How to do long division with 4 digits

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how to do long division with 4 digits

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How to Do Long Division with 4 Digits

Answer: Long division can initially seem challenging, particularly with 4-digit numbers, but with a systematic approach, it becomes manageable. Here’s a step-by-step guide on how to perform long division with 4-digit dividends:

Step-by-Step Guide

1. Setting Up the Problem:

  • Write the 4-digit dividend inside the long division bracket.
  • Write the divisor outside the bracket, to the left.

Example: Divide 7532 (dividend) by 23 (divisor).

\begin{array}{r|l} 23 & 7532 \\ \end{array}

2. Determine How Many Times the Divisor Fits into the Initial Digits of the Dividend:

  • Start by examining the first one or two digits of the dividend as needed.
  • Identify how many times the divisor fits into these digits without surpassing them.

Example: 23 does not fit into 7. Move to the next digit to make it 75. 23 fits into 75 three times (since 23 \times 3 = 69).

3. Write the Quotient Above the Bracket:

  • Place the number of times the divisor fits above the corresponding set of digits in the dividend.
\begin{array}{r|l} 23 & 7532 \\ & 3 \\ & 69 \\ \end{array}

4. Subtract the Result:

  • Subtract the multiplication result from the initial digits of the dividend.
\begin{array}{r|l} 23 & 7532 \\ & 3 \\ & 69 \\ & \underline{75 - 69} \\ & 06 \end{array}

5. Bring Down the Next Digit:

  • Bring down the next digit of the dividend next to the result of the subtraction.
\begin{array}{r|l} 23 & 7532 \\ & 3 \\ & 69 \\ & \underline{75 - 69} \\ & 063 \\ \end{array}

6. Repeat the Division, Multiplication, and Subtraction Steps:

  • Repeat the previous steps for the new number formed.

Example: 23 fits into 63 twice (23 \times 2 = 46).

\begin{array}{r|l} 23 & 7532 \\ & 32 \\ & 69 \\ & \underline{75 - 69} \\ & 063 \\ & 2 \\ & 46 \\ & \underline{63 - 46} \\ & 17 \\ \end{array}

7. Continue Until All Digits are Used:

  • Repeat the process until there are no more digits to bring down from the dividend.
\begin{array}{r|l} 23 & 7532 \\ & 327 \\ & 69 \\ & \underline{75 - 69} \\ & 063 \\ & 2 \\ & 46 \\ & \underline{63 - 46} \\ & 173 \\ & 03 \\ \end{array}

Final Result:

  • The quotient (final answer above the bracket) represents the number of times the divisor fits into the dividend.
  • Any remainder is the number left over after the final subtraction.

Example: The quotient for 7532 ÷ 23 is 327 with a remainder of 1.

Conclusion:

By following this systematic approach to long division with 4-digit numbers:

  1. Set Up the Problem: Place the dividend inside the bracket and the divisor outside.
  2. Work Digit by Digit: Determine, multiply, subtract, and then bring down the next digit.
  3. Continue the Process: Repeat until all digits are utilized.
  4. Result: The top numbers (quotient) and remainder, if any.

Practice will make this process smoother, and soon you will be able to perform long division with confidence!