📚 Year 7 Maths Topic Series 600: Essential Number Skills | 7年级数学主题系列600：核心数字技能
Welcome to Topic Series 600, a focused revision guide for Year 7 IGCSE Mathematics. This article builds strong foundations in number skills: place value, four operations, factors, primes, squares and roots, negative numbers, order of operations, fractions, decimals, percentages and word problems.
欢迎阅读主题系列600，这是一份针对7年级IGCSE数学的专题复习指南。本文帮助你夯实数字技能基础：位值、四则运算、因数、质数、平方与方根、负数、运算顺序、分数、小数、百分数以及应用题。
1. Place Value and Whole Numbers | 位值与整数
Every digit in a whole number has a place value: units, tens, hundreds, thousands, ten-thousands and so on. For example, in 5,638, the digit 5 stands for 5 thousands, 6 stands for 6 hundreds, 3 for 3 tens and 8 for 8 units.
每个整数中的数字都有位值：个位、十位、百位、千位、万位等。例如，在 5,638 中，数字 5 代表 5 个千，6 代表 6 个百，3 代表 3 个十，8 代表 8 个一。
0 + 8. Understanding place value helps with comparing, rounding and reading large numbers.
我们可以把一个数写成展开式：5,638 = 5,000 + 600 + 30 + 8。理解位值有助于比较、四舍五入和读出较大的数。
| Thousands 千位 | Hundreds 百位 | Tens 十位 | Units 个位 |
| 5 | 6 | 3 | 8 |
2. Addition and Subtraction | 加法与减法
Addition and subtraction are inverse operations. To add whole numbers, align digits by place value from the right, then carry extra tens, hundreds or thousands when a column total is 10 or more.
加法和减法互为逆运算。做整数加法时，从右向左按位值对齐，当某一列的和达到或超过 10 时，就要向前一位进位。
. Example: 703 − 258 = 445 because 3 cannot subtract 8, so we borrow from the tens column.
做减法时，也要对齐位数；当某一位数字不够减时，就从前一位借位。例如：703 − 258 = 445，因为 3 不够减 8，所以从十位借 1。
nswer by using the inverse operation: if 703 − 258 = 445, then 445 + 258 should equal 703.
做完后要用逆运算检验：如果 703 − 258 = 445，那么 445 + 258 应等于 703。
a + b = b + a but a − b ≠ b − a
3. Multiplication and Division | 乘法与除法
Multiplication is repeated addition, and division is repeated subtraction or splitting into equal groups. The product is the result of multiplying factors; the quotient is the result of dividing a dividend by a divisor.
乘法是重复加法，除法是重复减法或平均分组。因数相乘得到积；被除数除以除数得到商。
re key written methods. Example: 327 × 14 = 4,578. Division example: 378 ÷ 6 = 63 exactly.
列竖式乘法和长除法是重要的笔算方法。例如：327 × 14 = 4,578。除法例子：378 ÷ 6 = 63，正好整除。
Remainders can be written as whole numbers or fractions: 50 ÷ 8 = 6 remainder 2, or 6 ¼.
余数可以写成整数或分数：50 ÷ 8 = 6 余 2，或 6 ¼。
a × b = b × a but a ÷ b ≠ b ÷ a
4. Factors and Multiples | 因数与倍数
A factor of a whole number divides it exactly with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple is the product of a number and any whole number: the first five multiples of 7 are 7, 14, 21, 28 and 35.
如果一个整数能整除另一个整数且没有余数，那么这个整数就是它的因数。例如，12 的因数有 1、2、3、4、6 和 12。倍数是一个数与任意整数相乘的积：7 的前五个倍数是 7、14、21、28 和 35。
Common factors are factors shared by two or more numbers. The highest common factor (HCF) of 18 and 24 is 6. Common multiples include the lowest common multiple (LCM); the LCM of 4 and 6 is 12.
公因数是两个或多个数共有的因数。18 和 24 的最大公因数（HCF）是 6。公倍数中最小的称为最小公倍数（LCM）；4 和 6 的最小公倍数是 12。
HCF(18, 24) = 6 and LCM(4, 6) = 12
5. Prime Numbers and Prime Factorisation | 质数与质因数分解
A prime number has exactly two distinct factors: 1 and itself. The first prime numbers are 2, 3, 5, 7, 11, 13, 17 and 19. Note that 1 is not prime because it has only one factor.
质数只有两个不同的因数：1 和它本身。最小的几个质数是 2、3、5、7、11、13、17 和 19。注意：1 不是质数，因为它只有一个因数。
= 2² × 3 × 5. This is called prime factorisation and is usually found using a factor tree.
每个合数都可以写成质数的乘积。例如，60 = 2² × 3 × 5。这叫做质因数分解，通常用因数树来求。
Prime factorisation helps find HCF and LCM: write both numbers in prime factor form, then choose common factors for HCF and the highest powers for LCM.
质因数分解有助于求最大公因数和最小公倍数：先把两个数写成质因数形式，HCF 取共有的质因数，LCM 取所有质因数的最高次幂。
