4-digit addition & subtraction

1Summary 重點摘要

Align ones, work right to left.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Align before you calculateWhen writing a vertical sum, line the digits up first: ones under ones, tens under tens. For 1234 + 567, the 567 has only three digits, so its 7 sits under the 4 of 1234, and the tens and hundreds line up after it. Misaligned columns give wrong answers. Cover the other columns with a sheet of paper and focus on one place at a time. Another example: 405 + 396 — ones under ones (5 under 6), tens under tens (0 under 9), hundreds under hundreds (4 under 3); start calculating only after everything is lined up.
2. Part 2: Add from the onesAdd from the ones, and carry 1 to the left whenever a column makes ten or more. For 1234 + 567: 4+7=11, write 1 and carry 1; 3+6+1=10, write 0 and carry 1; 2+5+1=8; then write the 1 in the thousands. The answer is 1801. Another example: 405 + 396 — ones: 5+6=11, write 1 and carry 1; tens: 0+9+1=10, write 0 and carry 1; hundreds: 4+3+1=8, so the answer is 801. Write the little carried 1 beside the column so it is never forgotten.
3. Part 3: Borrow when you cannot subtractSubtract from the ones too. When a digit is too small, borrow 1 from the next place, which is worth 10. In 3000 − 1234, the ones cannot do 0−4, and the tens and hundreds are 0, so borrow all the way from the thousands. Then 10−4=6, 9−3=6, 9−2=7, 2−1=1. The answer is 1766. The rule is 'borrow 1, worth 10'; keep borrowing from the left until the column is large enough, and cross out and rewrite the changed digits — the column form must stay perfectly clear.
4. Part 4: See borrowing in column formWrite 3000 − 1234 in columns. After borrowing, update every digit: the thousands 3 becomes 2, the hundreds and tens become 9, and the ones become 10, then subtract place by place:
   
   　　3000
   
   － 1234
   
   ─────
   
   　　1766
   Each place lends out at most 1; in a number like 3000 with zeros in the middle, turn each 0 into 9 until the ones place becomes 10 before subtracting — the step that tests care the most.
5. Part 5: Check with the inverse operationAfter calculating, check with the inverse operation. For 1234 + 567 = 1801, work out 1801 − 567; if the answer is 1234, the sum is correct. For subtraction, add back: 1766 + 1234 = 3000, which matches the starting number, so it is correct. The principle is that addition and subtraction are inverse operations: the sum minus one addend should give the other addend, and the difference plus the subtrahend should give the minuend. Check every question and most slips in four-digit work are caught at once.
6. Part 6: Two-step word problemsIn word problems, decide what to work out first and what comes next. A school library has 2350 books, buys 480 more, then discards 120 old ones. Step 1: 2350 + 480 = 2830, the total after buying. Step 2: 2830 − 120 = 2710, so 2710 books are left. Decide add or subtract before writing: 'buys more' means adding, while 'discards' means subtracting; the answer should reply to the question in words, and 'the library now has 2710 books' makes it complete.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Column method step one: line up the ones
• Add from the ones and carry when a place reaches 10
• In subtraction, borrow from the next place when needed
• A place that lends 1 drops by 1; the borrower gains 10
• Check with the inverse operation to catch mistakes