Multiplying Integers– Sign Rules (Plus/Minus ka Game)

Intro

Ab tak humne integers ko add aur subtract karna sikha.
Ab multiplication aata hai.
Yahan sabse bada confusion hota hai: sign ka kya hoga?
Answer positive aayega ya negative?
Aaj hum sirf multiplication ke sign rules sikhenge.
Bilkul step-by-step, bina tension.

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Concept Explanation (What, Why, How)

Simple explanation

Integers multiply karte waqt 2 cheezein hoti hain:

1. Numbers ka size multiply hota hai (absolute values)
2. Sign rule se decide hota hai

Sign rules:

• +×+=+
• +×−=−
• −×+=−
• −×−=+

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Detailed explanation

What (Kya?)

Aapko questions milenge:

• 3×4
• 3×(−4)
• (−3)×4
• (−3)×(−4)

Why (Kyun?)

Sign ka logic direction jaisa hai:

• Positive = forward/gain
• Negative = backward/loss

Jab ek negative aata hai, direction change hoti hai.
Aur jab do negative aate hain, direction do baar change hoti hai, to wapas positive.

How (Kaise?)

Step-by-step method:

1. Absolute values multiply karo (sign ignore)
2. Sign count karo:
   • Negative signs odd (1,3,5…) → answer negative
   • Negative signs even (0,2,4…) → answer positive

Ye quick trick exam mein fast hai.

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More

Socho “minus” ek switch hai.
Ek switch press kiya to direction ulta.
Do switch press kiye to direction wapas seedhi.

• Ek minus → answer negative
• Do minus → answer positive

Aur number ka size?
Woh normal multiplication se aata hai.

Example:(−2)×(−3)
Size: 2×3=6
Minus minus: plus
Answer: +6

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Examples

Example 1

3 × (-4) = -12

Example 2

(-6) × 5 = -30

Example 3

(-7) × (-2) = 14

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Real life usage

Socho har din ₹50 ka loss ho raha hai.
Loss ko hum negative maan lete hain: -50.

Agar ye loss 3 din tak hua:
$-50 \times 3 = -150$−50×3=−150
Matlab total loss ₹150.

Ab socho “loss ko remove karna” (negative of negative) wali feeling:
Kabhi-kabhi math mein do negatives milkar positive banate hain—jaise wrong direction ko do baar flip karo to right direction.

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Try It Yourself

Sign rule laga kar solve karo:

1. 4×(−3)
2. (−8)×2
3. (−5)×(−6)
4. (−2)×(−3)×4

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Summary

• Multiply magnitude (absolute values) normally
• Sign rules:
  • Same signs → positive
  • Different signs → negative
• Negative signs odd → negative, even → positive

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Next

Next: Dividing Integers – sign rules same as multiplication