📚 Mastering Fractions, Decimals and Percentages | 掌握分数、小数与百分比
Fractions, decimals and percentages are three different ways of representing parts of a whole. In the Cambridge KS3 Mathematics course, converting between these forms and using them in calculations is a core skill that appears frequently in Checkpoint tests and lower secondary assessments. This article focuses on the key ideas often practised on page 116 of the coursebook, with clear methods, worked examples and common pitfalls.
分数、小数和百分比是表示“整体中的部分”的三种不同方式。在剑桥 KS3 数学课程中，三种形式之间的相互转换以及相关计算是核心技能，经常出现在 Checkpoint 测试和初中阶段评估中。本文聚焦教材第 116 页常见练习中的关键知识点，提供清晰的方法、例题和常见误区。
1. Understanding Equivalent Forms | 认识等价形式
A fraction, decimal and percentage can all show the same amount. For example, 1/2, 0.5 and 50% are equivalent. The word 'percent' means 'out of 100', so a percentage is simply a fraction with denominator 100. This idea underpins every conversion method you will meet in this topic.
分数、小数和百分比可以表示同一个量。例如，1/2、0.5 和 50% 是等价的。“percent” 一词表示“每 100 份中的”，因此百分比本质上就是分母为 100 的分数。这个思想是你在本主题中遇到的每一种转换方法的基础。
| Fraction 分数 | Decimal 小数 | Percentage 百分比 |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/10 | 0.1 | 10% |
| 1/5 | 0.2 | 20% |
2. Converting Fractions to Decimals | 分数转换为小数
. If the division repeats, write the decimal with a dot or bar notation as shown in your coursebook, but for most KS3 questions a terminating decimal is expected.
要把分数转换为小数，用分子除以分母。例如，3/8 表示 3 ÷ 8 = 0.375。如果除法出现循环，可按教材使用循环点或横线表示；但在大多数 KS3 题目中，结果通常是有限小数。
decimal = numerator ÷ denominator
Example: 7/20 = 7 ÷ 20 = 0.35
中文示例：7/20 = 7 ÷ 20 = 0.35
3. Converting Decimals to Percentages | 小数转换为百分比
Multiply the decimal by 100 and add the % the same as moving the decimal point two places to the right. For example, 0.85 × 100 = 85%, and 0.625 × 100 = 62.5%. This method works for any decimal, including decimals smaller than 0.1.
将小数乘以 100，再加上百分号。这相当于把小数点向右移动两位。例如，0.85 × 100 = 85%，0.625 × 100 = 62.5%。这个方法适用于任何小数，包括小于 0.1 的小数。
percentage = decimal × 100
Example: 0.05 × 100 = 5%
中文示例：0.05 × 100 = 5%
4. Converting Percentages to Fractions | 百分比转换为分数
Write the percentage as a fraction over 100, then simplify if possible. For example, 45% = 45/100 = 9/20. Mixed-number percentages such as 12 1/2% can be written as 12.5/100 = 1/8 after multiplying numerator and denominator by 10 or 2.
先把百分比写成分母为 100 的分数，再尽可能化简。例如，45% = 45/100 = 9/20。带分数百分比如 12 1/2% 可以先写成 12.5/100，再将分子分母同时扩大 10 倍或 2 倍得到 1/8。
45% = 45 ÷ 100 = 9/20
Example: 8% = 8/100 = 2/25
中文示例：8% = 8/100 = 2/25
5. Comparing FDP Values | 比较分数、小数和百分比
decimals and percentages as decimals, then compare the digits. For example, 3/5 = 0.6, 58% = 0.58, so 3/5 is greater than 58%.
要比较不同形式的数，先全部转换为同一种形式。通常转换成小数最方便：把分数和百分比都写成小数，然后比较各位数字。例如，3/5 = 0.6，58% = 0.58，所以 3/5 大于 58%。
- Step 1: Convert every value to a decimal. — 第一步：把每个数都转换为小数。
- Step 2: Compare place values from left to right. — 第二步：从左到右比较数位。
- Step 3: Write the original forms in the correct order. — 第三步：按正确顺序写回原来的形式。
6. Finding a Percentage of a Quantity | 求一个量的百分比
centage of an amount without a calculator, break the percentage into easy parts such as 10%, 5% and 1%. For example, 17.5% of £240 can be found as 10% = £24, 5% = £12, 2.5% = £6, so 17.5% = £24 + £12 + £6 = £42.
不用计算器求一个量的
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