Addition & Subtraction – IB / IGCSE Mathematics
(Core skills for every level – from whole numbers to fractions and decimals)
1. Simple Explanation
- Addition = joining two or more numbers to get a total.
- Subtraction = removing one number from another to find the remainder.
Both operations are commutative only for addition (a + b = b + a) but not for subtraction (a − b ≠ b − a).
2. Key Points
| Concept | What to remember | Quick tip |
|---|---|---|
| Aligning columns | Write numbers in vertical format, aligning units, tens, hundreds, decimal places, etc. | “Place all the same‑place digits under each other.” |
| Carrying (addition) | When a column sums to ≥10, write the unit digit below the line and carry the tens to the next column. | “Carry the 'extra' ten(s) to the left.” |
| Borrowing (subtraction) | When a column needs a smaller digit, borrow 1 from the next left column (i.e., 10). | “Borrow 1 ten → subtract 10 from the left column, add 10 to the current.” |
| Subtracting a larger from a smaller | Result is negative; write a minus sign or use the “opposite” rule: a − b = a + (−b). | “If you’re unsure, think of adding the negative instead.” |
| Decimal addition/subtraction | Align decimal points; treat zeros after the decimal as significant. | “Think of decimals as whole numbers and then place the decimal.” |
| Fraction addition/subtraction | Find a common denominator; then add/subtract numerators. | “Make the bottom the same, then add the tops.” |
| Mixed numbers | Convert to improper fractions first, then add/subtract. | “Turn 2 ¾ into 11/4 before adding.” |
| Using a number line | Good for mental addition/subtraction, especially with negative numbers. | “Move right for +, left for –.” |
| Checking work | Re‑add/subtract in reverse or use the “double-check” trick: add the two numbers, then subtract one from the sum. | “If you get the other number, you’re correct.” |
3. Worked Examples
3.1 Whole‑Number Addition
Problem: 3 576 + 2 489
| 3 576 | + | 2 489 | = | |
|---|---|---|---|---|
| Units | 6 | + | 9 | = 15 → write 5, carry 1 |
| Tens | 7 | + | 8 | + 1 (carry) = 16 → write 6, carry 1 |
| Hundreds | 5 | + | 4 | + 1 (carry) = 10 → write 0, carry 1 |
| Thousands | 3 | + | 2 | + 1 (carry) = 6 |
Answer: 6 065
3.2 Whole‑Number Subtraction
Problem: 5 842 − 3 619
| 5 842 | − | 3 619 | = | |
|---|---|---|---|---|
| Units | 2 | − | 9 | – need to borrow 1 from tens |
| Borrow | 5 842 → 5 832, tens become 3 | |||
| Units | 12 | − | 9 | = 3 |
| Tens | 3 | − | 1 | = 2 |
| Hundreds | 8 | − | 6 | = 2 |
| Thousands | 5 | − | 3 | = 2 |
Answer: 2 223
3.3 Decimal Addition
Problem: 12.75 + 3.6
Align decimals:
| 12.75 | + | 3.60 | = | |
|---|---|---|---|---|
| Hundredths | 5 | + | 0 | = 5 |
| Tenths | 7 | + | 6 | = 13 → write 3, carry 1 |
| Units | 2 | + | 3 | + 1 (carry) = 6 |
| Tens | 1 | + | 0 | = 1 |
Answer: 16.35
3.4 Decimal Subtraction
Problem: 10.50 − 4.2
| 10.50 | − | 4.20 | = | |
|---|---|---|---|---|
| Hundredths | 0 | − | 0 | = 0 |
| Tenths | 5 | − | 2 | = 3 |
| Units | 0 | − | 4 | borrow 1 from tens: 10 − 4 = 6 |
| Tens | 0 (after borrowing) | − | 0 | = |