The Complete Guide to Dividing 500 by 3 Using Long Division


Are you struggling with dividing 500 by 3 using long division? In this comprehensive guide, we will walk you through the step-by-step process of dividing 500 by 3, ensuring that you grasp the concept and gain confidence in your mathematical abilities.

What is Long Division?

Long division is a method of dividing numbers with multiple digits. It breaks down the division process into manageable steps, providing a structured approach that simplifies the process and ensures accurate results. By using long division, we can tackle more complex division problems and understand and manipulate numbers with multiple digits.

Dividing 500 by 3: Step-by-Step Process

In this section, we will break down the long division process for dividing 500 by 3 into several actionable steps. By following these steps, you will be able to determine the quotient and remainder accurately.

  1. Step 1: Set up the division problem
  2. To begin the division process, write the dividend (500) inside the long division bracket and the divisor (3) outside the bracket. Place the quotient placeholder on top.

  3. Step 2: Divide the first digit
  4. Look at the first digit of the dividend (5) and see how many times the divisor (3) can evenly divide into it. In this case, 3 can go into 5 once. Write the quotient (1) on top of the division bracket, above the line.

  5. Step 3: Multiply the quotient
  6. Multiply the quotient (1) with the divisor (3), and write the result (3) below the first digit of the dividend (5).

  7. Step 4: Subtract and bring down
  8. Subtract the result (3) from the first digit of the dividend (5) to get the difference (2). Bring down the next digit of the dividend (0) beside the difference.

  9. Step 5: Divide and repeat
  10. Look at the new number (20) formed by the difference and the next digit of the dividend. Repeat steps 2 to 4 to find the next digit of the quotient. In this case, 3 can go into 20 six times.

  11. Step 6: Repeat until the dividend is fully divided
  12. Continue to bring down the next digit of the dividend and repeat steps 2 to 5 until you have divided the entire dividend.

  13. Step 7: Determine the remainder
  14. After the entire dividend (500) is divided, check if there are any remaining digits. In this case, there is a remainder of 2.

  15. Step 8: Write the final quotient
  16. Write the quotient (166) as the final result of the division.

Tips for Successful Long Division

Long division can seem daunting, but with the right tips and strategies, you can perform it effectively and accurately. Here are some practical tips to help you succeed:

  • Stay Organized: Write down the dividend and divisor neatly and create a horizontal line to track your progress.
  • Break It Down: Divide the problem into smaller steps to make it more manageable.
  • Double-Check Your Work: Review your calculations to avoid mistakes and ensure accuracy.
  • Use Estimation: Round numbers to make calculations simpler and get a rough idea of the quotient.
  • Practice Regularly: Dedicate time to practice long division regularly to improve your skills.
  • Seek Help if Needed: Don’t hesitate to ask for assistance if you’re struggling with long division.

Real-World Applications

Dividing 500 by 3 using long division has practical implications in various fields. Let’s explore some real-world applications where this calculation is useful:

  1. Finance: Calculate financial ratios to analyze profitability and performance metrics.
  2. Engineering: Determine load distribution or divide distances in engineering systems and structures.
  3. Science: Divide sample populations for research experiments and data analysis.

Common Mistakes to Avoid

When dividing numbers using long division, there are common mistakes to watch out for. Here are a few examples:

  1. Swapping Numbers: Be careful not to subtract the larger number from the smaller one instead of the other way around.
  2. Incorrect Workings: Show the correct step-by-step workings in long division to avoid confusion.
  3. Order of Operations: Follow the correct order of operations to ensure accurate results.

Alternative Methods for Division

In addition to long division, there are alternative methods for dividing numbers:

  • Using a Calculator: Utilize the speed and accuracy of calculators for division calculations.
  • Employing Mental Math Techniques: Develop mental math skills for quick and approximate division calculations.

Practice Exercises

To enhance your division skills, practice dividing numbers by completing the following exercises:

  1. Divide 500 by 3
  2. Divide 450 by 3
  3. Divide 600 by 3
  4. Divide 420 by 3
  5. Divide 540 by 3


In conclusion, we have provided a step-by-step guide to help you divide 500 by 3 using long division. By following the outlined process and practicing regularly, you will enhance your division skills and gain confidence in tackling more complex division problems. Remember to stay organized, avoid common mistakes, and explore alternative methods for division. With effort and perseverance, you will become proficient in long division and be able to apply it to real-world scenarios.

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