Class 7th Math Ex- 1.2 Solved By PREM SIR

✅ Question 1: Find the product (गुणा करो)

Important Rule yaad rakho:

Positive × Positive = Positive

Positive × Negative = Negative

Negative × Positive = Negative

Negative × Negative = Positive



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(a) 3 × (–1) = –3

👉 Positive number × Negative number = Negative

(b) (–1) × 225 = –225

👉 Negative × Positive = Negative

(c) (–21) × (–30) = 630

👉 Negative × Negative = Positive

(d) –316 × (–1) = 316

👉 Dono negative, toh result positive

(e) (–15) × 0 × (–18) = 0

👉 Kisi bhi number ko 0 se multiply karo, result 0

(f) (–12) × (–11) × (10) = 132 × 10 = 1320

👉 Pehle 2 negative ka product positive, fir × 10

(g) 9 × (–3) × (–6) = –27 × (–6) = 162

👉 Ek negative se negative = positive

(h) (–18) × (–5) × (–4) = 90 × (–4) = –360

👉 2 negative = positive, fir × ek aur negative = negative

(i) (–1) × (–2) × (–3) × 4 = –24

👉 3 negative ka product = negative × 4 = –24

(j) (–3) × (–6) × (2) × (–1) = 36

👉 Even number of negative = final result positive


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✅ Question 2: Verify the Properties (गुणा का वितरित गुणधर्म)

(a)

18 × [7 + (–3)] = [18 × 7] + [18 × (–3)]
👉 Left side: 18 × 4 = 72
👉 Right side: 126 + (–54) = 72
✅ LHS = RHS, verified

(b)

(–21) × [(–4) + (–6)] = (–21 × –4) + (–21 × –6)
👉 LHS = –21 × (–10) = 210
👉 RHS = 84 + 126 = 210
✅ Verified

🧠 Property Name: Distributive Property of Multiplication over Addition


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✅ Question 3: Understanding (-1) × a

(i) (-1) × a = –a

👉 Kisi bhi number ko –1 se multiply karo, result uska ulta (opposite sign) hota hai.
Example: –1 × 5 = –5, –1 × (–8) = +8

(ii) Find the number jisko (–1) se multiply karne par +22 mile:

👉 Answer: (–1) × (–22) = +22 ✅


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✅ Question 4: Pattern samjho

Dekho pattern:

(–1) × 5 = –5

(–1) × 4 = –4

(–1) × 3 = –3

(–1) × 2 = –2

(–1) × 1 = –1

(–1) × 0 = 0

(–1) × (–1) = +1 ✅


🔍 Conclusion (निष्कर्ष):

Ek negative aur ek positive ka product = negative

Do negative ka product = positive



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✅ Bacchon ke liye Summary Table

Operation Type Result

(+) × (+) + (positive)
(–) × (+) / (+) × (–) – (negative)
(–) × (–) + (positive)
Any number × 0 0
(–1) × a –a
Integers - Exercise 1.2 | Prem Eternal Education

📘 Integers – Exercise 1.2 (Class 7)

👨‍🏫 Coaching: Prem ♾️ Eternal Education

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✅ Question 1: Find the Product

Multiply the following:
  • 3 × (–1) = –3
  • (–1) × 225 = –225
  • (–21) × (–30) = 630
  • (–316) × (–1) = 316
  • (–15) × 0 × (–18) = 0
  • (–12) × (–11) × 10 = 1320
  • 9 × (–3) × (–6) = 162
  • (–18) × (–5) × (–4) = –360
  • (–1) × (–2) × (–3) × 4 = –24
  • (–3) × (–6) × 2 × (–1) = 36
📌 Rule:
  • (+) × (+) = +
  • (–) × (+) = –
  • (–) × (–) = +
  • Any number × 0 = 0

✅ Question 2: Verify Using Distributive Property

  • 18 × [7 + (–3)] = [18 × 7] + [18 × (–3)]
  • (–21) × [(–4) + (–6)] = [(–21 × –4)] + [(–21 × –6)]
  • 18 × 4 = 72 ✅ = 126 + (–54)
  • (–21) × (–10) = 210 ✅ = 84 + 126
🔁 **LHS = RHS**, hence verified.

✅ Question 3: Understanding (–1) × a

  • (i) (–1) × a = –a (changes the sign)
  • (ii) (–1) × (–22) = 22 ✅

✅ Question 4: Pattern Observations

Starting from (–1) × 5:
  • (–1) × 5 = –5
  • (–1) × 4 = –4
  • (–1) × 3 = –3
  • (–1) × 2 = –2
  • (–1) × 1 = –1
  • (–1) × 0 = 0
  • ⭐ (–1) × (–1) = +1

Conclusion:
- Ek negative aur ek positive ka product = negative
- Do negative ka product = **positive**

📌 Final Rules Table

Operation Result
Positive × Positive Positive
Positive × Negative Negative
Negative × Negative Positive
Any number × 0 0
(–1) × a –a

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