Math Antics: Multi-Digit Multiplication

Introduction

• Previous lesson covered multiplying multi-digit numbers by one-digit numbers.
• Current lesson focuses on multiplying multi-digit numbers by another multi-digit number.

Procedure Overview

• Use a step-by-step multiplication process for each digit of the bottom number.
• For each bottom digit:
  • Multiply by each top digit, starting from the ones place and moving left.
  • Results in multiple intermediate answers.
• Final step involves adding the intermediate answers.

Example: Multiplying 324 by 46

• Step 1: Multiply the first bottom digit (6) by each top digit:

  • 6 × 4 = 24 (write down 4, carry 2)
  • 6 × 2 = 12 + 2 = 14 (write down 4, carry 1)
  • 6 × 3 = 18 + 1 = 19 (write down 19)

• Intermediate Result 1: 1944

• Step 2: Multiply second bottom digit (4 in the tens place) by each top digit:

  • Start by placing a zero in the ones place because 4 is in the tens place (value 40)
  • 4 × 4 = 16 (write down 6 next to zero, carry 1)
  • 4 × 2 = 8 + 1 = 9 (write down 9)
  • 4 × 3 = 12 (write down 12)

• Intermediate Result 2: 12960

Final Step: Adding Intermediate Results

• Align the results as in an addition problem:
  • 1944
  • +12960
• Add columns starting from the right:
  • 4 + 0 = 4
  • 4 + 6 = 10 (write 0, carry 1)
  • 1 + 9 + 9 = 19 (write 9, carry 1)
  • 1 + 1 + 2 = 4
  • Remaining digit: 1
• Final Answer: 14,904

Key Takeaways

• Each digit in the bottom number requires a complete iteration of multiplying by the top digits.
• Important to manage carrying and placement of additional zeros due to place value.
• Final result obtained by summing intermediate results.

Practice and Resources

• Practice examples are crucial for mastering the technique.
• Additional resources and exercises available at www.mathantics.com.

• Remember to approach multi-digit multiplication methodically.
• Review video lessons and practice problems as needed for reinforcement.