Addition & Subtraction – Quick & Easy Study Notes
(Ideal for IB/IGCSE Mathematics beginners)
1. What We’re Doing
- Addition: Putting numbers together.
- Subtraction: Taking one number away from another.
Think of it like a shopping list.
- Adding: “I have 2 apples and I buy 3 more → 5 apples.”
- Subtracting: “I had 5 apples and I eat 2 → 3 apples left.”
2. Basic Rules (no jargon)
| Operation | What to do | Example |
|---|---|---|
| Add | Write numbers one below the other, align the digits (ones under ones, tens under tens). Start adding from the rightmost column. | 23 + 17 |
| Subtract | Same alignment. Start subtracting from the rightmost column. If the top digit is smaller, borrow 10 from the next column. | 54 – 29 |
3. Step‑by‑Step
Adding Two Numbers
- Line up the numbers.
- Add the rightmost column (ones).
- If the sum is 10 or more, write the right‑hand digit and keep the carry (the extra 1) for the next column.
- Move left: add the next column + any carry.
- Write the final number.
Tiny example
23
+ 17
-----
40 ← 3+7 = 10 → write 0, carry 1
4+1+1 = 6 (carry 1 from the tens column)
Result: 40.
Subtracting Two Numbers
- Line up the numbers.
- Start from the rightmost column.
- If the top digit is smaller, borrow 10 from the next column (decrease that column by 1).
- Subtract the lower digit from the top digit (after borrowing if needed).
- Move left until all columns are done.
Tiny example
54
- 29
-----
25 ← 4-9 → borrow 10 → 14-9 = 5; 5-2 = 3
Result: 25.
4. Quick Tips
| Tip | Why it helps |
|---|---|
| Use a pencil for checking | You can easily correct mistakes. |
| Do the carry or borrow first | Reduces confusion later. |
| Practice with real life | Try adding the cost of snacks or subtracting items you buy. |
| Write digits clearly | Keeps columns straight and readable. |
5. Common Mistakes to Avoid
- Misaligning digits – always line up ones, tens, hundreds, etc.
- Skipping a carry/borrow – double‑check each column.
- Mixing up addition and subtraction – remember: add means “bring together”, subtract means “take away”.
6. Quick Practice Problems
| Problem | Quick Check |
|---|---|
| 14 + 28 | 42 |
| 73 – 19 | 54 |
| 5 + 8 | 13 |
| 60 – 37 | 23 |
Try solving them on paper first, then check with these answers.
7. Final Thought
Addition and subtraction are like simple conversations between numbers.
- Addition: “Let’s make a bigger number together.”
- Subtraction: “Let’s share it and see what’s left.”
With a little practice, you’ll get the hang of it quickly!