📚 Essential Maths Book 8i Answers | 《核心数学8i》答案解析与复习指南
This article provides a structured set of worked answers and revision notes for the main topics in Essential Maths Book 8i. It is designed to help Year 8 students check their working, understand common mistakes, and build confidence for class tests and end-of-year assessments.
本文为《Essential Maths Book 8i》的主要章节提供系统的解题答案与复习要点，帮助八年级学生检查计算过程、理解常见错误，并为课堂测验和年终考试建立信心。
1. Number and BIDMAS | 数与运算顺序
Always follow the order of operations: brackets, powers (or indices), multiplication and division from left to right, then addition and subtraction from left to right. The acronym BIDMAS is a useful checklist.
务必遵循运算顺序：先括号，再幂（指数），然后从左到右进行乘除，最后从左到右进行加减。助记词 BIDMAS 是一个有用的检查表。
² × 3. The power comes first: 2² = 4. Next multiply: 4 × 3 = 12. Finally add: 5 + 12 = 17.
示例：5 + 2² × 3。先算幂：2² = 4。再算乘法：4 × 3 = 12。最后相加：5 + 12 = 17。
, then 49 × 3 = 147 is wrong, because addition must wait until multiplication is complete.
常见错误：从左到右先算 5 + 2 = 7，再平方得 49，再乘以 3 得 147 是错误的，因为加法必须等乘法完成后再进行。
2. Negative Numbers and Powers | 负数与幂
moving left, so 4 + (−7) = −3. Subtracting a negative means moving right, so 5 − (−2) = 7.
加减负数时，可以想象一条数轴。加上负数相当于向左移动，所以 4 + (−7) = −3。减去负数相当于向右移动，所以 5 − (−2) = 7。
answer, different signs give a negative answer. Example: (−6) × 3 = −18; (−12) ÷ (−4) = 3.
乘法和除法规则：同号得正，异号得负。例如 (−6) × 3 = −18；(−12) ÷ (−4) = 3。
2) × (−2) = 4, but −2² = −(2²) = −4. This distinction is very common in Book 8i exercises.
幂运算中，只有紧靠指数的底数才被乘方。因此 (−2)² = (−2) × (−2) = 4，而 −2² = −(2²) = −4。这个区别在 Book 8i 练习中非常常见。
3. Fractions and Mixed Numbers | 分数与带分数
1/6, the lowest common denominator is 12, so 3/4 = 9/12, 1/6 = 2/12, and the sum is 11/12.
分数的加减法要先找到公分母。例如 3/4 + 1/6，最小公分母是 12，因此 3/4 = 9/12，1/6 = 2/12，和为 11/12。
(2×3)/(5×7) = 6/35. To divide, multiply by the reciprocal: 2/5 ÷ 3/7 = 2/5 × 7/3 = 14/15.
分数相乘时，分子乘分子，分母乘分母。例如 2/5 × 3/7 = (2×3)/(5×7) = 6/35。分数相除时，乘以倒数：2/5 ÷ 3/7 = 2/5 × 7/3 = 14/15。
Always simplify your final answer. Example: 6/8 = 3/4; 15/25 = 3/5.
最终答案一定要化简。例如 6/8 = 3/4；15/25 = 3/5。
4. Percentages and Conversions | 百分数与换算
by the denominator and multiply by 100. For 3/8, 3 ÷ 8 = 0.375, so the percentage is 37.5%.
将分数转换为百分数，用分子除以分母再乘以 100。例如 3/8，3 ÷ 8 = 0.375，所以百分数为 37.5%。
d a percentage of a quantity, convert the percentage to a decimal or fraction. Example: 15% of 80 = 0.15 × 80 = 12. To increase 80 by 15%, find 12 and add: 80 + 12 = 92.
求一个数量的百分数，先将百分数转换为小数或分数。例如 80 的 15% = 0.15 × 80 = 12。若要在 80 上增加 15%，先求出 12，再加：80 + 12 = 92。
5. Algebraic Expressions and Substitution | 代数表达式与代入
ons by collecting like terms. Example: 3a + 5b − 2a + 4b = (3a − 2a) + (5b + 4b) = a + 9b.
通过合并同类项来化简代数式。例如 3a + 5b − 2a + 4b = (3a − 2a) + (5b + 4b) = a + 9b。
ngle bracket, multiply the term outside by each term inside. Example: 4(2x − 3) = 8x − 12.
展开单项括号时，将括号外的项分别乘以括号内的每一项。例如 4(2x − 3) = 8x −
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