📚 Essential Maths Book 7C: Year 7 Mastery Guide | 核心数学 7C 七年级精通指南
Essential Maths Book 7C covers the core skills that Year 7 students need to secure before moving into Key Stage 3 extension work. This guide rehearses the main topics, from number operations to early algebra and geometry, with clear examples and paired explanations.
《核心数学 7C》涵盖了七年级学生在进入第三学段拓展学习之前必须掌握的核心技能。本指南复练主要专题，从数的运算到初步代数和几何，配有清晰的例子和中英对照讲解。
1. Place Value and Decimals | 位值与小数
Place value is the value given to a digit based on its position in a number. In a decimal number such as 347.528, the digit 3 means 300, the digit 4 means 40, and the digit 7 means 7 units. The digits after the point are tenths, hundredths and thousandths.
位值是根据数字在数中的位置赋予它的值。在像 347.528 这样的小数中，数字 3 表示 300，数字 4 表示 40，数字 7 表示 7 个一。小数点后的数字分别表示十分位、百分位和千分位。
by 10 moves every digit one place to the right. This means 0.6 × 10 = 6 and 45 ÷ 10 = 4.5.
乘以 10 时每一位数字向左移动一位，除以 10 时每一位数字向右移动一位。因此 0.6 × 10 = 6，45 ÷ 10 = 4.5。
To compare decimals, look at the place value columns from left to right. For example, 0.56 is greater than 0.529 because the hundredths digit 6 is greater than 2.
比较小数时，从左到右依次看位值列。例如 0.56 大于 0.529，因为百分位上的 6 大于 2。
347.528 = 300 + 40 + 7 + 0.5 + 0.02 + 0.008
2. Fractions, Decimals and Equivalence | 分数、小数与等值
A fraction such as ¾ can also be written as the decimal 0.75. The top number is the numerator and the bottom number is the denominator. The denominator tells how many equal parts the whole is divided into.
分数如 ¾ 也可以写成小数 0.75。上面的数是分子，下面的数是分母。分母表示整体被分成多少等份。
ace value digits as the numerator and simplify if possible. For example, 0.6 = 6/10 = 3/5.
要将分数转换为小数，用分子除以分母。要将小数转换为分数，把位值数字写成分子，并尽可能化简。例如 0.6 = 6/10 = 3/5。
nator by the same non-zero number to find equivalent forms. For example, 2/3 = 4/6 = 8/12.
等值分数具有相同的值。你可以将分子和分母同时乘以或除以同一个非零数来得到等值形式。例如 2/3 = 4/6 = 8/12。
¾ = 0.75 = 75%
3. Percentages of Amounts | 求一个数的百分比
A percentage is a number out of 100. The symbol % means 'out of 100'. To find a percentage of an amount, first find 1% by dividing by 100, then multiply by the percentage needed.
百分数表示每一百份中的多少份。符号 % 表示“每一百份中”。要求一个数的百分比，先除以 100 得到 1%，再乘以所需的百分数。
For example, to find 15% of 60, find 1% 60 (0.6) and multiply by 15 to get 9. Alternatively, write the percentage as a decimal: 15% = 0.15, so 0.15 × 60 = 9.
例如，要求 60 的 15%，先求 60 的 1%（即 0.6），再乘以 15 得到 9。也可以把百分数写成小数：15% = 0.15，因此 0.15 × 60 = 9。
alculate the percentage part and then add or subtract it. For example, increasing 80 by 10% gives 80 + 8 = 88.
要按百分数增加或减少一个量，先算出百分数对应的部分，然后加上或减去它。例如，把 80 增加 10% 得到 80 + 8 = 88。
15% of 60 = 0.15 × 60 = 9
4. Algebraic Notation and Substitution | 代数记号与代入
e 3 × a as 3a, and a × a as a². The number in front of a letter is called the coefficient.
在代数中，字母代表未知或变化的数。我们把 3 × a 写成 3a，把 a × a 写成 a²。字母前面的数称为系数。
× 2 = 16. Always follow the order of operations: work out multiplication before addition.
代入是指用数字替换字母。如果 a = 4，b = 2，那么 3a + 2b = 3 × 4 + 2 × 2 = 16。始终遵循运算顺序：先算乘除后算加减。
ou can simplify expressions by collecting like terms. For example, 5x + 3y − 2x = 3x + 3y.
同类项含有完全相同的字母和幂。你可以通过合并同类项来化简式子。例如 5x + 3y − 2x = 3x + 3y。
3a + 2b = 3 × 4 + 2 × 2 = 16
5. Solving Equations | 解方程
An equation is a statement that two expressions are equal. To solve an equation, keep it balanced by doing the same operation to both sides. The solution is the value of the unknown that makes the equation true.
方程是表示两个式子相等的语句。解方程时，要对两边做相同的运算，保持方程平衡。方程的解是使方程成立的未知数的值。
by 4: x = 5. Always check your answer by substituting it back into the original equation.
对于 x + 3 =
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