Mastering Ratio and Proportion for Cambridge KS3 Maths | 掌握剑桥KS3数学中的比与比例

📚 Mastering Ratio and Proportion for Cambridge KS3 Maths | 掌握剑桥KS3数学中的比与比例

Ratio and proportion are central to the Cambridge KS3 maths curriculum. They appear in number problems, algebra, scale drawing, and everyday comparisons. This article explains the key methods step by step so that you can simplify ratios, share amounts, and solve direct proportion questions accurately.

比和正比例是剑桥 KS3 数学课程的核心内容。它们出现在数值问题、代数、比例尺以及日常比较中。本文将一步步讲解关键方法，帮助你准确化简比、分配数量并解答正比例问题。

1. What Is a Ratio? | 什么是比？

A ratio compares two or more quantities in a fixed order. The ratio 3 : 2 means that for every 3 parts of the first quantity there are 2 parts of the second quantity.

比用于按固定顺序比较两个或多个数量。3 : 2 表示第一项每有 3 份，第二项就有 2 份。

Ratios describe relative size, not the actual total. For example, a class with 12 boys and 8 girls has the same ratio as a class with 30 boys and 20 girls because both simplify to 3 : 2.

比描述的是相对大小，而不是实际总量。例如，一个有 12 名男生和 8 名女生的班级，与一个有 30 名男生和 20 名女生的班级具有相同的比，因为它们都化简为 3 : 2。

• Ratio = relative comparison | 比 = 相对比较
• Part = one value in the ratio | 项 = 比中的一个数值
• Order matters | 顺序很重要

2. Simplifying Ratios | 化简比

To simplify a ratio, divide every part by the highest common factor, or HCF. Because a ratio is unchanged when all parts are multiplied or divided by the same number, simplification makes the numbers easier to compare.

化简比时，将比中的每一项除以它们的最大公因数，简称 HCF。由于比的所有项同时乘或除以同一个数时比值不变，化简后的数字更容易比较。

12 ÷ 4 : 8 ÷ 4 = 3 : 2

If the ratio includes decimals or fractions, multiply all parts by the same power of 10 or lowest common multiple to obtain integers first.

如果比中包含小数或分数，先给所有项同时乘以 10 的幂或最小公倍数，转化为整数比。

1.2 : 0.8 × 10 = 12 : 8 = 3 : 2

3. Equivalent Ratios | 等价比

Equivalent ratios are made by multiplying

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