Dividing Integers — Sign Rules Same as Multiplication

Intro

Math ka sabse bada dar kab aata hai?
Jab minus (−) aa jaye aur dimaag bole, “Ab toh gadbad hogi”
Par sach yeh hai: integers divide karna bahut simple hai.
Sirf ek hi cheez yaad rakho—sign rule.
Aaj hum sirf wahi rule, calmly, step-by-step, blackboard style me karenge.
No rush. Bas ek concept, ek rule, aur 4–5 easy examples.

---

Concept Explanation (What, Why, How)

Simple explanation

Dividing integers ka matlab: positive/negative numbers ko divide karna.
Rule bilkul multiplication jaisa hai:

• Like signs (same sign) ⇒ answer positive
• Unlike signs (different sign) ⇒ answer negative
  Ye rule division aur multiplication dono ke liye same hai.

---

Detailed explanation

Socho do numbers hain:

1. Same sign

• (+) ÷ (+) = (+)
• (−) ÷ (−) = (+)
  Dono ka “mood” same, result friendly: plus.

2. Different sign

• (+) ÷ (−) = (−)
• (−) ÷ (+) = (−)
  Ek plus, ek minus—result me “minus” aa jaata hai.

Aur jab multiple negatives (3 numbers, 4 numbers, etc.) ho (multiply/divide mix), tab ek aur super-helpful idea:

• Negative signs count karo.
• Odd number of negatives ⇒ answer negative
• Even number of negatives ⇒ answer positive

Division me normally 2 numbers hote hain, so “same sign / different sign” rule kaafi hai.
Par jab expression me multiple signs aa jaye, tab “odd-even negatives” wali trick bahut kaam aati hai.

---

More

Imagine karo plus matlab “smile” 😊 (sirf imagine), aur minus matlab “angry face” 😠 (sirf imagine).
Ab rule:

• Dono smile-smile ( + ÷ + ) ⇒ answer smile ( + )
• Dono angry-angry ( − ÷ − ) ⇒ angry cancels, answer smile ( + )
• Ek smile, ek angry ( + ÷ − ) or ( − ÷ + ) ⇒ answer angry ( − )

Bas itna.
Ab number ka division normal hota hai (12 ÷ 3 = 4).
Sign ka rule upar wala.
Pehele sign decide, phir numbers divide. Done.

---

DIVIDING INTEGERS SIGN RULES

(+) ÷ (+) = (+)
(−) ÷ (−) = (+)

(+) ÷ (−) = (−)
(−) ÷ (+) = (−)

Shortcut: Same sign → Positive, Different sign → Negative

---

Examples

Example 1

12 ÷ 3 = 4
Signs: (+) ÷ (+) ⇒ (+)
Answer: +4

Example 2

(−12) ÷ (−3) = 4
Signs: (−) ÷ (−) ⇒ (+)
Answer: +4

Example 3

(−15) ÷ 5 = 3
Signs: (−) ÷ (+) ⇒ (−)
Answer: −3

Example 4

18 ÷ (−6) = 3
Signs: (+) ÷ (−) ⇒ (−)
Answer: −3

Example 5

(−84) ÷ (−4) = 21
Same sign ⇒ positive
Answer: +21

---

Real life usage)

Socho aapka weekly profit/loss track ho raha hai.
Total loss = −126 (matlab loss).
Agar 7 days me equal loss hua, toh per day loss:
−126 ÷ 7 = −18
Sign negative aaya kyunki (−) ÷ (+) ⇒ (−).
Matlab har din 18 ka loss.

---

Try It Yourself (1 simple task)

Compute karo aur sirf sign rule pe dhyaan do:
(−56) ÷ 7 = ?

---

Summary

• Division of integers me sign rule sabse important.
• Same sign ⇒ Positive
• Different sign ⇒ Negative
• Shortcut (multi-sign expressions): odd negatives ⇒ negative, even negatives ⇒ positive.

---

Practice Questions

24 ÷ 6

2. (−24) ÷ 6

3. 24 ÷ (−6)

4. (−24) ÷ (−6)

5. 49 ÷ 7

6. (−49) ÷ 7

7. 49 ÷ (−7)

8. (−49) ÷ (−7)

9. 81 ÷ 9

10. (−81) ÷ 9

11. 81 ÷ (−9)

12. (−81) ÷ (−9)

13. (−64) ÷ 8

14. 64 ÷ (−8)

15. (−100) ÷ (−20)

16. 0 ÷ (−5)

17. (−72) ÷ 12

18. 96 ÷ (−3)

---

Next

Next we will practice mixed expressions where division and multiplication signs appear together.