Essential Maths Book 7C Answers: Key Worked Solutions | 《基础数学 7C》答案解析：核心例题精讲

📚 Essential Maths Book 7C Answers: Key Worked Solutions | 《基础数学 7C》答案解析：核心例题精讲

Essential Maths Book 7C is widely used in Year 7 to stretch students who are confident with Key Stage 3 basics. This article gives worked answers to selected 7C-style question types, focusing on methods rather than just final answers. Use it to check steps, correct mistakes and build independence.

《基础数学 7C》在 Year 7 广泛用于拓展已经掌握 KS3 基础的学生。本文精选 7C 风格题型给出解析答案，重在展示方法而不只是最后结果。你可以用它核对步骤、纠正错误并培养独立解题能力。

1. Order of Operations and Directed Numbers | 运算顺序与正负数

Many 7C exercises test whether you can apply BIDMAS and handle negative numbers correctly. Work inside brackets first, then powers, then division and multiplication from left to right, and finally addition and subtraction. This order is essential when a question combines subtraction with multiplication.

许多 7C 练习考查你能否正确使用 BIDMAS 并处理负数。先算括号，再算乘方，然后从左到右计算除法和乘法，最后计算加法和减法。当一个题目同时包含减法和乘法时，这个顺序至关重要。

Example: Calculate 15 − 3 × (4 + 2) ÷ 9.

例题：计算 15 − 3 × (4 + 2) ÷ 9。

Solution: Brackets first: 4 + 2 = 6. Then multiply and divide left to right: 3 × 6 = 18, then 18 ÷ 9 = 2. Finally subtract: 15 − 2 = 13.

解答：先算括号：4 + 2 = 6。然后从左到右计算乘除：3 × 6 = 18，接着 18 ÷ 9 = 2。最后计算减法：15 − 2 = 13。

For directed numbers, subtracting a negative is the same as adding a positive: 7 − (−3) = 7 + 3 = 10. Multiplying two negatives gives a positive, for example (−4) × (−5) = 20.

对于正负数，减去一个负数等于加上它的相反数：7 − (−3) = 7 + 3 = 10。两个负数相乘得正，例如 (−4) × (−5) = 20。

Common mistake: writing 15 − 3 × 6 as 12 × 6 = 72. The correct order gives 15 − 18 = −3.

常见错误：把 15 − 3 × 6 写成 12 × 6 = 72。正确的顺序应得 15 − 18 = −3。

---

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

Converting between fractions, decimals and percentages is a core 7C skill. To compare 3/8, 0.36 and 35%, write them all in the same form. This makes ordering and word problems much easier.

在分数、小数和百分数之间进行转换是 7C 的核心技能。要比较 3/8、0.36 和 35%，先把它们写成同一种形式。这样排序和应用题会容易得多。

Example: Write 3/8 as a decimal and a percentage.

例题：把 3/8 写成小数和百分数。

Solution: 3/8 = 3 ÷ 8 = 0.375. As a percentage: 0.375 × 100% = 37.5%.

解答：3/8 = 3 ÷ 8 = 0.375。写成百分数：0.375 × 100% = 37.5%。

Example: Increase 240 g by 15%.

例题：将 240 g 增加 15%。

Solution: 10% of 240 = 24 g, 5% = 12 g, so 15% = 36 g. New amount = 240 + 36 = 276 g.

解答：240 的 10% 是 24 g，5% 是 12 g，所以 15% 是 36 g。新数量 = 240 + 36 = 276 g。

Example: Work out 2/3 + 5/6.

例题：计算 2/3 + 5/6。

Solution: Use a common denominator of 6: 2/3 = 4/6, so 4/6 + 5/6 = 9/6 = 3/2 = 1½.

解答：使用公分母 6：2/3 = 4/6，所以 4/6 + 5/6 = 9/6 = 3/2 = 1½。

---

3. Simplifying Algebraic Expressions | 化简代数式

In 7C algebra, you collect like terms and use index notation. Only terms with exactly the same letter part can be combined. Constants are combined separately.

在 7C 代数中，你要合并同类项并使用指数记法。只有字母部分完全相同的项才能合并。常数项单独合并。

Example: Simplify 5a + 3b − 2a + 7b − 4.

例题：化简 5a + 3b − 2a + 7b − 4。

Solution: Collect a terms: 5a − 2a = 3a. Collect b terms: 3b + 7b = 10b. Constant: −4. Answer: 3a + 10b − 4.

解答：合并 a 项：5a − 2a = 3a。合并 b 项：3b + 7b = 10b。常数项：−4。答案：3a + 10b − 4。

Example: Write m × m × m × n × n using index notation.

例题：用指数记法表示 m × m × m × n × n。

Solution: There are three m’s and two n’s, so the answer is m³n².

解答：有三个 m 和两个 n，因此答案为 m³n²。

Example: Expand 3(2x − 5) and simplify 4x + 3(2x − 5).

例题：展开 3(2x − 5) 并化简 4x + 3(2x − 5)。

Solution: 3(2x − 5) = 6x − 15. Then 4x + 6x −

Published by TutorHao | Year 7 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）