📚 Fractions, Decimals and Percentages Made Easy | 分数、小数和百分比轻松学
Welcome to this KS3 Cambridge Mathematics revision guide. In this article, we will explore fractions, decimals and percentages, which are three different ways of representing parts of a whole. Mastering these skills is essential for solving problems in everyday life and in your exams.
欢迎阅读这篇 KS3 剑桥数学复习指南。在本文中，我们将探讨分数、小数和百分比，它们是表示整体部分数的三种不同方式。掌握这些技能对于解决日常生活和考试中的问题都至关重要。
1. Understanding Fractions | 理解分数
A fraction represents a part of a whole or a part of a group. It is written as a/b, where a is the numerator and b is the denominator. The denominator tells us how many equal parts the whole is divided into, and the numerator tells us how many of those parts we have.
分数表示一个整体或一组中的一部分。它写作 a/b，其中 a 是分子，b 是分母。分母告诉我们整体被分成了多少等份，分子告诉我们取了多少份。
For example, in the fraction 3/4, the denominator 4 means the whole is split into 4 equal parts, and the numerator 3 means we have 3 of those parts. Fractions can be proper (like 2/5), improper (like 7/4), or mixed numbers (like 1 1/2).
例如，在分数 3/4 中，分母 4 表示整体被分成 4 等份，分子 3 表示我们取了其中的 3 份。分数可以是真分数（如 2/5）、假分数（如 7/4）或带分数（如 1 1/2）。
- Proper fraction: numerator < denominator | 真分数：分子小于分母
- Improper fraction: numerator > denominator | 假分数：分子大于分母
- Mixed number: whole number + proper fraction | 带分数：整数 + 真分数
2. Equivalent Fractions and Simplifying | 等值分数与约分
Equivalent fractions are different fractions that represent the same value. You can create equivalent fractions by multiplying or dividing both the numerator and the denominator by the same non-zero number.
等值分数是表示相同值的不同分数。你可以通过将分子和分母同时乘以或除以同一个非零数来得到等值分数。
To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF). For example, 8/12 simplifies to 2/3 because the HCF of 8 and 12 is 4.
要化简分数，用分子和分母的最大公因数（HCF）同时除以它们。例如，8/12 化简为 2/3，因为 8 和 12 的最大公因数是 4。
8 ÷ 4 = 2 and 12 ÷ 4 = 3, so 8/12 = 2/3
- Use multiplication: 1/2 = 2/4 = 3/6 | 用乘法：1/2 = 2/4 = 3/6
- Use division: 15/25 = 3/5 (divide by 5) | 用除法：15/25 = 3/5（除以 5）
3. Converting Fractions to Decimals | 分数转小数
To convert a fraction to a decimal, divide the numerator by the denominator. You can use short division or long division. Some fractions produce terminating decimals, while others produce recurring decimals.
要将分数转换为小数，用分子除以分母。你可以使用短除法或长除法。有些分数会得到有限小数，而另一些会得到循环小数。
5. The fraction 1/3 = 0.333... is a recurring decimal because the digit 3 repeats forever.
例如，3/8 = 0.375，因为 3 除以 8 等于 0.375。分数 1/3 = 0.333... 是一个循环小数，因为数字 3 无限重复。
| Fraction | 分数 | Decimal | 小数 |
|---|---|
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
4. Converting Decimals to Fractions | 小数转分数
To convert a terminating decimal to a fraction, write the decimal as a fraction over a power of 10, then simplify. The number of decimal places tells you whether to use 10, 100, 1000, etc. as the denominator.
要将有限小数转换为分数，先将小数写成分母为 10 的幂的分数，然后化简。小数的位数决定了使用 10、100、1000 等作为分母。
Example: 0.75 has two decimal places, so write 75/100 and simplify to 3/4. For 0.125, write 125/1000 and simplify to 1/8.
例如：0.75 有两位小数，所以写成 75/100，化简为 3/4。对于 0.125，写成 125/1000，化简为 1/8。
For recurring decimals, such as
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