📚 Essential Maths 7S Homework Book: Core Skills for Year 7 | Essential Maths 7S 作业册：七年级核心技能
The Year 7 Essential Maths 7S Homework Book covers the key number, algebra, geometry and data topics that form the foundation of lower secondary mathematics. This bilingual revision guide summarises the most important skills you need to practise, with clear examples and English-Chinese explanations.
七年级 Essential Maths 7S 作业册涵盖了数字、代数、几何和数据等核心主题，它们是初中数学的基础。这篇双语复习指南总结了需要重点练习的技能，并配有清晰的示例和中英文讲解。
1. Place Value and Ordering Integers | 位值与整数排序
In Year 7 you must read, write and order whole numbers up to at least one million. Place value tells us the value of each digit. For example, in 4,306, the digit 4 stands for 4 thousands, 3 stands for 3 hundreds, 0 tens and 6 ones.
七年级需要能读写并排序至少到一百万的整数。位值表示每个数字的值。例如在 4,306 中，数字 4 表示 4 个千，3 表示 3 个百，0 个十，6 个一。
To order integers, compare digits from the left. The symbols < and > mean ‘is less than’ and ‘is greater than’. For example, 5,230 < 5,320 because 2 hundreds < 3 hundreds.
排序整数时从左到右逐位比较。符号 < 和 > 表示 ‘小于’ 和 ‘大于’。例如 5,230 < 5,320，因为 2 个百小于 3 个百。
2. Decimals and Rounding | 小数与四舍五入
Decimals extend place value into tenths, hundredths and thousandths. To add or subtract decimals, align the decimal points and fill empty places with zeros. For example, 3.4 + 0.25 = 3.65.
小数将位值扩展到十分位、百分位和千分位。加减小数时对齐小数点，空位补零。例如 3.4 + 0.25 = 3.65。
Rounding to one decimal place or two decimal places follows the same rule: look at the next digit. If it is 5 or more, round up; if it is less than 5, round down. So 7.846 rounded to 2 d.p. is 7.85.
四舍五入到一位或两位小数遵循相同规则：看下一位数字。如果大于或等于 5，则进位；如果小于 5，则舍去。所以 7.846 保留两位小数为 7.85。
3. Fractions, Equivalence and Simplifying | 分数、等价与约分
A fraction represents part of a whole. Equivalent fractions have the same value, such as 1/2, 2/4 and 3/6. To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF).
分数表示整体的一部分。等价分数具有相同的值，例如 1/2、2/4 和 3/6。约分时，用分子和分母的最大公因数（HCF）同时相除。
For example, 18/24 simplifies to 3/4 because the HCF of 18 and 24 is 6. Mixed numbers like 2 1/3 combine a whole number and a proper fraction.
例如 18/24 约分后为 3/4，因为 18 和 24 的最大公因数是 6。带分数如 2 1/3 结合了整数和真分数。
4. Percentage Conversions | 百分比转换
Percentage means ‘out of 100’. To convert a fraction to a percentage, find an equivalent fraction with denominator 100, or multiply by 100%. For example, 3/5 = 60/100 = 60%.
百分比表示 ‘每一百份’。将分数转换为百分数，可以找到分母为 100 的等价分数，或乘以 100%。例如 3/5 = 60/100 = 60%。
To convert a decimal to a percentage, multiply by 100. So 0.47 = 47%, and 1.25 = 125%. To convert a percentage to a decimal, divide by 100.
将小数转换为百分数时乘以 100。因此 0.47 = 47%，1.25 = 125%。将百分数转换为小数时除以 100。
5. Negative Numbers and the Number Line | 负数与数轴
Negative numbers are less than zero and are written with a minus sign. On a number line, numbers increase to the right and decrease to the left. For example, -7 is less than -3 because -7 lies further left.
负数小于零，书写时带负号。在数轴上，数字向右增大，向左减小。例如 -7 小于 -3，因为 -7 更靠左。
When adding or subtracting negative numbers, use rules such as a – (-b) = a + b. For example, 5 – (-2) = 5 + 2 = 7, and -3 + 5 = 2.
加减负数时使用规则，例如 a – (-b) = a + b。例如 5 – (-2) = 5 + 2 = 7，而 -3 + 5 = 2。
Multiplying or dividing two negative numbers gives a positive answer; multiplying or dividing a positive and a negative gives a negative answer. For example, -4 × -6 = 24, but -4 × 6 = -24.
两个负数相乘或相除得正数；一个正数与一个负数相乘或相除得负数。例如 -4 × -6 = 24，但 -4 × 6 = -24。
6. Algebraic Expressions and Simplifying | 代数表达式与化简
In algebra, letters stand for unknown numbers. A term is a number, a letter or a product such as 3a or 5xy. Like terms have the same letter parts, so 2a and 5a can be added to give 7a.
代数中，字母代表未知数。项是数字、字母或乘积，如 3a 或 5xy。同类项具有相同的字母部分，因此 2a 和 5a 可以相加得到 7a。
To simplify an expression, collect like terms. For example, 4x + 3y – 2x + y = 2x + 4y. You can also expand a bracket using the distributive law: 3(x + 5) = 3x + 15.
化简表达式时要合并同类项。例如 4x + 3y – 2x + y = 2x + 4y。还可以使用分配律展开括号：3(x + 5) = 3x + 15。
7. Solving Simple Equations | 解一元一次方程
An equation shows that two expressions are equal. To solve an equation, find the value of the unknown letter. Use inverse operations to keep the equation balanced.
方程表示两个表达式相等。解方程就是求出未知字母的值。使用逆运算保持等式平衡。
For example, x + 7 = 12, so x = 12 – 7 = 5. For 3x = 18, divide both sides by 3 to get x = 6. Always check by substituting the answer back into the original equation.
例如 x + 7 = 12，所以 x = 12 – 7 = 5。对于 3x = 18，两边同时除以 3 得 x = 6。始终通过将答案代回原方程进行检验。
8. Angles and Triangles | 角度与三角形
Angles are measured in degrees (°). Angles on a straight line add up to 180°, and angles around a point add up to 360°. Vertically opposite angles are equal when two lines cross.
角度以度（°）为单位。直线上相邻角之和为 180°，围绕一个点的角度之和为 360°。两条直线相交时对顶角相等。
In a triangle, the interior angles always add up to 180°. An equilateral triangle has three 60° angles, while an isosceles triangle has two equal angles.
三角形内角和始终为 180°。等边三角形有 3 个 60° 角，等腰三角形有两个相等的角。
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