Long Multiplication Lecture Notes

Introduction

• Focus on long multiplication technique
• Practical examples to illustrate the process

Example 1: 39 x 8

• Step 1: Multiply 8 by 9
  • 8 x 9 = 72
  • Write down 2, carry over 7
• Step 2: Multiply 8 by 3
  • 8 x 3 = 24
  • Add carried over 7: 24 + 7 = 31
• Final Answer: 312

Example 2: 56 x 9

• Step 1: Multiply 9 by 6
  • 9 x 6 = 54
  • Write down 4, carry over 5
• Step 2: Multiply 9 by 5
  • 9 x 5 = 45
  • Add carried over 5: 45 + 5 = 50
• Final Answer: 504

Example 3: 46 x 27

• Step 1: Multiply 7 by 6
  • 7 x 6 = 42
  • Write down 2, carry over 4
• Step 2: Multiply 7 by 4
  • 7 x 4 = 28
  • Add carried over 4: 28 + 4 = 32
• Step 3: Write down a 0 for the next row
• Step 4: Multiply 6 by 2
  • 6 x 2 = 12
  • Write down 2, carry over 1
• Step 5: Multiply 2 by 4
  • 2 x 4 = 8
  • Add carried over 1: 8 + 1 = 9
• Final Calculation:
  • Add results:
    • 2 + 0 = 2
    • 2 + 2 = 4
    • 3 + 9 = 12
• Final Answer: 1,242

Example 4: 76 x 52

• Step 1: Multiply 2 by 6
  • 2 x 6 = 12
  • Write down 2, carry over 1
• Step 2: Multiply 2 by 7
  • 2 x 7 = 14
  • Add carried over 1: 14 + 1 = 15
• Step 3: Write down a 0 for the next row
• Step 4: Multiply 5 by 6
  • 5 x 6 = 30
  • Write down 0, carry over 3
• Step 5: Multiply 5 by 7
  • 5 x 7 = 35
  • Add carried over 3: 35 + 3 = 38
• Final Calculation:
  • Add results:
    • 2 + 0 = 2
    • 5 + 0 = 5
    • 8 + 1 = 9
• Final Answer: 3,952

Example 5: 369 x 43

• Step 1: Multiply 3 by 9
  • 3 x 9 = 27
  • Write down 7, carry over 2
• Step 2: Multiply 3 by 6
  • 3 x 6 = 18
  • Add carried over 2: 18 + 2 = 20
• Step 3: Write down a 0 for the next row
• Step 4: Multiply 4 by 9
  • 4 x 9 = 36
  • Write down 6, carry over 3
• Step 5: Multiply 4 by 6
  • 4 x 6 = 24
  • Add carried over 3: 24 + 3 = 27
• Final Calculation:
  • Add results:
    • 7 + 6 = 13
    • 1 + 1 = 5
• Final Answer: 15,867

Example 6: 759 x 438 (Final Example)

• Step 1: Multiply 8 by 9
  • 8 x 9 = 72
  • Write down 2, carry over 7
• Step 2: Multiply 8 by 5
  • 8 x 5 = 40
  • Add carried over 7: 40 + 7 = 47
• Step 3: Multiply 8 by 7
  • 8 x 7 = 56
  • Add carried over 4: 56 + 4 = 60
• Step 4: Write down a 0 for the next row
• Step 5: Multiply 3 by 9
  • 3 x 9 = 27
  • Write down 7, carry over 2
• Step 6: Multiply 3 by 5
  • 3 x 5 = 15
  • Add carried over 2: 15 + 2 = 17
• Final Calculation:
  • Add results:
    • 2 + 7 = 9
    • 1 + 5 = 6
• Final Answer: 332,442

Conclusion

• Mastering long multiplication through practice and clear steps is essential for understanding larger calculations.