Addition and Subtraction
1. Addition of 3-Digit Numbers
Steps:
- Write numbers in COLUMNS — ones under ones, tens under tens, hundreds under hundreds.
- Start from the ONES place.
- CARRY if the sum is 10 or more.
Example 1:
Add 345 + 234
| H | T | O |
|---|---|---|
| 3 | 4 | 5 |
| +2 | +3 | +4 |
| 5 | 7 | 9 |
Answer: 579
Example 2 (with carry):
Add 456 + 378
| H | T | O |
|---|---|---|
| 4 | 5 | 6 |
| +3 | +7 | +8 |
| 1 | ||
| 8 | 3 | 4 |
Step 1: 6 + 8 = 14 → write 4, carry 1 Step 2: 5 + 7 + 1 = 13 → write 3, carry 1 Step 3: 4 + 3 + 1 = 8
Answer: 834
2. Addition of 4-Digit Numbers
Example:
Add 2,345 + 3,678
| Th | H | T | O |
|---|---|---|---|
| 2 | 3 | 4 | 5 |
| +3 | +6 | +7 | +8 |
| 1 | 1 | 1 | |
| 6 | 0 | 2 | 3 |
Answer: 6,023
3. Properties of Addition
| Property | Meaning | Example |
|---|---|---|
| Commutative | Order does NOT matter | 15 + 25 = 25 + 15 |
| Associative | Grouping does NOT matter | (10+20)+30 = 10+(20+30) |
| Identity | Adding 0 gives same number | 345 + 0 = 345 |
4. Subtraction of 3-Digit Numbers
Steps:
- Write numbers in COLUMNS — larger number on top.
- Start from the ONES place.
- BORROW if the top digit is smaller than the bottom digit.
Example 1:
Subtract 345 - 123
| H | T | O |
|---|---|---|
| 3 | 4 | 5 |
| -1 | -2 | -3 |
| 2 | 2 | 2 |
Answer: 222
Example 2 (with borrowing):
Subtract 423 - 256
| H | T | O |
|---|---|---|
| 3→2 | 12→11 | 13 |
| 4 | 2 | 3 |
| -2 | -5 | -6 |
| 1 | 6 | 7 |
Step 1: 3 - 6 → borrow 1 from tens. 13 - 6 = 7 Step 2: 1 (was 2, now 1) - 5 → borrow 1 from hundreds. 11 - 5 = 6 Step 3: 3 (was 4, now 3) - 2 = 1
Answer: 167
5. Subtraction of 4-Digit Numbers
Example:
Subtract 5,432 - 2,678
| Th | H | T | O |
|---|---|---|---|
| 4 | 12 | 3 | 12 |
| 5 | 4 | 3 | 2 |
| -2 | -6 | -7 | -8 |
| 2 | 7 | 5 | 4 |
Answer: 2,754
6. Mental Math
Adding 10, 100, or 1000:
- 345 + 10 = 355 (increase tens by 1)
- 345 + 100 = 445 (increase hundreds by 1)
- 345 + 1000 = 1,345 (increase thousands by 1)
Adding 9:
- 45 + 9 = 45 + 10 - 1 = 54
- 167 + 9 = 167 + 10 - 1 = 176
Doubles:
- 25 + 25 = 50
- 125 + 125 = 250
7. Word Problems
Problem 1:
Ria has 345 stickers. Her friend gives her 234 more. How many stickers does Ria have now?
Solution: 345 + 234 = 579 stickers
Problem 2:
A school library has 567 story books and 345 science books. How many total books?
Solution: 567 + 345 = 912 books
Problem 3:
Sam has 834 marbles. He gives 256 marbles to his brother. How many marbles does Sam have left?
Solution: 834 - 256 = 578 marbles
Problem 4:
A shop had 1,500 eggs. It sold 875 eggs. How many eggs are left?
Solution: 1,500 - 875 = 625 eggs
8. Common Mistakes
- Not aligning by place value: 'Always write ones under ones, tens under tens. Misalignment causes wrong answers!'
- Forgetting to carry: 'If 7 + 5 = 12, write 2 and carry 1 to the next column. If you forget the carry, your answer will be wrong.'
- Borrowing incorrectly: 'When you borrow, the digit you borrow from decreases by 1. The digit you borrow for increases by 10.'
- Subtracting smaller from larger in the wrong order: 'Always put the LARGER number on top. 567 - 234, NOT 234 - 567.'
9. Key Facts to Remember
- 'Add from the ONES place — always!'
- 'Carry when the sum is 10 or more.'
- 'Borrow when the top digit is smaller than the bottom digit.'
- 'Addition and subtraction are OPPOSITES. Use one to check the other.'
- 'Zero added to any number = the same number.'
10. Self-Test
Q1: Add: 456 + 378
Q2: Add: 2,345 + 1,678
Q3: Subtract: 723 - 456
Q4: Subtract: 3,456 - 1,789
Q5: Riya has 678 beads. She buys 234 more. How many does she have now?
Q6: There are 1,200 seats in a theatre. If 876 are filled, how many are empty?
Q7: Solve mentally: 567 + 100 = ?
Q8: Check: 567 - 234 = 333. Is this correct? Use addition to verify.
Answers:
A1: 834 A2: 4,023 A3: 267 A4: 1,667 A5: 678 + 234 = 912 beads A6: 1,200 - 876 = 324 seats A7: 667 A8: Check: 333 + 234 = 567. YES, it is correct.
