Long Division Methods for 3-4 Digit Dividends

Long Division Methods for Dividing 3 and 4 Digit Dividends by 2 Digit Divisors

Basic Steps of Long Division

1. Set Up the Division:

   • Write the dividend (3 or 4 digits) under the long division bar.
   • Write the divisor (2 digits) outside the bar.

2. Divide:

   • Determine how many times the divisor fits into the initial digit(s) of the dividend.
   • Write that number (quotient) above the division bar.

3. Multiply:

   • Multiply the divisor by the quotient part calculated.
   • Write the result below the dividend section you just used.

4. Subtract:

   • Subtract the multiplication result from the dividend section.
   • Bring down the next digit from the dividend next to the result of the subtraction.

5. Repeat:

   • Repeat the divide, multiply, and subtract steps for the new number formed.
   • Continue until all digits of the dividend are brought down.

6. Final Steps:

   • If there are no more digits to bring down, check if there is a remainder.
   • Remainder is noted beside the quotient or can be expressed as a fraction.

Tips for Success

• Estimate First: Before dividing, estimate how many times the divisor can fit into the dividend section for quicker calculations.
• Practice with Rounding: Rounding the divisor can simplify the process; adjust as necessary for accuracy.
• Write Intermediate Steps: Keep all calculations clear and organized to avoid confusion and errors.
• Check Work: Multiply the quotient by the divisor and add any remainder to verify the final answer matches the original dividend.

Example

• For 1234 ÷ 34:
  • Initial division: 34 fits into 123 two times (2).
  • Multiply: 34 × 2 = 68.
  • Subtract: 123 - 68 = 55.
  • Bring down the next digit (4) to make 554.
  • Repeat the process with 554 and proceed until complete.

Practice Problems

1. 2564 ÷ 12
2. 3145 ÷ 45
3. 1843 ÷ 23
4. 7890 ÷ 56

Common Errors to Avoid

• Misplacing Quotients: Ensure the quotient digits align correctly above the division bar.
• Inaccurate Multiplication: Double-check multiplication results before subtraction.
• Neglecting Remainders: Always include remainders in your final answer if they exist.

Long Division Methods

• Long division is a method used to divide large numbers (dividends) by smaller numbers (divisors).
• For 3 and 4 digit dividends, a step-by-step approach utilizing two-digit divisors is employed.
• The long division process is organized with the dividend under the division bar and the divisor outside it.

Step-by-Step Procedure

• Set Up: Position the dividend and divisor in the long division format.
• Divide: Determine how many times the divisor fits into the initial segment of the dividend.
• Multiply: Multiply the divisor by the estimated quotient value and write the result below the dividend section.
• Subtract: Subtract the product from the corresponding section of the dividend.
• Bring Down: Carry down the next digit from the dividend to the result of the subtraction.
• Repeat: Continue the division, multiplication, and subtraction steps with the newly formed number until all dividend digits are used.
• Final Steps: When no more digits are available, take note of any remaining value (remainder). The remainder can be expressed as a fraction or placed beside the quotient.

Tips for Success

• Estimate before dividing to simplify calculations.
• Rounding the divisor can make the process easier (adjust as needed for accuracy).
• Keep calculations clear and organized for efficient problem-solving.
• Check the solution by multiplying the quotient by the divisor and adding any remainder, which should equal the original dividend.

Example

• An example is provided for dividing 1234 ÷ 34.
• The initial division shows that 34 fits into 123 two times.
• The product of 34 × 2 is 68.
• Subtracting 68 from 123 leaves 55.
• The next digit (4) from the dividend is brought down to form 554.
• These steps are repeated iteratively until the entire division is completed.

Common Errors

• Misplacing quotients is a common mistake; ensure proper alignment above the division bar.
• Inaccurate multiplication can affect subsequent steps; confirm multiplication results before subtracting.
• Not accounting for remainders; include them in the final answer if they occur.

Dividing 3 and 4 Digit Dividends by 2 Digit Divisors

• Steps for Division:
  • Set Up the Problem: Place the dividend (3 or 4 digits) under the division symbol and the divisor (2 digits) outside.
  • Estimate the Quotient: Determine how many times the divisor fits into the first one or two digits of the dividend without exceeding.
  • Multiply and Subtract: Multiply the divisor by the estimated quotient and subtract the result from the dividend segment used.
  • Bring Down the Next Digit: Bring down the next digit of the dividend to form a new number for division.
  • Repeat the Process: Continue estimating, multiplying, subtracting, and bringing down digits until all digits are used.
  • Record the Quotient: The digits written above the division bar represent the quotient. Note any remainders.

Important Tips

• Double-check estimations to ensure accurate calculations.
• Express remainders when division is not perfect.
• Practice regularly to improve speed and accuracy in calculations.

Example

• Problem: 3456 ÷ 12
  • Estimate: 12 goes into 34 approximately 2 times.
  • Multiply: 12 x 2 = 24
  • Subtract: 34 - 24 = 10
  • Bring Down: Bring down the 5 (new number is 105)
  • Repeat: 12 goes into 105 about 8 times. Repeat multiplication, subtraction, and bring down the 6.
  • Final Quotient: 288 with no remainder.

Common Division Errors

• Misestimating the Quotient: Ensure the estimated quotient is accurate before multiplying.
• Forgetting to Bring Down Digits: Always bring down the next digit to continue calculations.
• Calculation Mistakes: Carefully double-check each multiplication and subtraction step.