Long Division with Big Divisors

Introduction

• Discussed basic long division from previous lesson.
• Aim: Understand division with larger divisors (two or three digits).

Key Concepts

1. Digit-by-Digit Division

   • Long division simplifies complex problems into smaller steps.
   • For one-digit divisors: straightforward digit-by-digit division.

2. Handling Larger Divisors

   • Two or three-digit divisors require a different approach.
   • Example Division Problems:
     • Problem 1: Dividing 52 by 2
       • Steps:
         • 2 fits into 5: 2 (2 x 2 = 4, remainder = 1)
         • Bring down next digit: 12, 2 fits into 12: 6 (6 x 2 = 12, remainder = 0)
         • Bring down last digit: 8, 2 fits into 8: 4 (4 x 2 = 8, remainder = 0)
       • Final Answer: 264
     • Problem 2: Dividing 52 by 8
       • 8 does not fit into 5.
       • Combine digits: 52, 8 fits into 52: 6 (6 x 8 = 48, remainder = 4)
       • Bring down last digit: 48, 8 fits into 48: 6 (6 x 8 = 48, remainder = 0)
       • Final Answer: 66

Important Observations

• Grouping Digits:
  • If the first digit is less than the divisor, group the next digit (or more).
  • For larger divisors, grouping more digits is often required and reduces steps, but increases complexity.

Two-Digit Divisors

• Example Problems with Estimation:
  • Dividing by 24:
    • Problem: 52 divided by 24.
      • Estimate 2 (since 2 x 24 = 48, remainder = 4).
      • Bring down next digit: 48, result is 2 (no remainder).
      • Final Answer: 22
  • Dividing by 88:
    • Problem: 52 divided by 88.
      • Needs three digits: 528.
      • Estimation: 6 (6 x 88 = 528, no remainder).
      • Final Answer: 6

Practical Considerations

1. Challenges with Grouping:

   • Grouping too many digits can complicate division.
   • Preferably, group smaller chunks for easier calculations.

2. Estimation Techniques:

   • Rounding numbers helps improve estimates and simplifies calculations.
   • Example: Rounding 88 and 528 to 90 and 500.

Long Division Example

• Complex Case: 817,152 divided by 38.
  • Steps:
    1. Estimate how many 38's fit into 81 (estimate: 2).
    2. Use remainder and next digit for further calculations.
    3. Finalize with all digits combined (zero if smaller than divisor).
  • Final Answer: 21,000

Conclusion

• Long division procedures remain the same, but more digits complicate the process.
• Recommendation: Use calculators for very complex divisions.
• Practice with long division, but remember math encompasses more than just division.

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