Lecture on Long Multiplication

Introduction to Long Multiplication

• Focus on the technique of long multiplication, a fundamental math skill taught in school.

Step-by-Step Examples

Example 1: 39 x 8

• Multiply 8 by 9:
  • 8 x 9 = 72
  • Write 2, carry over 7.
• Multiply 8 by 3:
  • 8 x 3 = 24
  • Add carried 7: 24 + 7 = 31
• Result: 312

Example 2: 56 x 9

• Multiply 9 by 6:
  • 9 x 6 = 54
  • Write 4, carry over 5.
• Multiply 9 by 5:
  • 9 x 5 = 45
  • Add carried 5: 45 + 5 = 50
• Result: 504

Example 3: 46 x 27

• Multiply 7 by 6:
  • 7 x 6 = 42
  • Write 2, carry over 4.
• Multiply 7 by 4:
  • 7 x 4 = 28
  • Add carried 4: 28 + 4 = 32
• Multiply 2 by 6:
  • Write a zero first.
  • 6 x 2 = 12
  • Write 2, carry over 1.
• Multiply 2 by 4:
  • 2 x 4 = 8
  • Add carried 1: 8 + 1 = 9
• Add partial results:
  • 2 + 0 = 2
  • 2 + 2 = 4
  • 3 + 9 = 12
• Result: 1242

Example 4: 76 x 52

• Multiply 2 by 6:
  • 2 x 6 = 12
  • Write 2, carry over 1.
• Multiply 2 by 7:
  • 2 x 7 = 14
  • Add carried 1: 14 + 1 = 15
• Write a zero.
• Multiply 5 by 6:
  • 5 x 6 = 30
  • Write 0, carry over 3.
• Multiply 5 by 7:
  • 5 x 7 = 35
  • Add carried 3: 35 + 3 = 38
• Add partial results:
  • 2, 5, 8 + 1 = 9, 3
• Result: 3952

Example 5: 369 x 43

• Multiply 3 by 9:
  • 3 x 9 = 27
  • Write 7, carry over 2.
• Multiply 3 by 6:
  • 3 x 6 = 18
  • Add carried 2: 18 + 2 = 20
  • Write 0, carry over 2.
• Multiply 3 by 3:
  • 3 x 3 = 9
  • Add carried 2: 9 + 2 = 11
• Add a zero.
• Multiply 4 by 9:
  • 4 x 9 = 36
  • Carry over 3.
• Multiply 4 by 6:
  • 4 x 6 = 24
  • Add carried 3: 24 + 3 = 27
  • Carry over 2.
• Multiply 4 by 3:
  • 4 x 3 = 12
  • Add carried 2: 12 + 2 = 14
• Add partial results:
  • 7, 6, 1 + 7 = 8
  • 1 + 4 = 5
• Result: 15867

Example 6: 759 x 438

• Multiply 8 by 9:
  • 8 x 9 = 72
  • Write 2, carry over 7.
• Multiply 8 by 5:
  • 8 x 5 = 40
  • Add carried 7: 40 + 7 = 47
  • Write 7, carry over 4.
• Multiply 8 by 7:
  • 8 x 7 = 56
  • Add carried 4: 56 + 4 = 60
• Write a zero.
• Multiply 3 by 9:
  • 3 x 9 = 27
  • Write 7, carry over 2.
• Multiply 3 by 5:
  • 3 x 5 = 15
  • Add carried 2: 15 + 2 = 17
  • Write 7, carry over 1.
• Multiply 3 by 7:
  • 3 x 7 = 21
  • Add carried 1: 21 + 1 = 22
• Write two zeros.
• Multiply 4 by 9:
  • 4 x 9 = 36
  • Carry over 3.
• Multiply 4 by 5:
  • 4 x 5 = 20
  • Add carried 3: 20 + 3 = 23
  • Write 3, carry over 2.
• Multiply 4 by 7:
  • 4 x 7 = 28
  • Add carried 2: 28 + 2 = 30
• Add partial results:
  • 2, 7 + 7 = 14
  • Write 4, carry over 1.
  • 1 + 7 + 6 = 14
  • Write 4, carry over 1.
  • 1 + 6 + 3 = 10
  • Write 0, carry over 1.
  • 1 + 2 = 3
• Result: 332442

Conclusion

• Mastery of long multiplication allows for efficient calculation of large number products.
• Practice these steps to gain confidence in handling more complex problems.