How to Do Long Division Step by Step?

Long division is a method used to divide larger numbers by smaller numbers. It's a step-by-step process that can be broken down into a series of simple steps.

Step 1: Set Up the Problem

1. Write the dividend (the number being divided) inside a division symbol.
2. Write the divisor (the number you are dividing by) outside the division symbol.

Example: Divide 125 by 5.

     ______
5 | 125 

Step 2: Divide the First Digit

1. Divide the first digit of the dividend by the divisor.
2. Write the quotient (the result of the division) above the first digit of the dividend.
3. Multiply the quotient by the divisor and write the product below the first digit of the dividend.

Example:

     2______
5 | 125 
     10

Step 3: Subtract and Bring Down

1. Subtract the product from the first digit of the dividend.
2. Bring down the next digit of the dividend next to the difference.

Example:

     2______
5 | 125 
     10
     --
      25

Step 4: Repeat Steps 2 and 3

1. Repeat steps 2 and 3 with the new number formed by the difference and the brought-down digit.
2. Continue this process until there are no more digits to bring down.

Example:

     25______
5 | 125 
     10
     --
      25
      25
      --
       0

Step 5: The Quotient and Remainder

1. The number above the division symbol is the quotient.
2. If there is a remainder, it is written below the last subtraction line.

Example: In this case, the quotient is 25 and the remainder is 0.

Practical Insights

• If the divisor is larger than the first digit of the dividend, consider the first two digits.
• If you encounter a remainder that is smaller than the divisor, you can add a decimal point and a zero to the dividend and continue the process.
• For larger numbers, you can break down the division into smaller steps, making it easier to manage.

Conclusion

Long division is a fundamental mathematical operation used for dividing numbers. By following these steps, you can confidently solve any long division problem.