Integer multiplication and division rules
Key Notes:
| 🔍 What Are Integers? |
- Integers are positive numbers, negative numbers, and zero.
Examples: … –3, –2, –1, 0, +1, +2, +3 …
| ✖️ ➗ Rules for Multiplying and Dividing Integers |
✅ Sign Rules for Both Multiplication and Division
| Case | Rule | Example | Result |
|---|---|---|---|
| 👍 Positive × Positive | Result is Positive | (+3) × (+4) | +12 |
| 👎 Negative × Negative | Result is Positive | (–5) × (–6) | +30 |
| 👍👎 Positive × Negative | Result is Negative | (+7) × (–2) | –14 |
| 👎👍 Negative × Positive | Result is Negative | (–8) × (+3) | –24 |
📌 Same Signs = Positive
📌 Different Signs = Negative
| 🧠 Important Points to Remember |
- ✅ Zero times any number is 0
- Example: 0 × (–6) = 0
- ✅ You can multiply or divide in any order (for two numbers)
- Example: (–4) × (+5) = (+5) × (–4) = –20
- ❌ Division by zero is not allowed
- Example: 5 ÷ 0 → undefined
| ✍️ Examples: Multiplication |
- (–3) × (–2) = +6
- (+4) × (–6) = –24
- (–9) × (+5) = –45
- (+7) × (+8) = +56
- (–10) × (0) = 0
| ✍️ Examples: Division |
- (–12) ÷ (–3) = +4
- (+30) ÷ (–5) = –6
- (–24) ÷ (+4) = –6
- (+16) ÷ (+2) = +8
- 0 ÷ (–8) = 0
| 📝 Practice Questions: |
Fill in the blanks:
- (–7) × (–5) = _____
- (+48) ÷ (–6) = _____
- (–9) × (+3) = _____
- (+56) ÷ (+7) = _____
- (–36) ÷ (–6) = _____
- (–8) × (0) = _____
| ✅ Answers: |
- +35
- –8
- –27
- +8
- +6
- 0
| 🎯 Quick Revision Tip: |
| Operation | Same Sign | Different Sign |
|---|---|---|
| Multiply | Positive | Negative |
| Divide | Positive | Negative |
| positive × positive = positive | 2 x 2 = 4 |
| negative × negative = positive | -3 x -2 = 6 |
| positive × negative = negative | 5 x -3 = -15 |
| negative × positive = negative | -2 x 4 = -8 |
| positive ÷ positive = positive | 2 ÷ 2 = 1 |
| negative ÷ negative = positive | -6 ÷ -2 = 3 |
| positive ÷ negative = negative | 15 ÷ -3 = -5 |
| negative ÷ positive = negative | -24 ÷ 4 = -6 |
Learn with an example
➡️ Is 2 × 3 positive or negative?
- positive
- negative
2 is positive. 3 is positive. Use the rule:
positive × positive = positive
So, 2 × 3 is positive.
Now check your answer by doing the maths.
2 × 3 = 6
Yes, the answer is positive.
➡️ Is 88 ÷ –11 positive or negative?
- positive
- negative
88 is positive. –11 is negative. Use the rule:
positive ÷ negative = negative
So, 88 ÷ –11 is negative.
Now check your answer by doing the maths.
88 ÷ –11 = –8
Yes, the answer is negative.
➡️ Is 60 ÷ –12 positive or negative?
- positive
- negative
60 is positive. –12 is negative. Use the rule:
positive ÷ negative = negative
So, 60 ÷ –12 is negative.
Now check your answer by doing the maths.
60 ÷ –12 = –5
Yes, the answer is negative.
Try some practice problems!
