Year 8 Essential Maths 8 Higher Homework Answers | Year 8 高阶数学作业答案精讲

📚 Year 8 Essential Maths 8 Higher Homework Answers | Year 8 高阶数学作业答案精讲

This article provides clear, worked answers to common homework questions in the Year 8 Essential Maths 8 Higher course. Each section focuses on one key topic, shows a typical question, and explains the method step by step. Use the answers to check your reasoning, not just your final number.

本文为 Year 8 Essential Maths 8 Higher 课程中的常见作业题提供清晰可查的答案与解题过程。每一节围绕一个核心主题，给出典型例题并逐步解释方法。请用这些答案来检查你的推理，而不只是核对最后的数字。

1. How to Use These Answers | 如何使用这些答案

Always attempt the question before looking at the answer. Write down each step, then compare your working with the method shown.

在查看答案之前，请先尝试完成题目。写下每一步，然后将你的过程与给出的方法进行对比。

If you get a different answer, find the first line where your working differs. That is usually where a sign, a bracket, or a fraction rule has been misapplied.

如果你得到不同的答案，请找出你的过程与示例第一次出现不同的那一行。那里通常是符号、括号或分数规则出错的地方。

Use these answers as a self-marking tool. Tick correct steps, circle errors, and redo any question that needed help.

把这些答案当作自我批改工具。在正确的步骤旁打勾，圈出错误，并重做任何需要帮助的题目。

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2. Number Skills: Fractions and Decimals | 数字技能：分数与小数

Typical question: Work out 3/4 + 2/5 and give the answer as a mixed number.

典型题目：计算 3/4 + 2/5，并以带分数形式给出答案。

Answer: The common denominator is 20. 3/4 = 15/20 and 2/5 = 8/20. Adding gives 23/20.

3/4 + 2/5 = 15/20 + 8/20 = 23/20 = 1 3/20

答案：公分母是 20。3/4 = 15/20，2/5 = 8/20。相加得到 23/20 = 1 3/20。

Many errors happen when students add numerators and denominators separately. Always change to equivalent fractions with the same denominator first.

许多错误发生在学生分别把分子和分母相加时。一定要先把分数化为同分母的等价分数。

Quick check: 3/4 + 2/5 is slightly more than 1, so 1 3/20 is reasonable.

快速检验：3/4 + 2/5 略大于 1，所以 1 3/20 是合理的。

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3. Percentages and Percentage Change | 百分数与百分比变化

Typical question: A jacket costs £80. In a sale it is reduced by 15%. Find the sale price.

典型题目：一件夹克售价 80 英镑。打折 15%。求折后价格。

Answer: 15% of 80 = 0.15 × 80 = 12. Sale price = 80 – 12 = £68.

80 × 0.85 = 68

答案：80 的 15% = 0.15 × 80 = 12。折后价 = 80 – 12 = 68 英镑。

Another common method is to multiply by 0.85 in one step: 80 × 0.85 = 68. This is efficient for percentage decrease.

另一种常用方法是一步乘以 0.85：80 × 0.85 = 68。这种方法对百分数减少问题很高效。

For percentage increase, add the percentage to 100% and change to a decimal. For example, a 6% rise means multiply by 1.06.

对于百分数增加，把百分数加到 100%，再转化为小数。例如，增加 6% 意味着乘以 1.06。

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4. Ratio and Proportion | 比与比例

Typical question: Divide £120 in the ratio 3 : 5.

典型题目：把 120 英镑按 3 : 5 的比例分配。

Answer: Total parts = 3 + 5 = 8. One part = 120 ÷ 8 = 15. The shares are 3 × 15 = £45 and 5 × 15 = £75.

3 parts = 3 × 15 = 45, 5 parts = 5 × 15 = 75

答案：总份数 = 3 + 5 = 8。一份 = 120 ÷ 8 = 15。分配为 3 × 15 = 45 英镑和 5 × 15 = 75 英镑。

Always check that the two amounts add back to the original total: 45 + 75 = 120.

一定要检查两个金额相加是否等于原来的总数：45 + 75 = 120。

If the ratio is given in simplified form, you can also use the fraction of the total: the smaller share is 3/8 of £120.

如果给出的比是最简形式，你也可以用总量的分数：较小的份额是 120 英镑的 3/8。

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5. Algebra Basics: Simplifying and Expanding | 代数基础：化简与展开

Typical question: Expand and simplify 3(x + 2) + 4(2x – 1).

典型题目：展开并化简 3(x +

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