Math Antics: Long Division with Larger Divisors

Introduction

• Review of Long Division:
  • Previously learned to divide multi-digit dividends by breaking them into smaller steps.
  • Focus was on one-digit divisors.

Division with Larger Divisors

• Problem with Larger Divisors:
  • Challenges arise when dividing by 2 or 3-digit numbers.
  • Need to adapt the digit-by-digit method for larger divisors.

Examples and Process

Example 1: Dividing by One-Digit Divisors

• Steps for Dividing 524 by 2:
  • Determine how many 2's fit in each digit of the dividend sequentially.
  • First Step: 2 fits into 5 two times.
  • Second Step: Remaining 1 carried to the next digit, 12 divided by 2 is 6.
  • Third Step: 8 divided by 2 is 4.
  • Result: 264 with no remainder.

Example 2: Larger Divisor than Initial Digit

• Steps for Dividing 524 by 8:
  • First Step Failure: 8 does not fit into 5; group first two digits (52).
  • Estimate: 8 fits into 52 approximately 6 times (6 x 8 = 48).
  • Second Step: 48 subtracted from 52, remainder 4, bring down 4 (48) divided by 8 is 6.
  • Result: 66 with no remainder.

Key Concepts

• Importance of Grouping Digits:
  • When the divisor is larger than a single digit of the dividend, group multiple digits.
  • Larger chunk grouping results in fewer steps but harder calculations.
• Comparison:
  • Three steps in first example, two steps in second.
  • Smaller steps are easier but more numerous; bigger steps are harder but fewer.

Division with Two-Digit Divisors

Example 3: Dividing by Two-Digit Divisors

• First Problem: 524 by 24
  • Start with first two digits (52).
  • Estimate: 2 (2 x 24 = 48), remainder 4.
  • Bring down last digit, 48 divided by 24 is 2.
  • Result: 22 with no remainder.

Example 4: More Complex Example

• Problem with Larger First Digit Group Needed:
  • Divisor larger than first digit group requires three-digit grouping.
  • Estimation is essential for making good guesses.

Estimation and Calculator Use

• Estimation Techniques:
  • Round numbers for easier estimation (e.g., 88 rounded to 90, 528 to 500).
  • Use multiplication estimates to check accuracy.
  • Adjust if remainder equals or exceeds the divisor.

Example 5: Complex Division (817,152 by 38)

• Method:
  • Round numbers for estimation, calculate step by step.
  • Importance of placing zeroes when necessary.
  • Use of estimation to simplify the process.

Conclusion

• Summary:
  • Long division with larger divisors follows the same principles but requires estimating and handling larger digit groups.
  • Estimating simplifies steps; calculators are recommended for complex problems.

Additional Resources

• Practice:
  • Try practice problems but avoid overexertion with long division.
• Learning More:
  • Visit Math Antics for further learning.