📚 Cambridge KS3 Maths: Core Skills for p293_1 Practice | 剑桥KS3数学：p293_1 练习核心技能
This bilingual revision guide supports learners working on Cambridge KS3 Mathematics, including focused practice sheets such as p293_1. It consolidates the core skills needed to solve mixed problems confidently: number, algebra, geometry, data handling and probability.
本双语复习指南帮助学习剑桥 KS3 数学的学生，包括 p293_1 一类的专项练习。它巩固混合题所需的数、代数、几何、数据处理和概率等核心技能。
1. Integers and Order of Operations | 整数与运算顺序
Directed numbers follow simple sign rules. Adding a negative is subtracting; subtracting a negative is adding. For example, 7 + (−2) = 5 and 9 − (−4) = 13.
有向数遵循简单的符号规则。加上负数等于减法；减去负数等于加法。例如 7 + (−2) = 5，9 − (−4) = 13。
7 + (−2) = 5
9 − (−4) = 13
Use BIDMAS/BODMAS: Brackets, Indices, Division and Multiplication, Addition and Subtraction. For 3 + 4 × 2, multiply first: 3 + 8 = 11.
使用 BIDMAS/BODMAS 规则：括号、指数、除法和乘法、加法和减法。如 3 + 4 × 2，先算乘法：3 + 8 = 11。
3 + 4 × 2 = 11
Always work from left to right for multiplication and division of equal priority. Example: 12 ÷ 3 × 2 = 4 × 2 = 8.
同级的乘法和除法按从左到右的顺序计算。例如 12 ÷ 3 × 2 = 4 × 2 = 8。
12 ÷ 3 × 2 = 8
2. Fractions, Decimals and Percentages | 分数、小数与百分数
To add or subtract fractions, find a common denominator first. Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
分数加减要先通分。例如 1/4 + 1/6 = 3/12 + 2/12 = 5/12。
1/4 + 1/6 = 3/12 + 2/12 = 5/12
To multiply fractions, multiply numerators and denominators separately: 2/3 × 5/7 = 10/21. To divide by a fraction, multiply by its reciprocal.
分数相乘时，分子乘分子、分母乘分母：2/3 × 5/7 = 10/21。除以一个分数等于乘以它的倒数。
2/3 × 5/7 = 10/21
Convert between fractions, decimals and percentages. For example, 3/8 = 0.375 = 37.5%. To change a fraction to a percentage, divide numerator by denominator and multiply by 100.
分数、小数和百分数可以互相转换。例如 3/8 = 0.375 = 37.5%。将分数化为百分数，用分子除以分母再乘 100。
3/8 = 0.375 = 37.5%
3. Ratio and Proportion | 比与比例
A ratio compares parts of a whole. If a line is divided in the ratio 3 : 5, the total number of parts is 3 + 5 = 8.
比用于比较整体中的部分。若一条线段按 3 : 5 分配，总份数为 3 + 5 = 8。
3 + 5 = 8
To share £64 in the ratio 3 : 5, find the value of one part: £64 ÷ 8 = £8. The shares are 3 × £8 = £24 and 5 × £8 = £40.
将 £64 按 3 : 5 分配，先求一份：£64 ÷ 8 = £8。两部分的份额为 3 × £8 = £24 和 5 × £8 = £40。
£64 ÷ 8 = £8
Direct proportion means two quantities increase or decrease at the same rate. If 5 pens cost £3, then 1 pen costs £0.60 and 8 pens cost 8 × £0.60 = £4.80.
正比例意味着两个量以相同的速率增加或减少。若 5 支笔 £3，则 1 支 £0.60，8 支为 8 × £0.60 = £4.80。
5 pens → £3, 1 pen → £0.60, 8 pens → £4.80
4. Algebraic Expressions and Substitution | 代数式与代入求值
Collect like terms to simplify: 3a + 5b − a + 2b = 2a + 7b. Only letters with the same power can be combined.
合并同类项来化简：3a + 5b − a + 2b = 2a + 7b。只有相同字母且相同指数才能合并。
3a + 5b − a + 2b = 2a + 7b
Use the distributive law to expand brackets: 3(x + 4) = 3x + 12 and 2(3y − 5) = 6y − 10.
使用分配律去括号：3(x + 4) = 3x + 12，2(3y − 5) = 6y − 10。
3(x + 4) = 3x +
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