KS3 Cambridge Maths: Ratio, Proportion and Percentage | KS3 剑桥数学：比、比例与百分比

📚 KS3 Cambridge Maths: Ratio, Proportion and Percentage | KS3 剑桥数学：比、比例与百分比

This revision article covers the Cambridge KS3 mathematics skills that typically appear together on worksheet page 244: ratio, proportion and percentage. You will learn how to compare quantities, share amounts fairly, scale shapes and solve real-world percentage problems. The methods shown here are designed to build confidence for both calculator and non-calculator questions.

本篇复习文章涵盖剑桥 KS3 数学练习页 244 常见综合考点：比、比例与百分比。你将学习如何比较数量、按比例分配、缩放图形，以及解决现实中的百分比问题。这里展示的方法旨在帮助你自信应对可以使用计算器和不能使用计算器的题目。

1. Understanding Ratio | 理解比

A ratio compares two or more quantities of the same kind. In a class of 12 boys and 8 girls, the ratio of boys to girls is written as 12 : 8. Order is crucial: 12 : 8 is not the same as 8 : 12.

比用来比较两个或两个以上同种类的量。在一个有 12 名男生和 8 名女生的班级中，男生与女生的比写作 12 : 8。顺序很关键：12 : 8 与 8 : 12 意义不同。

We read a : b as ‘a to b’. The first number is linked to the first quantity, and the second number to the second quantity. Units must be the same before writing a ratio, so 2 m to 50 cm should be compared as 200 cm : 50 cm after conversion.

a : b 读作 ‘a 比 b’。第一个数对应第一个量，第二个数对应第二个量。在写比之前，单位必须相同，因此 2 米与 50 厘米应在换算后写成 200 厘米 : 50 厘米再进行比较。

A ratio can also be written using the word ‘to’ or as a fraction, but the colon form is the most common in Cambridge KS3 questions. For example, 3 : 5 can be described as ‘3 to 5’.

比也可以用 ‘to’ 或分数的形式书写，但冒号形式在剑桥 KS3 题目中最常见。例如，3 : 5 可以读作 ‘3 比 5’。

2. Simplifying Ratios and Equivalent Ratios | 化简比与等比

To simplify a ratio, divide every part by the greatest common factor, often called the HCF. For example, 12 : 8 simplifies to 3 : 2 because both parts divide by 4.

化简比时，将每一部分都除以最大公因数，通常称为 HCF。例如 12 : 8 化简为 3 : 2，因为两部分都可以除以 4。

12 ÷ 4 : 8 ÷ 4 = 3 : 2

If a ratio contains fractions or decimals, multiply first to clear them. Start with 0.5 : 2 by multiplying both sides by 10 to get 5 : 20, then simplify to 1 : 4.

如果比中含有分数或小数，可以先乘一个适当的数化为整数。例如 0.5 : 2，两边同乘 10 得到 5 : 20，再化简为 1 : 4。

Ratios with three parts follow the same rule. The ratio 4 : 6 : 10 has a common factor of 2, so it simplifies to 2 : 3 : 5. Always check whether all parts can still be divided by the same number.

含有三个部分的比也遵循同样的规则。比 4 : 6 : 10 有公因数 2，所以化简为 2 : 3 : 5。一定要检查是否所有部分还能同时除以同一个数。

• 2 : 6 → 1 : 3
• 15 : 25 → 3 : 5
• 0.2 : 0.6 → multiply by 10 → 2 : 6 → 1 : 3

3. Dividing a Quantity in a Given Ratio | 按给定比分配数量

To share £45 in the ratio 2 : 3, first add the parts: 2 + 3 = 5 parts. One part is £45 ÷ 5 = £9. The shares are 2 × £9 = £18 and 3 × £9 = £27.

按 2 : 3 分配 45 英镑时，先求总份数：2 + 3 = 5 份。一份是 45 ÷ 5 = 9 英镑。两部分是 2 × 9 = 18 英镑，三部分是 3 × 9 = 27 英镑。

Always check that the individual shares add back to the original total: £18 + £27 = £45. This is a quick way to verify an exam answer before moving on.

务必检查各部分之和是否等于原总数：18 英镑 + 27 英镑 = 45 英镑。这是在继续答题前快速验算答案的好方法。

For three-part ratios, the method is identical. To divide 120 kg in the ratio 2 : 3 : 5, add the parts to get 10. One part is 120 ÷ 10 = 12 kg. The shares are 24 kg, 36 kg and 60 kg.

对于三部分比，方法相同。按 2 : 3 : 5 分配 120 千克，先把份数相加得到 10。一份是 120 ÷ 10 = 12 千克。三部分分别是 24 千克、36 千克和 60 千克。

When a question gives one part instead of the total, first find the value of one part. If the ratio 3 : 4 represents boys and girls and there are 12 boys, one part is 12 ÷ 3 = 4, so there are 4 × 4 = 16 girls.

当题目给出某一个部分而不是总数时，先求出一份的值。如果男生与女生的比是 3 : 4，男生有 12 人，那么一份是 12 ÷ 3 = 4，因此女生有 4 × 4 = 16 人。

4. Ratio and Fractions | 比与分数

A ratio can be converted into fractions of the whole. With boys : girls = 3 : 2, there

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