# 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!”