How To Do Long Division: A Step-by-Step Guide
Long division might seem daunting, but with a structured approach, it becomes manageable. This guide breaks down the process into easy-to-follow steps, helping you master this essential arithmetic skill. We'll cover the basics, tackle more complex problems, and offer tips to improve your accuracy and speed.
Understanding the Parts of a Long Division Problem
Before diving into the steps, let's familiarize ourselves with the terminology:
- Dividend: The number being divided (the larger number).
- Divisor: The number you're dividing by (the smaller number).
- Quotient: The result of the division (the answer).
- Remainder: The amount left over after dividing as completely as possible.
Step-by-Step Guide to Long Division
Let's illustrate the process with an example: 675 ÷ 5
1. Set up the Problem:
Write the problem in the standard long division format:
_____
5 | 675
2. Divide the First Digit:
Divide the first digit of the dividend (6) by the divisor (5). 5 goes into 6 one time (1). Write the 1 above the 6.
1
5 | 675
3. Multiply and Subtract:
Multiply the quotient (1) by the divisor (5): 1 x 5 = 5. Write the 5 below the 6 and subtract: 6 - 5 = 1.
1
5 | 675
- 5
1
4. Bring Down the Next Digit:
Bring down the next digit of the dividend (7) next to the remainder (1), making it 17.
1
5 | 675
- 5
17
5. Repeat Steps 2-4:
Divide 17 by 5. 5 goes into 17 three times (3). Write the 3 above the 7.
Multiply 3 x 5 = 15. Subtract 15 from 17: 17 - 15 = 2.
13
5 | 675
- 5
17
-15
2
6. Bring Down the Last Digit:
Bring down the last digit (5) next to the remainder (2), making it 25.
13
5 | 675
- 5
17
-15
25
7. Final Division:
Divide 25 by 5. 5 goes into 25 five times (5). Write the 5 above the 5.
Multiply 5 x 5 = 25. Subtract 25 from 25: 25 - 25 = 0.
135
5 | 675
- 5
17
-15
25
-25
0
8. The Result:
The quotient is 135, and the remainder is 0. Therefore, 675 ÷ 5 = 135.
Handling Remainders
Sometimes, you'll have a remainder. For instance, if we had 677 ÷ 5:
After following the steps, you'd end up with a remainder of 2. You can express the answer as 135 R 2 (135 with a remainder of 2) or as a decimal (135.4).
Tips for Success
- Practice Regularly: The key to mastering long division is consistent practice. Start with simple problems and gradually increase the difficulty.
- Check Your Work: Always double-check your calculations to ensure accuracy. You can multiply your quotient by the divisor and add any remainder to verify your answer.
- Break Down Complex Problems: If you're dealing with very large numbers, break the problem down into smaller, more manageable parts.
By following these steps and practicing regularly, you'll become proficient in long division. Remember, patience and persistence are key!
