrollLoadItem(‘a7bced7afab4c809a59225e4f1b08ead’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/a/ad/Find-the-Least-Common-Denominator-Step-3-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-3-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/a/ad/Find-the-Least-Common-Denominator-Step-3-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-3-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
3
重新写出原始数学式。要进行分数间的加减计算,你需要将分数换算成分母相同的分数,换算时要变换分子和分母,又要保持分数大小不变,你需要将分母乘以一个整数,变成最小公分母,然后用分子(分数线上面的数字)乘以相同的整数,这样换算后的分数大小不变。
例如:(15/15) * (1/2); (10/10) * (1/3); (6/6) * (1/5)
新的等式变为: 15/30 + 10/30 + 6/30

WH.shared.addScrollLoadItem(‘85196a17f6fb24dc25b49a8c00825b9e’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/d/d4/Find-the-Least-Common-Denominator-Step-4-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-4-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/d/d4/Find-the-Least-Common-Denominator-Step-4-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-4-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
4
计算等式。找到最小公倍数,并按上述方法换算分数后,你应该能轻松解决这个问题啦。在结束计算后,记得化简分数。
例如: 15/30 + 10/30 + 6/30 = 31/30 = 1 1/30

WH.ads.addBodyAd(‘method_ad_1’)

广告

WH.ads.addBodyAd(‘mobilemethod_ad_1’)

方法 2

方法 2 的 4:最大公因数法[3]
X
研究来源

WH.shared.addScrollLoadItem(‘f38cfc7eee46b15a095b5cb31e808729’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/9/93/Find-the-Least-Common-Denominator-Step-5-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-5-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/9/93/Find-the-Least-Common-Denominator-Step-5-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-5-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
1
列出每个分母的所有因数。把分母的因数都列出来,找到其中相等的最大的数,即最大公因数。因数是能被整数除尽的整数。[4]
X
研究来源

数字6有四个因数: 6、3、2和1。数字1是每个整数的因数,因为整数除以1是可以除尽的。
例如: 3/8 + 5/12.
数字8的因数: 1、2、4和8。
数字12的因数:1、 2、3、4、6、12。

WH.shared.addScrollLoadItem(‘68587c3c26855221d2aed1b44d92a3d6’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/c/cc/Find-the-Least-Common-Denominator-Step-6-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-6-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/c/cc/Find-the-Least-Common-Denominator-Step-6-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-6-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
2
确定两个分母的最大公因数。当你列出每个分母的所有因数后,圈出它们共同的因数。其中最大的一个因数就是最大公因数(GCF),我们可以用它解决分数计算的问题。
在我们的例子里,分母8和12的公因数有1、2和4。
最大公因数为4。

WH.shared.addScrollLoadItem(‘c134829f253e50e514339dacd4b780ba’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/d/db/Find-the-Least-Common-Denominator-Step-7-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-7-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/d/db/Find-the-Least-Common-Denominator-Step-7-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-7-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
3
将分母相乘。要使用最大公因数法来进行计算,你需要先将分母相乘。
继续解决例子里的问题:8 * 12 = 96

WH.shared.addScrollLoadItem(‘9e36d06eb32034edbd6feff8b12b593d’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/b/ba/Find-the-Least-Common-Denominator-Step-8-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-8-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/b/ba/Find-the-Least-Common-Denominator-Step-8-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-8-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
4
用得到的结果除以最大公因数。将分母相乘后,用得数除以你之前找到的最大公因数。计算得到的结果就是最小公分母。
例如:96 / 4 = 24

WH.shared.addScrollLoadItem(’48c835681c7bfa0b08bc92b5240b6f07′)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/b/b4/Find-the-Least-Common-Denominator-Step-9-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-9-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/b/b4/Find-the-Least-Common-Denominator-Step-9-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-9-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
5
用最小公分母除以原始分母。要进行分数间的加减计算,你需要将分数换算成分母相同的分数,换算时要变换分子和分母,又要保持分数大小不变,你需要先将最小公分母除以原始分母,再用得数乘以分子和分母。这样换算后,几个分数的分母大小相等,而且都等于最小公分母。
例如:24 / 8 = 3; 24 / 12 = 2
(3/3) * (3/8) = 9/24;(2/2) * (5/12) = 10/24
9/24 + 10/24

WH.shared.addScrollLoadItem(‘848b846e798c2dd1be49a2ebf628cb5d’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/6/63/Find-the-Least-Common-Denominator-Step-10-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-10-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/6/63/Find-the-Least-Common-Denominator-Step-10-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-10-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
6
计算等式。找到最小公倍数,并按上述方法换算分数后,你应该能轻松解决这个问题啦。结束计算后,记得化简分数。
例如:9/24 + 10/24 = 19/24

广告

WH.ads.addBodyAd(‘mobilemethod_ad_2’)

方法 3

方法 3 的 4:将分母分解为素数[5]
X
研究来源

WH.shared.addScrollLoadItem(‘0fc90b21039cc5da5ff04a0f6ef0fe56’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/b/b0/Find-the-Least-Common-Denominator-Step-11-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-11-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/b/b0/Find-the-Least-Common-Denominator-Step-11-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-11-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
1
把分母写成素数的乘积。每个分母都可以分解成一系列素数,这几个素数相乘等于分母。素数是不能被任何其它数整除的数。[6]
X
研究来源

例如:1/4 + 1/5 + 1/12
将数字4因式分解得到:2 * 2
将数字5因式分解得到: 5

将数字12因式分解得到: 2 * 2 * 3

WH.shared.addScrollLoadItem(‘f10ded4ab15d2e227bf1b42a0cac2d68’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/2/27/Find-the-Least-Common-Denominator-Step-12-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-12-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/2/27/Find-the-Least-Common-Denominator-Step-12-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-12-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
2
计算每个质数出现在因数分解中出现的次数。汇总分母中出现的所有质数的次数。
例如:4中出现了2个2;5中没有2,12中出现了2个2
4和5中没有3,12中有1个3
4和12中没有5,5中有一个5

WH.shared.addScrollLoadItem(’99e9a6bac5e83b1bf3e731324c299756′)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/2/20/Find-the-Least-Common-Denominator-Step-13-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-13-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/2/20/Find-the-Least-Common-Denominator-Step-13-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-13-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
3
找到每个质数出现的最大次数。确定分母中每个质数出现的最大次数,并记录下来。
例如2的最大数量是两个,3的最大数量是一个,5的最大数量是一个

WH.shared.addScrollLoadItem(‘d611b46d58c6a2d869f0d5bd8acad59a’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/0/0c/Find-the-Least-Common-Denominator-Step-14-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-14-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/0/0c/Find-the-Least-Common-Denominator-Step-14-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-14-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
4
将上一步的结果写出来,每个数字对应的数量有多少,就写几遍。不要将原分母中的每个质数都写出来,只需要按照它出现的最大次数,也就是上一步的结果,将每个质数写出来就可以了。
例如:2, 2, 3, 5

WH.shared.addScrollLoadItem(‘e2a896eaf59677b6f37fdd1df7ee8436’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/5/59/Find-the-Least-Common-Denominator-Step-15-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-15-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/5/59/Find-the-Least-Common-Denominator-Step-15-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-15-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
5
求出上一步中写出的所有质数的乘积。最终得到的结果就是原数字的最小公倍数。
例如: 2 * 2 * 3 * 5 = 60
最小公倍数 = 60

WH.shared.addScrollLoadItem(‘d84fe37d71a80299fa4812392a5a7271’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/9/90/Find-the-Least-Common-Denominator-Step-16-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-16-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/9/90/Find-the-Least-Common-Denominator-Step-16-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-16-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
6
用最小公倍数除以原分母。要得到使得每个分数的分母相等所需要的倍数,你需要使用分母的最小公倍数除以每个分母。然后用得到的倍数乘以每个分数的分子,这样所有的分数都转换成了分母均为最小公倍数的分数。
例如: 60/4 = 15; 60/5 = 12; 60/12 = 5
15 * (1/4) = 15/60; 12 * (1/5) = 12/60; 5 * (1/12) = 5/60
15/60 + 12/60 + 5/60

WH.shared.addScrollLoadItem(‘9c68f2147034d8f6d92b7cebe6cbd95e’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/c/c6/Find-the-Least-Common-Denominator-Step-17-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-17-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/c/c6/Find-the-Least-Common-Denominator-Step-17-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-17-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
7
计算新等式的结果。求出最小公倍数之后,你就可以按照一般的方法计算分数的和与差。记住,如果可能的话,最终得到的结果需要化简。
例如: 15/60 + 12/60 + 5/60 = 32/60 = 8/15

广告

WH.ads.addBodyAd(‘mobilemethod_ad_3’)

方法 4

方法 4 的 4:计算整数与带分数[7]
X
研究来源

WH.shared.addScrollLoadItem(‘4233daaa22702aa13b62d514629ed874’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/a/a7/Find-the-Least-Common-Denominator-Step-18-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-18-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/a/a7/Find-the-Least-Common-Denominator-Step-18-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-18-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
1
将整数和带分数转换为假分数。将带分数转换为假分数,需要用分母乘以整数之后,与分子相加作为分子,分母不变,这样就可以将带分数转换为假分数;将整数转换为假分数,只需要使用整数为分子,用“1”做分母即可。
例如: 8 + 2 1/4 + 2/3
8 = 8/1
2 1/4; 2 * 4 + 1 = 8 + 1 = 9; 9/4
重写为: 8/1 + 9/4 + 2/3

WH.shared.addScrollLoadItem(‘50449a78d16e903343048240aef463b8’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/4/45/Find-the-Least-Common-Denominator-Step-19-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-19-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/4/45/Find-the-Least-Common-Denominator-Step-19-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-19-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
2
寻找最小公分母。使用上面提到的任意方法求出分数的最小公分母。注意在本例中,我们将使用“列出倍数”法,列出每个分母的各个倍数,然后以此求出分母的最小公倍数。
注意,你不需要写出数字的1倍数,因为任何数的1倍都是它本身,也就是说,每个数都是1的倍数。
例如: 4 * 1 = 4; 4 * 2 = 8; 4 * 3 = 12; 4 * 4 = 16;等等。
3 * 1 = 3; 3 * 2 = 6; 3 * 3 = 9; 3 * 4 = 12; 等等。
最小公倍数 = 12

WH.shared.addScrollLoadItem(‘5acaf9daaae0f6adef11e8f46a0a9d5e’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/5/5e/Find-the-Least-Common-Denominator-Step-20-Version-2.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-20-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/5/5e/Find-the-Least-Common-Denominator-Step-20-Version-2.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-20-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
3
重写原来的分数。你不能只改变分母,而是应该让分子分母同时乘以相同的倍数,而这个倍数是使原分母变成最小公倍数所需要乘上的数字。
例如:(12/12) * (8/1) = 96/12; (3/3) * (9/4) = 27/12; (4/4) * (2/3) = 8/12
96/12 + 27/12 + 8/12

WH.shared.addScrollLoadItem(‘b9e299de13c546c458c52d56742ab0f4’)

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/4/4b/Find-the-Least-Common-Denominator-Step-21.jpg/v4-460px-Find-the-Least-Common-Denominator-Step-21.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/4/4b/Find-the-Least-Common-Denominator-Step-21.jpg/v4-728px-Find-the-Least-Common-Denominator-Step-21.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:”

“}
4
计算结果。得到最小公倍数,并将所有分数的分母变成该数字之后,你便可以毫不费力的对所有分数进行和差运算。记住,如果可以的话,化简最后的结果。
例如: 96/12 + 27/12 + 8/12 = 131/12 = 10 11/12

广告

WH.ads.addBodyAd(‘mobilemethod_ad_4’)

发表评论

您的电子邮箱地址不会被公开。 必填项已用*标注