📚 Ratio and Proportion: Cambridge KS3 Core Skills | 比例与比例推理：剑桥初中数学核心技法
Ratios and proportions appear throughout the Cambridge KS3 mathematics course, from sharing money and mixing ingredients to reading scale drawings and solving direct proportion problems. The skills in this article match the style of page 134 question 2, where you must choose the correct part of a ratio and apply it to a real situation.
比和比例贯穿剑桥初中数学课程的始终，从分配金钱、混合配料到读取比例尺图和解决正比例问题。本文所讲的技能与第134页第2题的题型一致，这类题目要求你正确找出比的各项，并将其应用到实际情境中。
1. Understanding Ratio | 理解比
A ratio compares two or more quantities in the same unit. For example, if a fruit bowl has 4 apples and 6 oranges, the ratio of apples to oranges is written as 4 : 6.
比用来比较两个或两个以上相同单位的量。例如，一个水果碗里有 4 个苹果和 6 个橙子，苹果与橙子的比就写作 4 : 6。
The order is always important: 4 : 6 is not the same as 6 : 4. The first number must match the first item named in the question.
顺序始终非常重要：4 : 6 不等于 6 : 4。第一个数字必须对应题目中最先提到的项目。
A ratio has no units after it is simplified. It only tells us the relative size of the parts, not the actual amounts.
比在化简后没有单位。它只表示各部分之间的相对大小，并不表示实际数量。
2. Simplifying Ratios | 化简比
To simplify a ratio, divide every part by the highest common factor, or HCF. For 4 : 6, the HCF is 2, so 4 ÷ 2 : 6 ÷ 2 = 2 : 3.
化简比时，要用最大公因数（HCF）去除比的每一项。例如 4 : 6 的最大公因数是 2，所以 4 ÷ 2 : 6 ÷ 2 = 2 : 3。
If a ratio contains decimals or fractions, multiply every part by the same power of 10 or the same denominator first. This makes all parts whole numbers.
如果比中含有小数或分数，要先给每一项乘上相同的 10 的幂或相同的分母，使所有部分都变成整数。
- Example: 0.5 : 1.5 = 5 : 15 = 1 : 3 | 示例：0.5 : 1.5 = 5 : 15 = 1 : 3
- Example: 1/2 : 1/4 = 2 : 1 | 示例：1/2 : 1/4 = 2 : 1
3. Writing Ratios in the Form 1 : n | 写成 1 : n 的形式
Cambridge questions often ask you to write a ratio in the form 1 : n. To do this, divide both sides of the ratio by the first number.
剑桥考试常要求将比写成 1 : n 的形式。方法是用第一个数去除比的两边。
For example, 3 : 12 becomes 1 : 4 because 3 ÷ 3 = 1 and 12 ÷ 3 = 4.
例如，3 : 12 可以写成 1 : 4，因为 3 ÷ 3 = 1，12 ÷ 3 = 4。
a : b → 1 : (b ÷ a)
Use this form when you need to compare one part to the other relative to a single unit. It is especially useful for scale drawings and rates.
当你需要以单位 1 为基准比较两个部分时，可以使用这种形式。它在比例尺图和速率问题中尤其有用。
| Original ratio | 原始比 | Form 1 : n | 1 : n 形式 |
| 5 : 20 | 1 : 4 |
| 2 : 5 | 1 : 2.5 |
4. Sharing in a Given Ratio | 按给定比例分配
To share a quantity in the ratio a : b, first add the parts to find the total number of parts. Then divide the quantity by that total to find the value of one part.
要按 a : b 分配一个量，先把各项相加求出总份数。然后用总量除以总份数，得到一份的大小。
Finally multiply the value of one part by each ratio term. This gives the actual amount for each share.
最后用一份的大小分别乘比的每一项，就能得到每一部分的实际数量。
One part = Total ÷ (a + b)
Example: Share £200 in the ratio 2 : 3.
示例：按 2 : 3 分配 200 英镑。
Total parts = 2 + 3 = 5, so one part = £200 ÷ 5 = £40. The shares are £40 × 2 = £80 and £40 × 3 = £120.
总份数 = 2 + 3 = 5，所以一份 = 200 ÷ 5 = 40 英镑。两部分分别是 40 × 2 = 80 英镑和 40 × 3 = 120 英镑。
Always check that the shares add back to the original total: £80 + £120 = £200.
一定要检验各部分相加是否等于原来的总量：80 + 120 = 200 英镑。
5. Three-Part Ratios | 三项比
When three quantities are compared, such as red : blue : green = 3 : 5 : 7, the total number of parts is 3 + 5 + 7 = 15.
当比较三个量时，例如红 : 蓝 : 绿 = 3 : 5 : 7，总份数为 3 + 5 + 7 = 15。
Three-part ratio problems work exactly the same way as two-part ratio problems. Find one part first, then multiply by each term.
三项比的解题方法与两项比完全相同。先求出一份的大小，再分别乘以每一项。
Example: 300 ml of juice is made from syrup, water and sparkling water in the ratio 1 : 2 : 3.
示例：300 毫升果汁由糖浆、水和气泡水按 1 : 2 : 3 的比例混合而成。
Total parts = 1 + 2 + 3 = 6. One part = 300 ÷ 6 = 50 ml. Amounts are 50 ml, 100 ml and 150 ml.
总份数 = 1 + 2 + 3 = 6。一份 = 300 ÷ 6 = 50 毫升。各量分别为 50 毫升、100 毫升和 150 毫升。
Check: 50 + 100 + 150 = 300 ml and the simplified ratio is 50 : 100 : 150 = 1 : 2 : 3.
检验：50 + 100 + 150 = 300 毫升，化简后为 50 : 100 : 150 = 1 : 2 : 3。
6. Direct Proportion | 正比例
Two quantities are in direct proportion if one increases at the same rate as the other. The ratio between the two quantities remains constant.
如果两个量以相同的速率增长，它们就成正比例。两个量之间的比保持不变。
For example, if 5 pens cost £3, then 10 pens cost £6. The cost per pen is £3 ÷ 5 = £0.60.
例如，5 支笔花费 3 英镑，那么 10 支笔花费 6 英镑。每支笔的价格是 3 ÷ 5 =
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