Cambridge KS3 Maths: Mixed Exercise p297_2 Revision | 剑桥 KS3 数学：p297_2 混合练习复习

📚 Cambridge KS3 Maths: Mixed Exercise p297_2 Revision | 剑桥 KS3 数学：p297_2 混合练习复习

This revision article covers a mixed set of Cambridge KS3 Mathematics skills similar to those found in page 297 exercise 2. You will review fractions, decimals, percentages, negative numbers, algebraic simplification, simple equations, angle facts, area and perimeter, ratio, probability, and data interpretation. Work through each section, check the worked examples, and then try similar questions on your own.

本复习文章涵盖一组剑桥 KS3 数学混合技能，题型与第 297 页第 2 题相似。你将复习分数、小数、百分比、负数、代数式化简、简单方程、角度知识、面积与周长、比、概率以及数据解读。逐节学习并检查示例，然后自己尝试类似的问题。

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1. Working with Fractions | 分数运算

To add or subtract fractions, first rewrite them with a common denominator. For example, to work out 1/3 + 1/4, use denominator 12 because 12 is the lowest common multiple of 3 and 4.

进行分数加减法时，先通分为同分母。例如计算 1/3 + 1/4，使用公分母 12，因为 12 是 3 和 4 的最小公倍数。

1/3 + 1/4 = 4/12 + 3/12 = 7/12

To multiply fractions, multiply the numerators and denominators separately. Always write your final answer in its simplest form by dividing the top and bottom by any common factor.

分数相乘时，分子乘分子，分母乘分母。最后答案要化为最简形式，将分子分母同时除以公因数。

2/5 × 3/4 = 6/20 = 3/10

To divide by a fraction, keep the first fraction, change the division sign to multiplication, and flip the second fraction. Simplify if possible.

除以一个分数时，保留第一个分数，将除号改为乘号，并把第二个分数取倒数。结果能约分则约分。

3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1 1/8

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2. Fractions, Decimals and Percentages | 分数、小数和百分比转换

To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percentage, multiply by 100. These skills are needed for comparing quantities in mixed questions.

分数化小数的方法是分子除以分母；小数化百分比的方法是乘以 100。在混合题中比较数量时经常需要这些技能。

3/8 = 0.375 and 0.375 × 100 = 37.5%

To convert a percentage to a fraction, write the percentage over 100 and simplify. For example, 45% becomes 45/100, which simplifies to 9/20.

百分比化分数时，先写成百分之几再约分。例如 45% 写成 45/100，约分后为 9/20。

45% = 45/100 = 9/20

When comparing values, change them all to the same form. For example, 0.4, 2/5 and 40% are equal, so choosing the correct form depends on the question.

比较数值时，将所有数值化成相同形式。例如 0.4、2/5 和 40% 是相等的，因此选择哪种形式取决于题目要求。

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3. Negative Numbers | 负数运算

When adding and subtracting negative numbers, a number line can help. Moving right is positive; moving left is negative. For example, start at -3 and move 5 places right to reach 2.

进行负数加减法时，数轴可以帮助理解。向右移动为正，向左移动为负。例如从 -3 出发向右移动 5 位到达 2。

-3 + 5 = 2 and -4 - 3 = -7

Multiplying or dividing two negative numbers gives a positive result. If the signs are different, the result is negative. This sign rule is often tested in mixed arithmetic questions.

两个负数相乘或相除结果为正；异号相乘或相除结果为负。混合算术题中经常考查这一符号规则。

(-6) × (-4) = 24 and 12 ÷ (-3) = -4

Use brackets to keep signs clear. For example, 5 - (-2) is the same as 5 + 2. Be careful when a negative sign appears next to a subtraction sign.

使用括号使符号清晰。例如 5 - (-2) 等于 5 + 2。当负号与减号相邻时要特别小心。

5 - (-2) = 5 + 2 = 7

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4. Simplifying Algebraic Expressions | 化简代数式

Collect like terms by adding or subtracting the coefficients of terms that have the same variable. Constant terms without a variable are also like terms and should be combined separately.

合并同类项时，将含有相同变量的项的系数相加减。不含变量的常数项也属于同类项，应单独合并。

3a + 5b - 2a + 7b = a + 12b

Use the distributive law to expand brackets. Multiply each term inside the bracket by the term outside, paying attention to signs.

使用分配律展开括号。括号外的项要与括号内每一项相乘，并注意符号。

4(2x + 3) = 8x + 12

To factorise an expression, find the highest common factor of the terms and write it outside a bracket. Check your answer by expanding the bracket again.

因式分解时，找出各项的最高公因式并写在括号外。可以通过再次展开括号来检查答案。

6x + 9 = 3(2x + 3)

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5. Solving Linear Equations | 解一次方程

Keep an equation balanced by doing the same operation to both sides. Your aim is to isolate the variable on one side of the equals sign.

解方程时保持等式两边平衡，对方程两边同时进行相同运算。目标是使变量单独位于等号一边。

x + 5 = 12 → x = 12 - 5 = 7

If the variable has a multiplier, divide both sides by that number. If the variable is divided by a number, multiply both sides by that number.

若变量前有系数，两边同时除以该系数；若变量除以某数，两边同时乘以该数。

5x = 35 → x = 7

For equations with x on both sides, collect variable terms on one side and constants on the other. Finish by dividing to

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