To do long division, follow these clear steps:
- Set up the problem: Write the dividend (the number to be divided) under the division bar (also called the "bus stop") and the divisor (the number you are dividing by) to the left of the bar.
- Divide: Look at the leftmost digit(s) of the dividend. Determine how many times the divisor can go into this part without exceeding it. Write that number (the quotient digit) above the division bar aligned with the last digit you considered.
- Multiply: Multiply the divisor by the quotient digit you just wrote and write the product under the digits you divided into.
- Subtract: Subtract this product from the digits above it to find the remainder.
- Bring down: Bring down the next digit of the dividend next to the remainder to form a new number.
- Repeat: Repeat the divide, multiply, subtract, and bring down steps until all digits of the dividend have been brought down.
- Finish: When there are no more digits to bring down, the number left after subtraction is the remainder (if any). The numbers written on top form the quotient (the answer).
Example: Divide 768 by 3
- Divide 7 by 3 → 2 times. Write 2 on top.
- Multiply 2 × 3 = 6. Write 6 under 7.
- Subtract 7 - 6 = 1.
- Bring down 6 → new number is 16.
- Divide 16 by 3 → 5 times. Write 5 on top.
- Multiply 5 × 3 = 15. Write 15 under 16.
- Subtract 16 - 15 = 1.
- Bring down 8 → new number is 18.
- Divide 18 by 3 → 6 times. Write 6 on top.
- Multiply 6 × 3 = 18. Write 18 under 18.
- Subtract 18 - 18 = 0. No remainder.
- Quotient is 256.
This method is often remembered by the acronym DMSB : Divide, Multiply, Subtract, Bring down
. This process works for any size of numbers and can be extended to decimals as well. If the remainder is not zero after all digits are brought down, you can express the answer as a quotient with a remainder or convert the remainder into a decimal or fraction. For more detailed examples and visual guides, instructional videos and calculators are available online to practice long division step-by-step
