📚 Find a Percent of a Number | 求一个数的百分之几
In IGCSE Mathematics and in everyday life, percentages appear in test scores, discounts, interest, tax, and data comparisons. Finding a percent of a number means calculating a part of a whole when the whole is given, using the meaning of 'per cent' as 'per hundred'.
在 IGCSE 数学和日常生活中，百分数出现在考试分数、折扣、利息、税收和数据比较中。求一个数的百分之几，就是在已知整体的情况下，计算其中的一部分，利用的是百分数 'per cent'（每一百）的含义。
1. What Does Percent Mean? | 百分数表示什么？
The word percent comes from Latin per centum, meaning 'by the hundred'. A percentage is a ratio with denominator 100. For example, 25% means 25 out of every 100, which can be written as 25/100, 0.25, or 1/4.
百分数一词来自拉丁语 per centum，意思是 '每一百'。百分数是一个分母为 100 的比。例如，25% 表示每一百中有 25，可以写成 25/100、0.25 或 1/4。
mber, you are finding that same fraction of the total. If a school has 200 students and 25% come by bus, then 25% of 200 = 0.25 × 200 = 50 students.
当你求一个数的百分之几时，你实际上是在求总量的相同分数。如果一所学校有 200 名学生，25% 乘公交上学，那么 200 的 25% = 0.25 × 200 = 50 名学生。
2. From Percent to Fraction and Decimal | 百分数、分数与小数的转换
t as a fraction with denominator 100, then simplify, or divide by 100 to get a decimal. 75% = 75/100 = 3/4 = 0.75.
要用百分数进行计算，首先将其改写为分母为 100 的分数再化简，或者除以 100 得到小数。75% = 75/100 = 3/4 = 0.75。
Common conversions should be memorised because they make mental arithmetic faster:
常见换算应当熟记，因为它们能加快心算速度：
| Percent | Decimal | Fraction |
|---|---|---|
| 10% | 0.1 | 1/10 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1.0 | 1 |
Being able to move quickly between these three forms is essential for solving percentage problems accurately and efficiently.
能够在这三种形式之间快速转换，是准确、高效解决百分数问题的关键。
3. The Key Method: Multiply by the Decimal | 核心方法：乘以小数
To find P% of a number n, convert P% to a decimal by dividing P by 100, then multiply by n. The formula is:
要求一个数 n 的 P%，先把 P% 除以 100 转化为小数，再乘以 n。公式为：
P% of n = (P ÷ 100) × n
Example: Find 15% of 240. Step 1: 15% = 15 ÷ 100 = 0.15. Step 2: 0.15 × 240 = 36. Therefore, 15% of 240 is 36.
示例：求 240 的 15%。第一步：15% = 15 ÷ 100 = 0.15。第二步：0.15 × 240 = 36。因此，240 的 15% 是 36。
For decimal percentages, the same rule applies. 3.5% of 600 = 0.035 × 600 = 21.
对于小数百分数，规则相同。600 的 3.5% = 0.035 × 600 = 21。
4. Using Fractions for Mental Math | 用分数进行心算
Some percentages are easier to handle as simplified fractions. 50% of 84 = 1/2 × 84 = 42; 25% of 84 = 1/4 × 84 = 21; 10% of 84 = 1/10 × 84 = 8.4.
有些百分数用化简后的分数处理更简单
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