Long division is a mathematical method used to divide large numbers into smaller and more manageable parts. It is an essential arithmetic skill that helps us solve division problems that cannot be easily solved mentally or with basic division techniques. By using long division, we can break down complex division problems into simpler steps, making it easier to find the quotient and remainder.

Now, let’s dive into a specific division problem: dividing 500 by 3. You might be wondering why this particular division is relevant. Well, understanding how to divide 500 by 3 using long division not only helps us practice the technique itself, but it also allows us to apply it to real-world scenarios.

For example, imagine you have 500 apples and want to share them equally among 3 friends. By using long division, you can determine how many apples each person will receive and if there are any remaining apples. This problem-solving skill is not only useful in mathematics but also in various fields such as finance, engineering, and scientific research.

Step 1: Writing the Division Problem

When we want to divide a number, such as 500, by another number, like 3, we need to write it as a division problem. This helps us organize the calculation and understand the process better.

To write the division problem for 500 ÷ 3, we use the dividend and divisor values. The dividend is the number that we want to divide (in this case, 500), and the divisor is the number we divide by (in this case, 3).

So, we can write the problem as:

500 ÷ 3

The division symbol (÷) represents the action of dividing the dividend by the divisor. It indicates that we are going to split the number 500 into equal groups of 3.

By writing the division problem in this way, we set the stage for the long division process, which will help us find the quotient and remainder. Now that we have the division problem set up, let’s move on to the next step.

If you would like to visualize the long division process for 500 ÷ 3, you can visit Visual Fractions, where you can find step-by-step instructions and a calculator to assist you.

Step 2: Dividing the First Digit

When dividing the first digit of the dividend by the divisor, it is important to understand the concept of the quotient and the remainder. Let’s take the example of dividing 500 by 3.

To start, we look at the first digit of the dividend, which is 5. Now we need to determine how many times the divisor, which is 3, can be divided into 5.

When we divide 5 by 3, we find that it cannot be divided evenly. In other words, 3 cannot go into 5 without leaving a remainder. This means that there will be a remainder when we perform the division.

The remainder is the amount left over after the division is complete. In this case, the remainder is 2, because 5 divided by 3 equals 1 remainder 2. The remainder is important to consider as it represents the leftover part that cannot be divided evenly.

If you’re looking for further assistance with dividing fractions or simplifying fractions, you can utilize the Fraction Calculator on This calculator allows you to enter a fraction and reduce it to its simplest form. It also provides step-by-step solutions and the ability to perform various operations with fractions.

So, when dividing the first digit of the dividend by the divisor, be aware of any remainders that may arise. Understanding the concept of remainders is crucial in long division and helps us accurately represent the division problem. Let’s move on to the next step where we’ll bring down the next digit and continue the division process.

Step 3: Bringing Down the Next Digit

In this step of long division, we will learn how to bring down the next digit of the dividend and place it next to the previous quotient. This step is crucial to continue the division process and find the accurate result.

After dividing the first digit of the dividend by the divisor in the previous step, we need to bring down the next digit of the dividend. This digit will be placed next to the quotient we obtained earlier.

To understand this better, let’s consider the example of dividing 500 by 3. In the previous step, we obtained a quotient of 1. Now, the next digit is 0. We bring down the 0 and place it next to the quotient, making it 10.

The new dividend becomes 100, which is derived by multiplying the previous quotient (1) by the divisor (3) and adding the next digit (0).

It’s important to note that each time we bring down a digit, we are essentially creating a new divisor. In our example, the new divisor becomes 30 because we have brought down a zero to form 10.

By bringing down the next digit and creating a new dividend, we are able to continue the division process. This step ensures that we consider all the digits of the dividend and accurately find the quotient.

Remember, practice makes perfect when it comes to long division. By following these step-by-step instructions, you will gain a solid understanding of the process and be able to solve long division problems with ease.

If you want to try out long division for yourself or check your answers, you can use a helpful online tool like the Long Division Calculator at It provides step-by-step explanations and accurate results, making it a great resource to support your learning.

Additionally, if you prefer visual instructions, you can refer to the article on how to do long division. It includes detailed steps and illustrated examples to help you grasp the concept.

Now that we have successfully brought down the next digit, we are ready to move on to the next step of dividing the new dividend. Stay tuned!

Step 4: Dividing the New Dividend

After completing the previous step of bringing down the next digit, we can now continue the division process with the new dividend. This step is crucial in obtaining the final quotient when dividing 500 by 3 using long division.

To divide the new dividend, we follow a series of steps:

  1. Divide the first digit of the new dividend by the divisor (3). In this case, we divide 5 by 3. The quotient is 1 (since 3 can be divided evenly into 5 once) and the remainder is 2.
  2. Write the quotient above the line.
  3. Multiply the divisor (3) by the quotient (1). The result is 3.
  4. Subtract the result from the new dividend. In this case, we subtract 3 from 5, resulting in a new dividend of 2.
  5. Bring down the next digit of the original dividend (0) and place it next to the previous remainder (2). This creates a new dividend of 20.
  6. Repeat steps 1 to 5 with the new dividend (20) until the process is complete.

Following these steps, we can continue dividing the new dividend (20) by the divisor (3).

  1. Divide the first digit of the new dividend (2) by the divisor (3). Since 2 is smaller than 3, we cannot divide them evenly. Thus, the quotient is 0 and the remainder is 2.
  2. Write the quotient (0) above the line.
  3. Multiply the divisor (3) by the quotient (0). The result is 0.
  4. Subtract the result (0) from the new dividend (2). The new dividend remains as 2.
  5. There are no more digits to bring down, so the division process is complete.

By following these steps, we have successfully divided 500 by 3 using long division. The final quotient is the series of quotients obtained in each step, which in this case is 166. The remainder is the last remainder obtained, which is 2.

Understanding and practicing long division is essential for mastering division skills. By following the step-by-step process, you can solve division problems accurately and efficiently. Remember, practice makes perfect!

If you need further assistance or want to practice more division problems, you can use online tools such as the CoolConversion Long Division Calculator, EverydayCalculation Long Division Calculator, or CalculatorSoup Long Division Calculator. These calculators provide step-by-step guidance and can help you check your answers.

Step 5: Understanding the Remainder

In the process of dividing 500 by 3 using long division, we encounter the concept of remainder. Understanding the remainder is crucial in determining the final quotient.

When we divide 500 by 3, we find that the quotient is 166 with a remainder of 2. This can be expressed as 500 ÷ 3 = 166 R 2. But what does this remainder actually mean?

To better comprehend the significance of remainders, let’s explore some real-world examples. Suppose you have 500 cookies and you want to distribute them equally among 3 friends. Each friend will receive 166 cookies, but there will be 2 cookies left over, represented by the remainder.

The remainder represents the quantity that cannot be divided equally or shared completely. It indicates the amount that is left over after dividing as much as possible.

In division, the divisor determines the size of the groups or portions, and the dividend represents the total quantity being divided. The quotient gives us the number of complete groups or portions, while the remainder represents the amount that could not be evenly divided among the groups.

For further understanding, you can refer to resources such as the Khan Academy article on interpreting remainders in division and the calculator on for long division and remainder calculations. Additionally, the remainder calculator on Omni Calculator can be useful for exploring the concept of remainder in various scenarios.

In conclusion, the remainder in division plays a significant role in understanding the completeness of the division process. It represents the quantity that is left over after dividing as much as possible and provides valuable information in real-world scenarios.


Dividing 500 by 3 using long division can seem daunting at first, but with practice and understanding, it becomes easier to grasp. By following the step-by-step process, we have successfully divided 500 by 3 and obtained the result of 166.6.

The key takeaway from this division is the importance of practice. Math skills, especially division, require regular practice to become proficient. The more you practice, the more comfortable you will become with long division and its various steps.

However, practice alone is not enough. It is essential to understand the underlying concepts of division, such as the relationship between the dividend and divisor, the process of bringing down digits, and determining remainders. Understanding these concepts will enable you to apply them in different scenarios and solve division problems more efficiently.

Division is a foundational skill in mathematics with real-world applications. It is used in everyday situations, such as dividing items equally among friends or calculating ratios and proportions. By mastering division, you develop problem-solving and analytical thinking skills that are beneficial beyond the realm of mathematics.

In conclusion, dividing 500 by 3 using long division requires practice and understanding. By consistently practicing and gaining a deep understanding of the division process, you will become more confident and proficient in solving division problems. Remember, division is not just about obtaining the correct quotient; it is about developing critical thinking skills that will serve you in various areas of life.

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