📚 Essential Maths Book 7i Answers: Year 7 Key Topic Worked Solutions | 《Essential Maths 7i》答案解析：Year 7 核心主题例题讲解
This article gives worked examples and concise answers for the core Year 7 topics in Essential Maths Book 7i. Use the explanations to check your method, not just the final answer.
本文针对《Essential Maths 7i》中 Year 7 核心主题，提供典型例题的解答过程和简明答案。请重点核对解题方法，而不只是看最终答案。
1. Place Value and Number Operations | 位值与数的运算
In Year 7 you must be confident with place value, ordering integers, and the four operations. For example, the number 34 062 is built from 30 000 + 4 000 + 60 + 2. Always line up digits by place value when adding or subtracting decimals.
七年级需要熟练掌握位值、整数排序和四则运算。例如，34 062 由 30 000 + 4 000 + 60 + 2 组成。进行小数加减时，一定要按位值对齐数字。
Worked example: Calculate 2 847 + 356. Add the hundreds: 800 + 300 = 1 100, so carry 1 000. The total is 2 000 + 1 100 + 100 + 3 = 3 203.
例题：计算 2 847 + 356。百位相加：800 + 300 = 1 100，因此进位 1 000。总和为 2 000 + 1 100 + 100 + 3 = 3 203。
Another common Book 7i task is long multiplication: 23 × 46. Work out 20 × 46 = 920 and 3 × 46 = 138, then add to get 1 058.
书中常见的长乘法题目如：23 × 46。先算 20 × 46 = 920，再算 3 × 46 = 138，相加得到 1 058。
2. Factors, Multiples and Primes | 因数、倍数与质数
A factor divides exactly into a number; a multiple is the result of multiplying by an integer. A prime number has exactly two factors: 1 and itself.
因数能整除某个数；倍数是某个数乘以整数得到的结果。质数只有两个因数：1 和它本身。
Example: Find the HCF and LCM of 24 and 36. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The highest common factor is 12. Multiples of 24 include 24, 48, 72 … and multiples of 36 include 36, 72 … so the LCM is 72.
例题：求 24 和 36 的最大公因数（HCF）与最小公倍数（LCM）。24 的因数有 1、2、3、4、6、8、12、24；36 的因数有 1、2、3、4、6、9、12、18、36。最大公因数是 12。24 的倍数包括 24、48、72……36 的倍数包括 36、72……所以 LCM 是 72。
3. Fractions: Simplifying and Equivalent Forms | 分数：化简与等值形式
To simplify a fraction, divide the numerator and denominator by their HCF. Equivalent fractions are made by multiplying or dividing both parts by the same non-zero number.
化简分数时，分子和分母同时除以它们的最大公因数。等值分数通过将分子和分母同时乘或除以同一个非零数得到。
Example: Simplify 18/24. The HCF of 18 and 24 is 6, so 18 ÷ 6 = 3 and 24 ÷ 6 = 4. The simplified fraction is 3/4. To write an equivalent fraction, multiply top and bottom: 3/4 = 9/12 = 15/20.
例题：化简 18/24。18 和 24 的最大公因数是 6，所以 18 ÷ 6 = 3，24 ÷ 6 = 4。化简结果为 3/4。要写出等值分数，可以将分子分母同时相乘：3/4 = 9/12 = 15/20。
For addition, use a common denominator: 2/5 + 1/10 becomes 4/10 + 1/10 = 5/10, which simplifies to 1/2.
进行分数加法时要先通分：2/5 + 1/10 变为 4/10 + 1/10 = 5/10，化简为 1/2。
4. Decimal Operations and Rounding | 小数运算与四舍五入
Decimal calculations follow the same rules as integers, but the decimal point must stay aligned in addition and subtraction. For multiplication, count total decimal places in the question.
小数计算遵循与整数相同的规则，但加减时小数点必须对齐。乘法时，先按整数计算，再根据题目中小数位数总和确定小数点位置。
Example: Work out 3.7 + 2.85. Write 3.70 + 2.85, align tenths and hundredths, and add to get 6.55. For rounding, 3.276 to two decimal places is 3.28 because the third decimal digit is 6, so we round up.
例题：计算 3.7 + 2.85。写成 3.70 + 2.85，将十分位和百分位对齐，相加得到 6.55。保留两位小数时，3.276 约等于 3.28，因为第三位小数是 6，需要进位。
5. Percentages and Conversions | 百分数与转换
Percentage means ‘out of 100’. To convert a fraction or decimal to a percentage, multiply by 100. To find a percentage of a quantity, change the percentage to a fraction or decimal and multiply.
百分数表示“每一百份中的多少”。将分数或小数转换为百分数时乘以 100。求一个量的百分之几时，先把百分数转为分数或小数，再相乘。
Example: Find 15% of 80. 15% = 15/100 = 0.15, so 0.15 × 80 = 12. Convert 0.45 to a percentage: 0.45 × 100% = 45%. Convert 3/5 to a percentage: 3 ÷ 5 = 0.6, then 0.6 × 100% = 60%.
例题：求 80 的 15%。15% = 15/100 = 0.15，所以 0.15 × 80 = 12。将 0.45 转换为百分数：0.45 × 100% = 45%。将 3/5 转换为百分数：3 ÷ 5 = 0.6，再 0.6 × 100% = 60%。
6. Algebraic Expressions and Substitution | 代数表达式与代入
In algebra, letters stand for unknown numbers. Collect like terms by adding or subtracting the coefficients of the same letter. Substitution means replacing a letter with a number and using the correct order of operations.
在代数中，字母表示未知数。合并同类项就是将与同一个字母相乘的系数相加或相减。代入法是指用数字替换字母，并按照正确的运算顺序计算。
Example: Simplify 5a + 3b – 2a + b. Collect like terms: 5a – 2a = 3a and 3b + b = 4b, giving 3a + 4b. If a = 3 and b = -2, evaluate 4a – b. Substitute: 4 × 3 – (-2) = 12 + 2 = 14.
例题：化简 5a + 3b – 2a + b。合并同类项：5a – 2a = 3a，3b + b = 4b，结果为 3a + 4b。若 a = 3、b = -2，求 4a – b 的值。代入：4 × 3 – (-2) = 12 + 2 = 14。
7. Solving Linear Equations | 解一元一次方程
To solve an equation, use inverse operations to isolate the unknown. Always do the same to both sides of the equation, and check your solution by substituting it back into the original equation.
解方程时使用逆运算将未知数单独留在等号一边。等式两边必须同时进行相同运算，并把解代回原方程检验。
Example: Solve 5x – 3 = 2x + 9. Subtract 2x from both sides: 3x – 3 = 9. Add 3: 3x = 12. Divide by 3: x = 4. Check: 5 × 4 – 3 = 17 and 2 × 4 + 9 = 17, so the answer is correct.
例题：解方程 5x – 3 = 2x + 9。两边同时减去 2x：3x – 3 = 9。两边加 3：3x = 12。两边除以 3：x = 4。检验：5 × 4 – 3 = 17，2 × 4 + 9 = 17，答案正确。
8. Angles and Properties of Shapes | 角与图形性质
Angles on a straight line add to 180°, angles around a point add to 360°, and interior angles in a triangle add to 180°. Use these facts to find missing angles in diagrams.
直线上的角相加为 180°，一个点周围的角相加为 360°，三角形内角和为 180°。利用这些基本事实可以求出图形中的未知角。
Example: In a triangle, two angles are 68° and 47°. Find the third angle. Sum of known angles: 68° + 47° = 115°. Subtract from 180°: 180° – 115° = 65°. The missing angle is 65°.
例题：三角形中两个角分别为 68° 和 47°，求第三个角。已知角之和：68° + 47° = 115°。用 180° 减去：180° – 115° = 65°。未知角为 65°。
If an angle on a straight line is 132°, the other angle is 180° – 132° = 48°.
如果直线上的一个角为 132°，则另一个角为 180° – 132° = 48°。
9. Perimeter, Area and Volume | 周长、面积与体积
Perimeter is the distance around a shape. Area of a rectangle is length × width. Volume of a cuboid is length × width × height. Always include the correct units: cm, cm² or cm³.
周长是围绕图形一周的长度。长方形面积 = 长 × 宽。长方体体积 = 长 × 宽 × 高。务必写明正确单位：cm、cm² 或 cm³。
Example: A rectangle has length 12 cm and width 5 cm. Perimeter = 2 × (12 + 5) = 2 × 17 = 34 cm. Area = 12 × 5 = 60 cm². A cuboid with length 4 cm, width 3 cm and height 2 cm has volume = 4 × 3 × 2 = 24 cm³.
例题：一个长方形的长为 12 cm、宽为 5 cm。周长 = 2 × (12 + 5) = 2 × 17 = 34 cm。面积 = 12 × 5 = 60 cm²。一个长方体长 4 cm、宽 3 cm、高 2 cm，体积 = 4 × 3 × 2 = 24 cm³。
10. Coordinates and Graphs | 坐标与图像
Coordinates are written in the form (x, y), where x is the horizontal position and y is the vertical position. For a linear graph, make a table of
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