📚 Year 8 Essential Maths Book 8 Answers Compressed | Year 8 数学 Essential Maths Book 8 压缩答案精华
The Essential Maths Book 8 is a core practice book for Year 8 students in many schools. The compressed answers file brings together the final answers and key working steps in one quick-reference document. This guide shows you how to use these answers for revision and highlights the main mathematical ideas you will meet.
《Essential Maths Book 8》是许多学校 8 年级学生的核心练习册。压缩答案文件将最终答案和关键解题步骤汇总在一份快速查阅文档中。本指南将介绍如何利用这些答案进行复习，并梳理你会遇到的主要数学知识点。
1. How to Use the Compressed Answer Guide | 如何使用压缩答案指南
Do not simply copy the final answer. Cover the solution, attempt the question first, then check your method step by step.
不要直接抄最终答案。先盖住答案，独立尝试题目，然后一步一步对照你的解题过程。
Use the compressed answers as a diagnostic tool: if your answer differs, find the exact line where your working diverges and correct that specific skill.
把压缩答案当作诊断工具：如果你的答案不同，找出你的解题过程在哪一步出现分歧，并针对这一技能进行纠正。
2. Number and Place Value | 数字与位值
Year 8 number work includes rounding to decimal places and significant figures, estimating calculations, and using powers of 10.
8 年级的数字运算包括按小数位和有效数字四舍五入、估算计算，以及使用 10 的幂。
10³ = 1000, 2.5 × 10⁴ = 25 000
For example, 47 286 rounded to 2 significant figures is 47 000 because the third significant figure is 2, so we round down.
例如，47 286 保留 2 位有效数字为 47 000，因为第三位有效数字是 2，所以要舍去。
3. Fractions, Decimals and Percentages | 分数、小数和百分数
You must be able to convert fluently between fractions, decimals and percentages. The key conversions often appear in Book 8 answers.
你必须能在分数、小数和百分数之间熟练转换。这些关键转换经常出现在 Book 8 的答案中。
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/4 | 0.25 | 25% |
| 3/8 | 0.375 | 37.5% |
| 2/5 | 0.4 | 40% |
Percentage increase and decrease are tested regularly: an increase of 15% on £80 gives £80 × 1.15 = £92.
百分比增加和减少是常考内容：80 英镑增加 15%，就是 80 × 1.15 = 92 英镑。
4. Directed Numbers | 有向数
Directed numbers include positive and negative values. Remember the sign rules for multiplication and division: same signs give a positive result, different signs give a negative result.
有向数包括正数和负数。记住乘除法的符号规则：同号得正，异号得负。
(−4) × (−6) = 24, (−8) ÷ 2 = −4, 5 − (−3) = 8
number line; when subtracting a negative number, move right. For example, −2 + (−5) = −7.
加上一个负数时，在数轴上向左移动；减去一个负数时，向右移动。例如，−2 + (−5) = −7。
5. Algebraic Expressions and Simplification | 代数表达式与化简
Simplifying expressions means collecting like terms. Only terms with exactly the same letter and power can be combined.
化简代数式就是合并同类项。只有字母和次数完全相同的项才能合并。
3a + 5b − a + 2b = 2a + 7b
Expanding brackets uses the distributive law: multiply each term inside the bracket by the term outside. Factorising is the reverse process.
去括号使用分配
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