📚 Essential Maths Book 7i Answers Explained | KS3 数学基础 7i 答案解析
This article provides a detailed walkthrough of selected answers and key concepts from Essential Maths Book 7i, a popular KS3 textbook. Each section explains a typical question, the correct solution, and the reasoning behind it, helping students build a solid foundation in Year 7 mathematics.
本文精选了《Essential Maths Book 7i》中的典型题目，逐一解析答案与核心知识点。通过中英双语对照讲解，帮助 KS3 学生理解解题思路，巩固七年级数学基础。
1. Place Value and Ordering Numbers | 位值与数字排序
Q: Write the number 604 781 in words and state the value of the digit 6. Answer: Six hundred and four thousand, seven hundred and eighty-one. The digit 6 is in the hundred thousands place, so its value is 600 000.
题目：用文字写出数字 604 781，并说出数字 6 的值。答案：六十万四千七百八十一。数字 6 在十万位，因此它的值是 600 000。
2. Addition and Subtraction | 加法与减法
Q: Calculate 2347 + 896 and check by subtraction. Answer: 2347 + 896 = 3243. Check: 3243 − 896 = 2347. The column method with carrying ensures accuracy; always align digits by place value.
计算 2347 + 896 并用减法验算。答案：2347 + 896 = 3243。验算：3243 − 896 = 2347。列竖式时注意进位，数位对齐是保证计算正确的关键。
3. Multiplication and Division | 乘法与除法
Q: Find 27 × 34 using the grid method, then divide 918 by 27 to verify. Answer: 27 × 34 = (20×30)+(20×4)+(7×30)+(7×4) = 600 + 80 + 210 + 28 = 918. 918 ÷ 27 = 34, so the result is correct.
用格子法计算 27 × 34，再用除法 918 ÷ 27 验证。答案：27 × 34 = (20×30)+(20×4)+(7×30)+(7×4) = 600 + 80 + 210 + 28 = 918。918 ÷ 27 = 34，结果正确。
4. Understanding Fractions | 理解分数
Q: Shade 3/8 of a rectangle divided into 8 equal parts and write an equivalent fraction. Answer: Shade 3 parts out of 8. Equivalent fraction: 3/8 = 6/16 (multiply numerator and denominator by 2).
将一个分成 8 等份的长方形涂色表示 3/8，并写出一个等值分数。答案：涂 3 份。等值分数：3/8 = 6/16（分子分母同乘 2）。
5. Decimals and Place Value | 小数与位值
Q: Write 4.07 as a mixed number and find the value of the digit 7. Answer: 4.07 = 4 7/100. The digit 7 is in the hundredths place, so its value is 0.07.
将 4.07 写成带分数，并说出数字 7 的值。答案：4.07 = 4 7/100。数字 7 在百分位，因此它的值是 0.07。
6. Introduction to Percentages | 百分数入门
Q: Convert 0.65 to a percentage and find 65% of 80 kg. Answer: 0.65 = 65%. 65% of 80 kg = 0.65 × 80 = 52 kg. It is useful to remember that ‘per cent’ means out of 100.
将 0.65 化为百分数，并求 80 kg 的 65% 是多少。答案：0.65 = 65%。80 kg 的 65% = 0.65 × 80 = 52 kg。记住“百分数”就是每一百份中的多少份。
7. Algebraic Expressions | 代数表达式
Q: Simplify 3a + 2b − a + 4b. Answer: Collect like terms: 3a − a = 2a, 2b + 4b = 6b, so the simplified expression is 2a + 6b.
化简 3a + 2b − a + 4b。答案：合并同类项：3a − a = 2a，2b + 4b = 6b，化简结果为 2a + 6b。
8. Solving Simple Equations | 解简单方程
Q: Solve y + 5 = 13. Answer: Subtract 5 from both sides: y + 5 − 5 = 13 − 5, so y = 8. Always check by substituting y = 8 back into the original equation: 8 + 5 = 13, which is correct.
解方程 y + 5 = 13。答案：两边同时减去 5：y + 5 − 5 = 13 − 5，得 y = 8。将 y = 8 代回原方程检验：8 + 5 = 13，正确。
9. Angles and Lines | 角与线
Q: On a straight line, one angle is 72°. Find the other angle. Answer: Angles on a straight line add up to 180°. So the other angle = 180° − 72° = 108°.
一条直线上有一个角是 72°，求另一个角。答案：直线上的邻角之和为 180°，因此另一个角 = 180° − 72° = 108°。
10. Perimeter and Area | 周长与面积
Q: A rectangle has length 8 cm and width 5 cm. Calculate its perimeter and area. Answer: Perimeter = 2 × (8 + 5) = 26 cm. Area = 8 × 5 = 40 cm². Remember to use correct units.
一个长方形的长是 8 cm，宽是 5 cm，求周长和面积。答案：周长 = 2 × (8 + 5) = 26 cm。面积 = 8 × 5 = 40 cm²。注意单位的使用。
11. Collecting and Interpreting Data | 数据收集与解读
Q: The frequency table shows favourite colours: Red 6, Blue 9, Green 5. Draw a bar chart and find the mode. Answer: Bar chart with bars of heights 6, 9, 5. The mode is Blue because it has the highest frequency (9).
频数表显示最喜欢的颜色：红色 6 人，蓝色 9 人，绿色 5 人。画条形图并找出众数。答案：条形高度分别为 6, 9, 5。众数是蓝色，因为它的频数最高 (9)。
12. Real-Life Problem Solving | 实际问题解决
Q: A box holds 24 pencils. How many boxes are needed for 150 pencils? How many pencils are left over? Answer: 150 ÷ 24 = 6 remainder 6. So 6 full boxes are needed, and 6 pencils will be left over. Division with remainders is essential for sharing problems.
一个盒子装 24 支铅笔。150 支铅笔需要多少个盒子？剩下多少支？答案：150 ÷ 24 = 6 余 6。因此需要 6 个满的盒子，剩下 6 支铅笔。带余数的除法在分配问题中非常实用。
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