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.
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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
- Memorize multiplication tables.
- Write neatly and stay organized; use graph paper if needed.
- Start with smaller dividends and gradually work on larger ones.
- 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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