Multiply and divide integers

Key Notes :

🔹 What are Integers?

• Integers are whole numbers and their opposites.
• Examples: …, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …

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🔹 Multiplication Rules for Integers

Positive × Positive = Positive

• Example: 3×4=12

Negative × Negative = Positive

• Example: (−3)×(−4)=12

Positive × Negative = Negative

• Example: 3×(−4)=−12

Negative × Positive = Negative

• Example: (−3)×4=−12

👉 Rule of Thumb:

• If the signs are same, the product is positive.
• If the signs are different, the product is negative.

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🔹 Division Rules for Integers

Positive ÷ Positive = Positive

• Example: 12÷3=4

Negative ÷ Negative = Positive

• Example: (−12)÷(−3)=4

Positive ÷ Negative = Negative

• Example: 12÷(−3)=−4

Negative ÷ Positive = Negative

• Example: (−12)÷3=−4

👉 Rule of Thumb:

• If the signs are same, the quotient is positive.
• If the signs are different, the quotient is negative.

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🔹 Important Properties

Commutative Property (Multiplication):

• a×b=b×a
• Example: (−2)×3=3×(−2)=−6

❌ Not true for division.

Associative Property (Multiplication):

• (a×b)×c=a×(b×c)
• Example: (2×−3)×4=2×(−12)=−24

Distributive Property:

• a×(b+c)=(a×b)+(a×c)
• Example: 2×(3+−5)=(2×3)+(2×−5)=6−10=−4

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🔹 Worked Examples

1. (−7)×(−5)=35
2. (−36)÷(9)=−4
3. (45)÷(−9)=−5
4. (−8)×(6)=−48
5. (−10)÷(−2)=5

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🔹 Word Problem

• Example: A submarine descends 50 meters each minute. How far does it descend in 8 minutes?
• 👉 −50×8=−400
• Answer: The submarine descends 400 meters below sea level.

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🔹 Quick Tips

✅ Multiplying/Dividing integers with same sign → Positive
✅ Multiplying/Dividing integers with different sign → Negative
✅ Zero times any integer = 0
✅ Division by zero is not defined

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📌 Summary:

• Multiplication and division of integers follow sign rules.
• Same signs = positive result.
• Different signs = negative result.
• Properties like commutative, associative, and distributive help in simplifying problems.

Learn with an example

Let’s practice!🖊️