📚 Essential Maths Book 7S Compact Core Skills for Year 7 | Year 7 数学核心技能精讲
The Essential Maths Book 7S offers a structured Year 7 course covering number, geometry, algebra and measures. This bilingual revision guide summarises the key skills you need to master, with clear examples for quick checking.
《Essential Maths Book 7S》提供系统的七年级数学课程，涵盖数、几何、代数和度量。本双语复习指南总结你需要掌握的核心技能，并配有清晰的示例供快速检查。
1. Place Value and the Decimal System | 数位与十进制
In Year 7, you must read, write and order whole numbers up to at least one million. Each digit has a place value: units, tens, hundreds, thousands, ten-thousands, hundred-thousands and millions.
在七年级，你需要读写并排序至少到一百万以内的整数。每个数字都有一个数位：个位、十位、百位、千位、万位、十万位和百万位。
For example, in 3 405 278, the digit 4 means four hundred thousand, and the digit 7 means seventy. Decimal places extend this idea to tenths, hundredths and thousandths after the decimal point.
例如，在 3 405 278 中，数字 4 表示四十万，数字 7 表示七十。小数点后的数位则把这一概念扩展到十分位、百分位和千分位。
2. Ordering and Rounding Integers | 整数排序与四舍五入
To order integers, compare digits from the left. For example, 56 293 is greater than 56 239 because 9 tens is greater than 3 tens.
比较整数时，从最左边的数字开始。例如，56 293 大于 56 239，因为 9 个十大于 3 个十。
When rounding to the nearest 10, 100 or 1000, look at the digit immediately to the right of the place you are rounding to. If that digit is 5 or more, round up; if it is 4 or less, round down.
四舍五入到最近的 10、100 或 1000 时，要看保留位右边的一位数字。如果该位是 5 或更大，就向上进位；如果是 4 或更小，就舍去。
Example: 4 672 rounded to the nearest 100 is 4 700, because the tens digit is 7.
示例：4 672 四舍五入到最近的 100 是 4 700，因为十位数字是 7。
3. Addition and Subtraction | 加法与减法
For column addition and subtraction, align digits by place value. Carry or exchange correctly when a column total exceeds 9 or when subtracting a larger digit from a smaller one.
列竖式加减法时，要将相同数位对齐。当某一列的和超过 9，或需要从较小数字中减去较大数字时，要正确进位或借位。
le, 6 498 + 2 305 is about 6 500 + 2 300 = 8 800, so the exact answer 8 803 is reasonable.
始终使用估算来检查答案。例如，6 498 + 2 305 大约是 6 500 + 2 300 = 8 800，因此精确答案 8 803 是合理的。
6 498 + 2 305 = 8 803
4. Multiplication and Division Methods | 乘法与除法
Strong times-table recall is essential for Year 7. Use short multiplication for a two- or three-digit number by one digit, and long multiplication for two multi-digit numbers.
熟练的乘法表记忆是七年级的基础。用短乘法计算两位数或三位数乘一位数，用长乘法计算两个多位数相乘。
For division, use short division for a single-digit divisor and long division for a two-digit divisor. Check a division by multiplying the quotient by the divisor and adding any remainder.
除法中，除数是一位数时用短除法，除数是两位数时用长除法。用商乘除数再加上余数来检验除法。
Example: 342 × 6 = 2 052 and 2 052 ÷ 6 = 342.
示例：342 × 6 = 2 052，并且 2 052 ÷ 6 = 342。
5. Factors, Multiples and Prime Numbers | 因数、倍数与质数
A factor divides exactly into a number. A multiple is the product of a number and any integer. A prime number has exactly two factors: 1 and itself.
因数能整除一个数。倍数是某个数与任意整数的乘积。质数只有两个因数：1 和它本身。
The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Note that 1 is not prime.
前十个质数是 2、3、5、7、11、13、17、19、23 和 29。注意 1 不是质数。
ctors, keep dividing by the smallest prime until you reach 1. For example, 12 = 2 × 2 × 3.
求质因数时，不断除以最小的质数，直到得到 1。例如，12 = 2 × 2 × 3。
6. Understanding Fractions | 分数的理解
A fraction is written as numerator over denominator. The denominator tells how many equal parts the whole is divided into; the numerator tells how many parts are taken.
分数写作分子在分母之上。分母表示整体被平均分成多少份；分子表示取了多少份。
Equivalent fractions have the same value but different numerators and denominators. To simplify a fraction, divide the numerator and denominator by their highest common factor.
等值分数数值相同，但分子和分母不同。化简分数时，用分子和分母的最大公因数同时除以它们。
Example: 12/18 = 2/3 because both 12 and 18 are divided by 6.
示例：12/18 = 2/3，因为 12 和 18 都除以 6。
7. Decimals and Conversion | 小数与转换
Decimals are another way to write fractions with denominators 10, 100, 1000 and so on. The first decimal place is tenths, the second is hundredths, and the third is thousandths.
小数是表示分母为 10、100、1000 等的分数的另一种方式。小数点后第一位是十分位，第二位是百分位，第三位是千分位。
a fraction to a decimal, divide the numerator by the denominator. For example, 3/4 = 0.75.
将分数转换为小数，用分子除以分母。例如，3/4 = 0.75。
When rounding decimals, look at the digit after the required place. For example, 2.386 rounded to two decimal places is 2.39.
小数四舍五入时，看保留位后一位。例如，2.386 保留两位小数是 2.39。
8. Percentages | 百分数
A percentage means 'out of 100'. To convert a percentage to a fraction, write it over 100 and simplify. To convert to a decimal, divide by 100.
百分数表示“每 100 份中的多少份”。将百分数转换为分数，把它写在 100 之上并化简；转换为小数时除以 100。
Common conversions to remember: 50% = 1/2 = 0.5, 25% = 1/4 = 0.25,
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