Introduction to Subtraction
Subtraction is the operation of finding how much remains when one quantity is taken from another. It is the inverse of addition.
Three Meanings of Subtraction
| Situation | What it means | Example |
|---|---|---|
| Take away | Remove an amount from a total | 12 − 5 = 7 |
| Find the difference | How far apart are two numbers? | 12 − 5 = 7 |
| Find the missing part | Total and one part known | 12 − ? = 5, so ? = 7 |
Key Properties
- Subtraction is not commutative: 8 − 3 ≠ 3 − 8.
- Subtracting zero gives the original: 7 − 0 = 7.
- Subtracting a number from itself gives zero: 9 − 9 = 0.
Checking with Addition
The inverse of subtraction is addition. Always verify: difference + subtrahend = minuend.
15 − 6 = 9 → check: 9 + 6 = 15 ✓
Worked Examples
Easy
9 − 4 = 5. Check: 5 + 4 = 9 ✓
Medium
73 − 28 = 45. Check: 45 + 28 = 73 ✓
Advanced
1000 − 347 = 653. Check: 653 + 347 = 1000 ✓
Real-Life Applications
- Calculating change from a purchase.
- Finding how many days remain until an event.
- Calculating profit (revenue − cost).
Key Takeaways
- Subtraction finds what remains, the difference, or the missing part.
- It is not commutative — order matters.
- Always check with addition: difference + subtrahend = minuend.
Practice Questions
- Calculate 17 − 9 and check using addition.
- Find the difference between 45 and 28.
- A bag has 24 sweets; 9 are eaten. How many remain?
- What is 100 − 37?
- Complete: 56 − ? = 31.