Math Antics: Long Division

Introduction

• Long Division: A method to break down large division problems into a series of shorter steps.
• Prerequisite: Watch the basic division video for easier understanding.

Key Concepts

• Digit-by-Digit: Approach division problems digit by digit from left to right.
• Dividend: The number being divided.
• Divisor: The number you divide by.

Basic Steps in Long Division

1. Identify the First Digit

   • Start with the largest place value digit.
   • Example: In 936 ÷ 4, start with 9.

2. Divide Step by Step

   • Divide each digit of the dividend by the divisor.
   • Multiply and subtract as in basic division.
   • Example: 9 divided by 4 gives 2, remainder 1.

3. Bring Down the Next Digit

   • Include the remainder with the next digit.
   • Example: Bring down 3 to make 13 (remainder combined with the next digit).
   • Divide, multiply, subtract, and repeat.

4. Continue Until All Digits Are Used

   • Continue the process digit by digit until no digits are left.
   • Example: Obtain final result of 936 ÷ 4 = 234.

Examples

• 936 ÷ 4: Solved in three division steps.
• 72 ÷ 8: Single step problem (8 is a factor of 72).
• 72 ÷ 3: Two-step problem (digit-by-digit required).

Special Cases

• If the divisor is too large for the digit, write 0 and proceed.
• Example: 72 ÷ 8 could have been a two-step problem but skipped because 8 doesn’t divide into 7.

Complex Example: 315,270 ÷ 5

1. Recognize 5 won’t divide into smaller digits (e.g., 3, 2) without combining.
2. Follow the same digit-by-digit procedure.
3. Final answer: 63,054.

Tips for Practice

• Memorize Multiplication Table: Facilitates quicker division.
• Neat Writing: Maintain alignment in columns to avoid errors.
• Start Small: Begin with smaller dividends to build confidence.
• Check with Calculator: Verify results to identify and learn from mistakes.

Conclusion

• Practice is key to mastering long division.
• Keep organized and double-check work.

For more resources, visit Math Antics.