📚 Adding and Subtracting Whole Numbers in IGCSE Maths | IGCSE 数学中的整数加减法
Whole number addition and subtraction are the first numerical skills you meet, but they appear again and again in IGCSE questions involving algebra, geometry, statistics, and everyday money or measurement problems. A small carrying or borrowing error can cost several marks, so this article reviews column methods, inverse checks, estimation, directed numbers, and word-problem strategies.
整数加减法是你最早接触的运算技能，但在 IGCSE 题目中它们反复出现于代数、几何、统计以及日常的金钱或测量问题。一个小的进位或借位错误可能丢掉好几分，因此本文复习竖式方法、逆运算检查、估算、有向数以及应用题策略。
1. Why Whole Number Operations Matter | 为什么整数运算很重要
Addition and subtraction are not only tested directly; they are embedded in solving equations, simplifying expressions, finding averages, and calculating perimeter or change. If your written arithmetic is accurate and fast, you can focus on higher-level reasoning instead of losing marks on basic steps.
加减法不仅会被直接考查，还贯穿于解方程、化简表达式、求平均数以及计算周长或找零之中。如果你的笔算准确且快速，你就能专注于更高层次的推理，而不会在基本步骤上丢分。
In IGCSE Core papers, you are expected to add and subtract whole numbers up to at least four digits, including borrowing across zeros. In Extended papers the same skills are applied to more complex problems, so fluency here is essential.
在 IGCSE 核心试卷中，你应当能够对至少四位数的整数进行加减，包括跨零借位。在扩展试卷中，同样的技能会应用于更复杂的问题，因此熟练掌握这部分内容至关重要。
2. Place Value and Column Addition | 位值与竖式加法
Before you add, write each digit in the correct place-value column: ones, tens, hundreds, and thousands. Align the numbers to the right so that ones sit above ones, tens above tens, and so on. For example, 2456 + 378 should be aligned as 2456 and 0378, not 2456 and 3780.
在相加之前，要将每个数字写在正确的位值列中：个位、十位、百位和千位。将数字右对齐，使个位对个位、十位对十位。例如，2456 + 378 应对齐为 2456 和 0378，而不是错位成 3780。
| Number | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|
| 2456 | 2 | 4 | 5 | 6 |
| 0378 | 0 | 3 | 7 | 8 |
Then add the tens: 5 + 7 + 1 = 13, write 3 and carry 1. Continue this process to the left.
现在从右向左相加。在个位列中，6 + 8 = 14，因此写 4 并向十位列进 1。然后加十位：5 + 7 + 1 = 13，写 3 并进 1。继续向左执行这一过程。
2456 + 378 = 2834
3. Column Subtraction and Regrouping | 竖式减法与借位
Column subtraction becomes tricky when the top digit is smaller than the bottom digit. You then need to regroup, or borrow, from the next column to the left. If that column is zero, you must continue moving left until you find a non-zero digit.
当上方的数字小于下方的数字时，竖式减法就会变得棘手。这时你需要从左边相邻列重组，也就是借位。如果那一列是零，则必须继续向左移动，直到找到非零数字。
Consider 7305 - 367. In the ones column, 5 - 7 is not possible, so borrow from the tens column. The tens digit is 0, so borrow from hundreds. The hundreds digit is 3, so it becomes 2, the tens 0 becomes 10, then the tens lends to ones: tens becomes 9 and ones becomes 15. Now subtract each column.
以 7305 - 367 为例。个位列中 5 - 7 不够减，因此从十位列借位。十位数字是 0，所以从百位借。百位数字是 3，它变成 2；十位 0 变成 10；然后十位再借给个位：十位变成 9，个位变成 15。现在逐列相减。
7305 - 367 = 6938
A fast check is to add the answer to the subtracted number: 6938 + 367 should return 7305. This catches most borrowing mistakes.
快速检查的方法是把答案与被减数相加：6938 + 367 应等于 7305。这能发现大多数借位错误。
4. Inverse Operations and Checking | 逆运算与验算
lationship is useful both for checking your arithmetic and for solving missing-number problems.
加法和减法互为逆运算。如果 243 + 189 = 432，那么 432 - 189 = 243，且 432 - 243 = 189。这种逆关系对于检查算术和解决缺失数字问题都很有用。
1346 + 654. You should get 2000. This habit can turn a certain mistake into a correct answer before you move on.
在考试中，完成竖式减法后，可以进行快速的心算或笔算加法检查。例如，算出 2000 - 654 = 1346 后，再计算 1346 + 654，应得到 2000。这个习惯可以在你继续下一题之前把已经犯下的错误改正过来。
5. Mental Strategies and Estimation | 心算策略与估算
o 500 + 300 = 800. The exact sum is 783, which is close to 800, so the answer is sensible.
估算有助于判断精确答案是否合理。在进行心算之前，先将数字四舍五入到最近的百位或十位。对于 487 + 296，可近似为 500 + 300 = 800。精确和是 783，与 800 接近，因此答案合理。
0, then 300 + 44 = 344. This strategy, often called compensation, reduces carrying errors.
有用的心算策略包括拆分数字、调整和使用数轴。对于 298 + 46，可以先算 298 + 2 = 300，再算 300 + 44 = 344。这种策略通常称为补偿策略，能减少进位错误。
- Partition: 345 + 230 = 300 + 200 + 40 + 5 + 30 = 500 + 70 + 5 = 575
- Compensate: 999 + 47 = 1000 + 47 - 1 = 1046
- Number line: count up from 58 to 100 in steps: +2, +40, +23
In IGCSE, you may not receive full marks if you only give an unreasonable exact answer with no working. Estimation shows whether you have misread a digit or misplaced a column.
在 IGCSE 中，如果你只给出一个明显不合理的精确答案而没有过程，通常不能得满分。估算可以显示你是否看错了数字或弄错了数位。
6. Directed Numbers on a Number Line | 数轴上的有向数
IGCSE questions often combine whole number operations with negative numbers. Think of addition as moving right on a number line and subtraction as moving left. Adding a negative number moves left, while subtracting a negative number moves right.
IGCSE 题目经常将整数运算与负数结合在一起。可以把加法看作在数轴上向右移动，把减法看作向左移动。加一个负数向左移动，减一个负数向右移动。
−5 + 3 = −2
Start at −5, move 3 places right, and you reach −2. For subtraction,
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