Long Division - Math Antics

Jul 4, 2024

Long Division - Math Antics

Introduction

  • Long division breaks a larger division problem into smaller, manageable steps.
  • Helpful to have watched the basic division video first for better understanding.

Key Concepts and Steps

  • Digit-by-digit approach: Divide one digit at a time from left to right.
    • This is opposite of multiplication and addition which start from the smallest digit and work right to left.
  • Example Problem: 936 ÷ 4

    • Step 1: Divide the first digit (9) by 4.
      • Process:
      • How many 4s in 9? → 2 (above 9)
      • 2 × 4 = 8 (write it below 9)
      • 9 - 8 = 1 (remainder)
    • Step 2: Drop down the next digit (3) to form 13 with the remainder (1).
      • How many 4s in 13? → 3 (above 3)
      • 3 × 4 = 12 (write it below 13)
      • 13 - 12 = 1 (remainder)
    • Step 3: Drop down last digit (6) to form 16.
      • How many 4s in 16? → 4 (above 6)
      • 4 × 4 = 16 (write it below 16)
      • 16 - 16 = 0 (no remainder)
    • Result: 936 ÷ 4 = 234

Additional Practice

  • Different dividends and divisors can affect the number of steps.
    • Example: 72 ÷ 8 (one-step) vs. 72 ÷ 3 (two-step)
    • Example:
      • 72 ÷ 8 = 9 (straight from multiplication table)
      • 72 ÷ 3:
        • 7 ÷ 3 = 2 with remainder 1
        • Bring down 2 → 12
        • 12 ÷ 3 = 4
      • Result: 72 ÷ 3 = 24

Practice Problem with Lengthy Dividend

  • Example: 315,270 ÷ 5
    • Steps:
      • 3 ÷ 5 = 0 (too small, skip)
      • 31 ÷ 5 = 6 (6 × 5 = 30, remainder 1)
      • 15 ÷ 5 = 3 (3 × 5 = 15, remainder 0)
      • 2 ÷ 5 = 0 (too small, skip)
      • 27 ÷ 5 = 5 (5 × 5 = 25, remainder 2)
      • 20 ÷ 5 = 4 (4 × 5 = 20, remainder 0)
    • Result: 315,270 ÷ 5 = 63,054

Tips for Practice

  1. Memorize multiplication tables.
  2. Write neatly and stay organized; use graph paper if needed.
  3. Start with smaller dividends and gradually work on larger ones.
  4. Check your answer with a calculator to catch and learn from mistakes.

Conclusion

  • Long division requires practice but is manageable step-by-step.
  • Practice regularly to master the procedure.

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