[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"grammar-page-zh-beishu-fenshu-yu-baifenbi":3,"grammar-exercises-by-page-01a0e1ad-b3b8-7f0b-9166-ac2a29c79ab2":349,"exercise-list-path-zh-none":365},{"id":4,"title":5,"slug":6,"seoDescription":7,"content":8,"language":9,"level":10,"displayOrder":11,"grammarTopics":12,"createdAt":18,"updatedAt":19,"vocabularyLists":20,"readyImages":348},"01a0e1ad-b3b8-7f0b-9166-ac2a29c79ab2","倍数、分数与百分比","beishu-fenshu-yu-baifenbi","掌握汉语倍数、分数与百分比的常用结构，准确说明数量比较、部分占比和增减变化。区分是原来的几倍与增加了几倍，理解分母在前、分子在后的表达顺序，辨别增加到与增加了、减少到与减少了。结合价格、产量和调查数据，分清百分比与百分点，明确比较标准，避免把变化后的总量当作增加的量，并理解翻番与一半的用法。","比较价格、说明调查结果或介绍数量变化时，需要分清三个问题：现在是多少、比原来增加或减少了多少、某一部分占整体多少。**倍数、分数和百分比**可以表达这些关系，但比较的标准必须清楚。\n\n下面重点区分**是……的几倍**与**增加了几倍**、**增加到**与**增加了**，并说明分数的语序、百分比的用法，以及**百分比**和**百分点**的区别。\n\n## 1. 倍数：总量还是增加的量\n\n表达倍数时，常用以下结构。注意：**是……的几倍**比较两个总量，**比……增加了几倍**比较增加的量与原来的量。\n\n| 结构 | 例句 | 数量关系 |\n| --- | --- | --- |\n| 甲是乙的＋倍数 | 甲店的面积是乙店的三倍。 | 乙店一百平方米，甲店三百平方米 |\n| 比原来增加了＋倍数 | 员工人数比原来增加了两倍。 | 原来十人，现在三十人 |\n| 增加到原来的＋倍数 | 员工人数增加到原来的两倍。 | 原来十人，现在二十人 |\n| 翻了一番 | 今年的销售额比去年翻了一番。 | 去年十万元，今年二十万元 |\n\n**增加一倍**表示增加的量等于原来的量，因此总量变成原来的**两倍**。**翻一番**也表示变成两倍；翻两番则变成四倍。\n\n:::example\n某工厂原来每天生产二百件产品，现在每天生产六百件。\n\n- 现在的日产量**是原来的三倍**。\n- 日产量**比原来增加了两倍**。\n- 日产量**增加到了原来的三倍**。\n\n三句话描述的是同一个变化。\n:::\n\n:::warning\n**两倍**和**一倍**在这里不能互换：从二百增加到六百，是原来的三倍，不是增加了三倍。\n\n“多两倍”“增长两倍”等说法在实际交流中有时会被混用。需要准确说明数据时，可以同时写出原来的数量和现在的数量。\n:::\n\n## 2. 分数：先说分母，再说分子\n\n汉语分数的基本顺序是**分母＋分之＋分子**。分母说明平均分成多少份，分子说明取其中多少份。\n\n| 数字 | 汉语读法 | 例句 |\n| --- | --- | --- |\n| 1\u002F3 | 三分之一 | 这笔费用是总预算的三分之一。 |\n| 2\u002F5 | 五分之二 | 五分之二的受访者选择了公交车。 |\n| 3\u002F4 | 四分之三 | 我已经看完了这本书的四分之三。 |\n| 1\u002F2 | 二分之一，也常说“一半” | 一半的学生住在学校附近。 |\n\n分数通常有两种常见位置：\n\n- **分数＋的＋名词**：三分之一的学生参加了活动。强调这一部分学生。\n- **整体＋的＋分数**：参加活动的学生人数是全校学生总人数的三分之一。明确说明部分与整体的关系。\n\n:::tip\n看到“甲的三分之一”，先问：整体是什么？例如，“预算的三分之一”以全部预算为整体，不是以已经花掉的钱为整体。\n:::\n\n## 3. 百分比：表达比例与占比\n\n百分比可以看作分母是一百的分数。**25%**读作**百分之二十五**，与**四分之一**表示的比例相同。\n\n表达部分在整体中的比例时，常用**部分＋占＋整体＋的＋百分比**。\n\n:::example\n这次调查共有四百人参加，其中一百人每天骑车上班。\n\n- 每天骑车上班的人**占受访者总人数的百分之二十五**。\n- **百分之二十五的受访者**每天骑车上班。\n- 每天骑车上班的人数**是受访者总人数的四分之一**。\n:::\n\n整体已经清楚时，可以说：“这次调查中，每天骑车上班的人占百分之二十五。”正式介绍数据时，最好交代清楚整体，避免把受访者比例误当成全体居民的比例。\n\n**比例可以超过百分之百**，但要看比较关系。例如，“今年的产量是去年的百分之一百二十”是合理的，因为比较的是两年的产量。若说明某一部分在同一整体中的占比，该部分不能超过整体。\n\n## 4. 数量变化：“了”和“到”\n\n**增加了、减少了**后面的数值表示变化的量；**增加到、减少到**后面的数值表示变化后的结果。用比例表达变化时，还要说明以什么数量为标准。\n\n以下各句都以原价二百元为标准：\n\n| 表达 | 现在的价格 | 说明 |\n| --- | --- | --- |\n| 价格比原来上涨了百分之二十。 | 二百四十元 | 增加四十元 |\n| 价格上涨到原来的百分之一百二十。 | 二百四十元 | 现价是原价的百分之一百二十 |\n| 价格比原来降低了四分之一。 | 一百五十元 | 减少五十元 |\n| 价格降低到原来的四分之一。 | 五十元 | 现价只剩原价的四分之一 |\n\n:::warning\n表达减少时，不宜用“减少一倍”“降低两倍”等说法。它们不能清楚地表示剩余多少。\n\n如果价格从二百元变成一百元，可以说：\n\n- 价格**降低了一半**。\n- 价格**降低到原来的一半**。\n\n这里两句结果相同，是因为减少的部分与剩下的部分恰好都是一半；换成“四分之一”，两句的结果就不同了。\n:::\n\n## 5. 百分比与百分点\n\n当比较的两个数本身都是百分比时，可以用**百分点**表示它们之间的直接差值。**提高了百分之几**则通常表示相对于原来数值的增长比例。\n\n:::example\n某公司的市场份额从百分之二十升到百分之三十。\n\n- 市场份额**提高了十个百分点**：三十减二十，差十。\n- 市场份额**比原来提高了百分之五十**：增加的十相当于原来的二十的一半。\n:::\n\n这两种表达描述同一个变化，但计算方式不同。\n\n| 变化 | 百分点的变化 | 相对于原来的变化 |\n| --- | --- | --- |\n| 合格率从百分之八十升到百分之八十八 | 提高八个百分点 | 提高百分之十 |\n| 合格率从百分之八十降到百分之七十二 | 下降八个百分点 | 下降百分之十 |\n\n:::note\n**百分点**用于比较百分比数值，不能直接表示人数或价格的增减。可以说“合格率提高了五个百分点”，不能用“人数增加了五个百分点”来表示人数增长了百分之五。\n:::\n\n## 6. 表达前的检查顺序\n\n1. **找准标准**：比较的是去年、原价，还是全体受访者？\n2. **判断关系**：表达总量的倍数、部分的占比，还是数量的变化？\n3. **区分变化和结果**：增加了多少，还是增加到多少？\n4. 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