Long division is a method for dividing large numbers. It breaks down the division process into smaller, manageable steps. This guide details how to perform long division, step-by-step.
Setting Up the Problem
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Write the Dividend and Divisor: The dividend (the number being divided) is placed under the division bar, and the divisor (the number you're dividing by) is placed outside the bar. For example, to divide 845 by 3, write it as:
3 | 845
Performing the Long Division
Let's use the example of 845 รท 3.
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Divide: Begin by dividing the first digit of the dividend (8) by the divisor (3). 3 goes into 8 two times (3 x 2 = 6). Write the "2" above the 8.
2 3 | 845 -
Multiply: Multiply the quotient (2) by the divisor (3): 2 x 3 = 6. Write this result below the first digit of the dividend.
2 3 | 845 6 -
Subtract: Subtract the result from the corresponding digit in the dividend (8 - 6 = 2).
2 3 | 845 6 - 2 -
Bring Down: Bring down the next digit from the dividend (4) next to the remainder (2), creating the number 24.
2 3 | 845 6 - 24 -
Repeat: Repeat steps 1-4 with the new number (24). 3 goes into 24 eight times (3 x 8 = 24). Write the "8" above the 4. Multiply (8 x 3 = 24), subtract (24 - 24 = 0), and bring down the next digit (5).
28 3 | 845 6 - 24 24 - 05 -
Final Steps: Repeat steps 1-4 one last time. 3 goes into 5 one time (3 x 1 = 3). Write the "1" above the 5. Subtract (5 - 3 = 2). This is the remainder.
281 R 2 3 | 845 6 - 24 24 - 05 3 - 2
Interpreting the Result
The final answer is 281 with a remainder of 2. This can be written as 281 R 2 or as a mixed number (281 and 2/3) or a decimal (281.666...).
The process explained above uses the steps outlined in the provided references, including setting up the problem, dividing, multiplying, subtracting, bringing down the next digit, repeating the steps, and handling the remainder.
