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Multiplication | गुणा

✖️ Multiplication / गुणा

Multiplication is repeated addition of the same number.
एक ही संख्या को बार-बार जोड़ना गुणा कहलाता है।

Multiplication Sign / गुणा का चिन्ह

× = Multiply / गुणा

Example

3 × 4 = 12

This means:

4 + 4 + 4 = 12

या

3 groups of 4 = 12

3 समूह, प्रत्येक में 4 वस्तुएँ = कुल 12 वस्तुएँ।

🟢 Multiplication with Objects / वस्तुओं से गुणा

Example 1

🍎 🍎 🍎
🍎 🍎 🍎
🍎 🍎 🍎

There are 3 groups of 3 apples.

3 × 3 = 9

Example 2

⭐⭐⭐⭐
⭐⭐⭐⭐
⭐⭐⭐⭐

3 × 4 = 12

Practice

  1. 🍎 🍎 / 🍎 🍎 = _____
  2. ⭐ ⭐ ⭐ / ⭐ ⭐ ⭐ = _____
  3. ⚽ ⚽ / ⚽ ⚽ / ⚽ ⚽ = _____
  4. 🌸 🌸 🌸 / 🌸 🌸 🌸 / 🌸 🌸 🌸 = _____
  5. 🐟 🐟 🐟 🐟 / 🐟 🐟 🐟 🐟 = _____

Answers: 4, 6, 6, 9, 8

🔵 Multiplication as Repeated Addition

बार-बार जोड़ के रूप में गुणा

Example 1

2 × 5

means:

5 + 5 = 10

Therefore:

2 × 5 = 10

Example 2

4 × 3

means:

3 + 3 + 3 + 3 = 12

Therefore:

4 × 3 = 12

Example 3

5 × 2

means:

2 + 2 + 2 + 2 + 2 = 10

Therefore:

5 × 2 = 10

✏️ Practice

Write as repeated addition:

  1. 2 × 3 = __________
  2. 3 × 4 = __________
  3. 4 × 2 = __________
  4. 5 × 3 = __________
  5. 3 × 5 = __________
  6. 4 × 4 = __________
  7. 2 × 6 = __________
  8. 5 × 4 = __________

Answers

  1. 3 + 3 = 6
  2. 4 + 4 + 4 = 12
  3. 2 + 2 + 2 + 2 = 8
  4. 3 + 3 + 3 + 3 + 3 = 15
  5. 5 + 5 + 5 = 15
  6. 4 + 4 + 4 + 4 = 16
  7. 6 + 6 = 12
  8. 4 + 4 + 4 + 4 + 4 = 20

⭐ Important Multiplication Facts

Any number × 1

Any number multiplied by 1 remains the same.

किसी भी संख्या को 1 से गुणा करने पर वही संख्या प्राप्त होती है।

  • 5 × 1 = 5
  • 12 × 1 = 12
  • 25 × 1 = 25
  • 100 × 1 = 100

Any number × 0

Any number multiplied by 0 is 0.

किसी भी संख्या को 0 से गुणा करने पर उत्तर 0 होता है।

  • 5 × 0 = 0
  • 12 × 0 = 0
  • 50 × 0 = 0
  • 100 × 0 = 0

🔢 Multiplication Tables / पहाड़े

Table of 2 / 2 का पहाड़ा

×Answer
2 × 12
2 × 24
2 × 36
2 × 48
2 × 510
2 × 612
2 × 714
2 × 816
2 × 918
2 × 1020

Table of 3 / 3 का पहाड़ा

3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Table of 4 / 4 का पहाड़ा

4, 8, 12, 16, 20, 24, 28, 32, 36, 40

Table of 5 / 5 का पहाड़ा

5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Table of 6 / 6 का पहाड़ा

6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Table of 7 / 7 का पहाड़ा

7, 14, 21, 28, 35, 42, 49, 56, 63, 70

Table of 8 / 8 का पहाड़ा

8, 16, 24, 32, 40, 48, 56, 64, 72, 80

Table of 9 / 9 का पहाड़ा

9, 18, 27, 36, 45, 54, 63, 72, 81, 90

Table of 10 / 10 का पहाड़ा

10, 20, 30, 40, 50, 60, 70, 80, 90, 100

🟠 Multiplication by 10 / 10 से गुणा

When we multiply a number by 10, we put 0 after the number.

10 से गुणा करने पर संख्या के बाद 0 लग जाता है।

  • 2 × 10 = 20
  • 5 × 10 = 50
  • 12 × 10 = 120
  • 25 × 10 = 250
  • 100 × 10 = 1000

🔢 Two-Digit × One-Digit

दो अंकों की संख्या × एक अंक

Example

23 × 3

Break 23 into 20 + 3:

20 × 3 = 60

3 × 3 = 9

Therefore:

60 + 9 = 69

23 × 3 = 69

More Examples

12 × 4 = 48

21 × 3 = 63

32 × 2 = 64

14 × 5 = 70

25 × 4 = 100

✏️ Practice

  1. 12 × 3 = _____
  2. 15 × 2 = _____
  3. 21 × 4 = _____
  4. 23 × 3 = _____
  5. 32 × 2 = _____
  6. 14 × 5 = _____
  7. 25 × 3 = _____
  8. 31 × 4 = _____
  9. 42 × 2 = _____
  10. 15 × 6 = _____

Answers

36, 30, 84, 69, 64, 70, 75, 124, 84, 90

🔴 Two-Digit × One-Digit with Carrying

Example

27 × 4

First multiply Ones:

7 × 4 = 28

Write 8 and carry 2.

Then:

2 × 4 + 2 = 10

Therefore:

27 × 4 = 108

Practice

  1. 18 × 4 = _____
  2. 26 × 3 = _____
  3. 37 × 2 = _____
  4. 28 × 4 = _____
  5. 45 × 3 = _____
  6. 56 × 2 = _____
  7. 39 × 4 = _____
  8. 47 × 3 = _____
  9. 68 × 2 = _____
  10. 29 × 5 = _____

Answers

72, 78, 74, 112, 135, 112, 156, 141, 136, 145

🔢 Three-Digit × One-Digit

तीन अंकों की संख्या × एक अंक

Example

123 × 3

  123
×   3
-----
  369

Step-by-step:

3 × 3 = 9

2 × 3 = 6

1 × 3 = 3

Answer:

369

Example with Carrying

246 × 3

    1
  246
×   3
-----
  738
  • 6 × 3 = 18 → write 8, carry 1
  • 4 × 3 + 1 = 13 → write 3, carry 1
  • 2 × 3 + 1 = 7

Answer = 738

✏️ Three-Digit Practice

No.QuestionAnswer
1123 × 2246
2145 × 3435
3212 × 4848
4231 × 3693
5125 × 5625
6246 × 3738
7315 × 41,260
8428 × 2856
9357 × 31,071
10486 × 41,944

🔢 Two-Digit × Two-Digit

दो अंकों की संख्या × दो अंक

Example

23 × 12

Break 12 into 10 + 2.

23 × 10 = 230

23 × 2 = 46

Now add:

230 + 46 = 276

Therefore:

23 × 12 = 276

✏️ Practice

  1. 12 × 11 = _____
  2. 15 × 12 = _____
  3. 21 × 13 = _____
  4. 22 × 14 = _____
  5. 25 × 12 = _____
  6. 31 × 11 = _____
  7. 32 × 12 = _____
  8. 24 × 15 = _____
  9. 35 × 14 = _____
  10. 42 × 12 = _____

Answers

132, 180, 273, 308, 300, 341, 384, 360, 490, 504

🛒 Word Problems / शब्द-प्रश्न

1.

One pencil costs ₹5. How much will 6 pencils cost?

एक पेंसिल की कीमत ₹5 है। 6 पेंसिलों की कीमत कितनी होगी?

5 × 6 = ₹30

✅ Answer: ₹30

2.

There are 8 students in each group. There are 5 groups. How many students are there?

प्रत्येक समूह में 8 विद्यार्थी हैं। ऐसे 5 समूह हैं।

8 × 5 = 40

✅ Answer: 40 students

3.

A box contains 24 chocolates. There are 4 boxes. How many chocolates are there?

एक डिब्बे में 24 chocolates हैं। ऐसे 4 डिब्बे हैं।

24 × 4 = 96

✅ Answer: 96 chocolates

4.

A farmer plants 125 trees in each field. He has 3 fields.

125 × 3 = 375

✅ Answer: 375 trees

🧠 Mental Multiplication / मानसिक गुणा

  1. 2 × 5 = _____
  2. 3 × 10 = _____
  3. 5 × 10 = _____
  4. 10 × 10 = _____
  5. 20 × 2 = _____
  6. 30 × 3 = _____
  7. 50 × 2 = _____
  8. 100 × 5 = _____
  9. 200 × 3 = _____
  10. 500 × 2 = _____

Answers

10, 30, 50, 100, 40, 90, 100, 500, 600, 1,000

🎯 Classroom Activities / कक्षा गतिविधियाँ

🎲 Dice Multiplication

दो dice फेंकें।

अगर numbers आए:

4 and 6

Then:

4 × 6 = 24

🧮 Array Activity

बच्चों को objects की rows और columns बनवाएँ।

⭐⭐⭐⭐
⭐⭐⭐⭐
⭐⭐⭐⭐

3 rows × 4 stars:

3 × 4 = 12

इससे multiplication को visual तरीके से समझना आसान होता है।

📝 Final Practice Test / अंतिम अभ्यास

A. Basic

  1. 4 × 3 = _____
  2. 6 × 5 = _____
  3. 7 × 4 = _____
  4. 8 × 6 = _____
  5. 9 × 7 = _____

B. Two-Digit × One-Digit

  1. 23 × 4 = _____
  2. 36 × 3 = _____
  3. 45 × 2 = _____
  4. 27 × 5 = _____
  5. 48 × 3 = _____

C. Three-Digit × One-Digit

  1. 125 × 3 = _____
  2. 234 × 2 = _____
  3. 315 × 4 = _____
  4. 426 × 3 = _____
  5. 508 × 2 = _____

D. Two-Digit × Two-Digit

  1. 12 × 15 = _____
  2. 21 × 14 = _____
  3. 25 × 16 = _____
  4. 32 × 12 = _____
  5. 45 × 11 = _____

✅ Answer Key

  1. 12
  2. 30
  3. 28
  4. 48
  5. 63
  6. 92
  7. 108
  8. 90
  9. 135
  10. 144
  11. 375
  12. 468
  13. 1,260
  14. 1,278
  15. 1,016
  16. 180
  17. 294
  18. 400
  19. 384
  20. 495

🏠 Homework / गृहकार्य

  • 2 से 10 तक पहाड़े लिखो और बोलकर याद करो।
  • 10 basic multiplication questions हल करो।
  • 5 two-digit × one-digit questions हल करो।
  • 5 three-digit × one-digit questions हल करो।
  • 3 multiplication word problems बनाकर हल करो।

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