Integer multiplication and division rules

key notes:

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🔹 What are Integers?

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

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🔹 Multiplication of Integers

Rule 1: (+) × (+) = (+)

• Positive × Positive = Positive
• 👉 Example: 3 × 4 = 12

Rule 2: (-) × (-) = (+)

• Negative × Negative = Positive
• 👉 Example: (-5) × (-2) = 10

Rule 3: (+) × (-) = (-)

• Positive × Negative = Negative
• 👉 Example: 7 × (-3) = -21

Rule 4: (-) × (+) = (-)

• Negative × Positive = Negative
• 👉 Example: (-6) × 8 = -48

📌 Shortcut:

• If the signs are same → result is positive.
• If the signs are different → result is negative.

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🔹 Division of Integers

Rule 1: (+) ÷ (+) = (+)

• 👉 Example: 12 ÷ 3 = 4

Rule 2: (-) ÷ (-) = (+)

• 👉 Example: (-16) ÷ (-4) = 4

Rule 3: (+) ÷ (-) = (-)

• 👉 Example: 20 ÷ (-5) = -4

Rule 4: (-) ÷ (+) = (-)

• 👉 Example: (-35) ÷ 7 = -5

📌 Shortcut:

• Same signs → Quotient is Positive
• Different signs → Quotient is Negative

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🔹 Special Cases

• 0 × any integer = 0
• 0 ÷ any non-zero integer = 0
• Division by 0 is not defined ❌

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🔹 Quick Examples

1. (-7) × (-9) = +63
2. (-56) ÷ (-7) = +8
3. (-12) ÷ 3 = -4
4. 8 × (-5) = -40
5. 0 ÷ 9 = 0

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🔹 Practice Questions

1. 25 × (-4) = ?
2. (-6) × (-7) = ?
3. (-81) ÷ 9 = ?
4. (-72) ÷ (-8) = ?
5. 0 × (-15) = ?

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✅ Summary:

• Same signs → Positive
• Different signs → Negative
• Zero rule: Multiplying with 0 gives 0; division by 0 is not possible.

Learn with an example

Let’s practice!🖊️