📚 Fractions, Decimals and Percentages for KS3 Cambridge Mathematics | KS3 剑桥数学：分数、小数与百分数
In KS3 Cambridge Mathematics, fractions, decimals and percentages are three connected ways of describing parts of a whole. This revision guide covers the key methods you need to convert, compare, add, subtract, multiply and divide with confidence, and shows how these skills appear in Checkpoint-style questions.
在 KS3 剑桥数学中，分数、小数和百分数是描述整体的一部分的三种相互关联的方式。本复习指南涵盖转换、比较、加减乘除等核心方法，并说明这些技能在 Checkpoint 风格题目中的常见考法。
1. What Are Fractions, Decimals and Percentages? | 什么是分数、小数和百分数？
A fraction shows a number of equal parts out of a whole. The top number is the numerator, and the bottom number is the denominator.
分数表示整体中的若干等份。上面的数是分子，下面的数是分母。
A decimal uses place value tenths, hundredths, thousandths and so on. For example, 0.25 means 2 tenths + 5 hundredths.
小数利用十分位、百分位、千分位等位值表示数。例如 0.25 表示 2 个十分之一加 5 个百分之一。
A percentage is a fraction out of 100. The symbol % means ‘per 100’, so 25% = 25/100.
百分数是分母为 100 的分数。符号 % 表示每一百，所以 25% = 25/100。
| Form | Meaning | Example |
|---|---|---|
| Fraction | Parts out of equal parts | 3/4 |
| Decimal | Place value using powers of ten | 0.75 |
| Percentage | Parts out of 100 | 75% |
2. Equivalent Fractions and Simplifying | 等值分数与化简
Equivalent fractions have the same value but use different numerators and denominators. Multiply or divide the top and bottom by the same non-zero number.
等值分数数值相同，但分子和分母不同。将分子和分母同时乘以或除以同一个非零数，可得到等值分数。
a/b = (a×k)/(b×k), k ≠ 0
To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF). For example, 12/18 = 2/3 because HCF(12,18) = 6.
化简分数时，用分子和分母的最大公因数（HCF）同时除两者。例如 12/18 = 2/3，因为 HCF(12,18) = 6。
Always check whether a fraction can be simplified before giving your final answer. This is a common requirement in Cambridge Checkpoint tests.
在给出最终答案之前，始终检查分数是否可以化简。这是剑桥 Checkpoint 考试中的常见要求。
3. Converting Between Fractions and Decimals | 分数与小数之间的转换
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/8 = 3 ÷ 8 = 0.375.
将分数转换为小数，用分子除以分母。例如 3/8 = 3 ÷ 8 = 0.375。
To convert a terminating decimal to a fraction, write the decimal as tenths, hundredths or thousandths and simplify. Example: 0.45 = 45/100 = 9/20.
将有限小数转换为分数时，先写成十分之几、百分之几或千分之几，再化简。例如 0.45 = 45/100 = 9/20。
Recurring decimals can be written with dot notation, but at KS3 you are usually asked to round or compare them. A recurring decimal such as 0.333… can be written as 0.3 with a dot above the 3.
循环小数可以用点记号表示，但在 KS3 阶段通常要求你将其四舍五入或用于比较。例如循环小数 0.333… 可以写成 0.3 并在 3 上方加点。
4. Converting Decimals to Percentages and Back | 小数与百分数的相互转换
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