Adding Integers – Same Sign / Different Sign Rule (Absolute Value Trick)

Intro

Pichhli post mein humne number line par walk karke addition kiya.
Woh method bilkul safe hai.
Par exam mein kabhi-kabhi number line banana time leta hai.
Isliye aaj hum ek simple trick sikhenge: Same sign / Different sign rule.
Ye rule bilkul logical hai, yaad rakhne wala “magic” nahi.
Dheere-dheere samjhenge.

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Concept Explanation (What, Why, How)

Simple explanation

Integers add karte time 2 cases hote hain:

1. Same sign (dono + ya dono -)
   • Absolute values add karo
   • Sign same rakho
2. Different sign (ek +, ek -)
   • Absolute values subtract karo (bada – chhota)
   • Sign us number ka rakho jiska absolute value bada hai

Yahan “absolute value” ka matlab: number ka size, sign ignore karke.

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Detailed explanation

What (Kya kar rahe hain?)

Aapko aise sums milenge:

• −6+(−2)
• 9+(−4)
• −7+3

Inmein sign decide karna main confusion hota hai.

Why (Kyun ye rule kaam karta hai?)

• Same sign: Dono ek hi direction mein ja rahe hain.
  Right+Right ya Left+Left.
  Isliye size add hota hai aur direction (sign) same rehti hai.
• Different sign: Ek right, ek left.
  Matlab “tug of war” hai.
  Jo side zyada strong (bada absolute value) hai, wahi jeetega.
  Isliye subtract karte hain aur winner side ka sign rakhte hain.

How (Step-by-step)

Har question mein ye 3 steps follow karo:

1. Signs check karo: same ya different?
2. Absolute value ka kaam:
   • same sign → add
   • different sign → subtract (bada – chhota)
3. Final sign decide karo:
   • same sign → same sign
   • different sign → bigger absolute value wala sign

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More

Socho do log rope kheenchte hain.

• Agar dono same side kheenchen (dono + ya dono -), rope aur zyada usi side jaayegi.
  Isliye numbers ka size add ho jaata hai, sign same rehta hai.
• Agar ek right kheench raha hai (+) aur ek left kheench raha hai (-), toh fight hogi.
  Jo zyada strong hai (bada number), wahi jeetega.
  Isliye hum dono ka difference nikaalte hain.
  Aur sign winner ka rakhte hain.

Bas yehi rule hai.

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Examples

Example 1: Same sign (both negative)

-6 + (-2) = -8

Why: same sign → 6 + 2 = 8, sign negative.

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Example 2: Different sign (positive bigger)

9 + (-4) = 5

Why: different sign → 9 – 4 = 5, bigger absolute value is 9 (positive) → answer positive.

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Example 3: Different sign (negative bigger)

-7 + 3 = -4

Why: different sign → 7 – 3 = 4, bigger absolute value is 7 (negative) → answer negative.

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Real life usage

Socho aapke paas ₹200 hain (positive).
Aap par ₹450 ka udhaar hai (negative).
Net position kya?

₹200 + (-₹450)
Different sign case hai.
450 bada hai, isliye result negative hoga.
450 – 200 = 250
Net = -₹250 (matlab abhi bhi ₹250 debt).

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Try It Yourself

Same rule laga kar solve karo:

1. $6 + 8$6+8
2. $-9 + (-3)$−9+(−3)
3. $10 + (-7)$10+(−7)
4. $-12 + 5$−12+5

Apne answers likho.

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Summary

• Same sign: absolute values add karo, sign same rakho
• Different sign: absolute values subtract karo (bada – chhota), sign bigger absolute value wale ka rakho
• Ye rule number line ki logic se hi aata hai

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Next: Subtracting Integers – “Add the opposite” rule