Long Division with Larger Divisors

Overview

• Previous Video: Learned basics of long division with single-digit divisors using multi-digit dividends.
• Current Lesson: Applying long division techniques for problems with two or three-digit divisors.

Key Concepts

Single-Digit Divisors

• Digit-by-Digit Division: Break down the problem into smaller division steps, one digit at a time, for ease.
• Example 1 (Divisor = 2):
  • 5 ÷ 2 = 2 (remainder 1)
  • 12 ÷ 2 = 6
  • 8 ÷ 2 = 4
  • Answer: 264
• Example 2 (Divisor = 8):
  • 5 ÷ 8 = 0 (group first two digits to form 52)
  • 52 ÷ 8 = 6 (remainder 4)
  • 48 ÷ 8 = 6
  • Answer: 66

Observations

• When Divisor > First Digit: Group more digits of the dividend to proceed with division.
• Flexibility in Digit Grouping:
  • Can divide the entire chunk of digits instead of one digit at a time, but requires more complex calculations.

Division with Two-Digit Divisors

• Need to group at least two digits of the dividend since the divisor itself has two digits.
• Example 1 (Divisor = 24):
  • 52 ÷ 24 ≈ 2 (remainder 4)
  • 48 ÷ 24 = 2
  • Answer: 22

Estimation for Two-Digit Divisors

• Helps to round off to nearby numbers for easier calculation.
• Example 2 (Divisor = 88):
  • 52 ÷ 88 = 0 (group next digit to form 528)
  • Estimate: 88 ≈ 90, 528 ≈ 500
  • 500 ÷ 100 ≈ 5
  • 528 - 440 (5×88) = 88 (try 6 instead of 5)
  • Answer: 6

Complex Division Problems (Three or More Digits Divisors)

• Two-digit divisors require taking bigger steps and estimating more.
• Example:
  • 817,152 ÷ 38
  • Steps involve rounding and estimating closely to find the answer.

Tips and Best Practices

• Estimation: Round numbers to nearest values to make division easier.
• Use of Calculators: For very complex problems, calculators are recommended.
• Continuous Practice: Important to understand and get comfortable with estimation and digit grouping.

Conclusion

• Long division with larger divisors follows the same basic principles but requires more estimation and mental math.
• Focus on understanding underlying math principles and problem-solving skills.
• For more example problems and explanations, visit Math Antics.

Quote: “The reason we study math is to become good problem solvers and to be able to understand all sorts of important math ideas, and there’s a lot more to math than division!”