Math Antics - Long Division

Introduction

• Overview of long division with multi-digit dividends.
• Key concept: Break down big division problems into smaller, easier steps.
• Focus on digit-by-digit division.

Example Problems

Problem with One-Digit Divisor

• First example:
  • Question: How many 2's fit into 5?
  • Answer: 2 (2 x 2 = 4, remainder 1).
  • Next digit: Combine with remainder to make 12.
  • Answer: 6 (2 x 6 = 12, no remainder).
  • Final digit: 8 (Answer: 4, 2 x 4 = 8, no remainder).
  • Final answer: 264.

Problem with Larger Divisor

• Second example:
  • Question: How many 8's fit into 5?
  • Answer: None, 8 is too big.
  • Group first two digits (52) and ask how many 8's fit into 52.
  • Answer: 6 (6 x 8 = 48, remainder 4).
  • Final digit: Combine remainder and last digit (48).
  • Answer: 6 (6 x 8 = 48, no remainder).
  • Final answer: 66.

Key Takeaways

• When the divisor is bigger than the first digit of the dividend, group more digits.
• You can take larger chunks of the dividend to minimize steps, but it makes the division harder.
• Fewer steps may seem appealing, but each step can be more challenging.

Division with Two-Digit Divisors

• New examples with two-digit divisors:
  • First problem (24 into 528):
    • Group first two digits (52).
    • Estimate (2 x 24 = 48, remainder 4).
    • Bring down last digit (4).
    • Answer: 22.
  • Second problem (88 into 528):
    • Group first three digits (528).
    • Estimate (6 x 88 = 528, no remainder).
    • Final answer: 6.

Long Division Procedure with Two-Digit Divisors

• Example: 817,152 divided by 38.
  1. Group first two digits (81).
  2. Estimate (2 x 38 = 76, remainder 5).
  3. Bring down next digit (5) and combine (57).
  4. Estimate (1 x 38 = 38, remainder 19).
  5. Bring down 1 (191).
  6. Estimate (5 x 38 = 190, remainder 1).
  7. Bring down 2 (152).
  8. Estimate (4 x 38 = 152, no remainder).
  • Final answer: 21,432.

Conclusion

• Importance of estimating and rounding in division problems.

• Long division steps become more complex with larger divisors.

• Encouragement to use calculators for complex problems.

• Reminder: Math is about problem-solving, not just division.

• For more resources: mathantics.com