795 Divided By 5 Long Division Explained Step-by-Step

Introduction: Mastering the Art of Long Division

In the realm of mathematics, long division stands as a fundamental operation, a cornerstone upon which more complex calculations are built. For students and lifelong learners alike, mastering this skill is crucial for tackling a wide range of mathematical problems. In this comprehensive guide, we will dissect the division problem of 795 divided by 5, providing a clear, step-by-step solution that will empower you to confidently conquer similar challenges. Our exploration will not only focus on the mechanics of the calculation but also delve into the underlying principles that make long division so effective. Whether you're a student seeking to improve your grades, a parent assisting with homework, or simply an individual eager to refresh your mathematical skills, this guide is designed to provide the clarity and support you need. We will break down each step, offering explanations and insights that go beyond rote memorization, ensuring a deep and lasting understanding of the process. So, let's embark on this mathematical journey together and unlock the secrets of long division.

Understanding the Problem: 795 ÷ 5

Before diving into the solution, let's clearly define the problem at hand: 795 divided by 5. In mathematical terms, this can be expressed as 795 ÷ 5. Here, 795 is the dividend, the number being divided, and 5 is the divisor, the number by which we are dividing. The result of this division will be the quotient, which represents how many times the divisor (5) fits into the dividend (795). To effectively solve this problem using long division, we will systematically break down the dividend into smaller, more manageable parts. This involves assessing how many times the divisor can be subtracted from each part of the dividend, starting from the leftmost digit. By carefully following this process, we can accurately determine the quotient and any remainder, if applicable. Understanding the roles of the dividend, divisor, and quotient is paramount to mastering long division, as it provides a framework for approaching the problem with clarity and precision. In the subsequent sections, we will meticulously walk through each step of the long division process, ensuring that you grasp not only the mechanics but also the logic behind the calculations.

Step 1: Setting Up the Long Division Problem

The first crucial step in solving 795 divided by 5 using long division is to set up the problem correctly. This involves writing the dividend (795) inside the division symbol (also known as the long division bracket) and the divisor (5) outside, to the left of the bracket. This visual arrangement is essential for organizing the steps of the long division process. The setup allows us to systematically work through the digits of the dividend, determining how many times the divisor fits into each part. Think of it as creating a structured roadmap for the calculation, guiding us from the initial setup to the final answer. Proper setup not only prevents errors but also makes the process more intuitive and easier to follow. The division symbol acts as a visual cue, reminding us of the operation we are performing and the relationship between the dividend and the divisor. With the problem correctly set up, we are now ready to embark on the core steps of long division, beginning with the leftmost digit of the dividend.

Step 2: Dividing the First Digit

Now that we have set up the long division problem for 795 divided by 5, the next step is to focus on the first digit of the dividend, which is 7. We ask ourselves: how many times does 5 fit into 7? The answer is 1, as 5 multiplied by 1 equals 5, which is less than 7. This is the first part of our quotient. We write the '1' above the 7 in the quotient space. Next, we multiply the divisor (5) by the quotient digit we just found (1), which gives us 5. We write this '5' directly below the 7 in the dividend. This step is crucial because it allows us to quantify the portion of the dividend that has been accounted for by the divisor. By carefully aligning the numbers, we maintain clarity and prevent potential errors in subsequent steps. This process of dividing, multiplying, and writing down the results forms the foundation of long division, and it will be repeated for each digit of the dividend. With the first digit addressed, we move on to the next step, where we subtract to determine the remaining portion of the dividend.

Step 3: Subtracting and Bringing Down

Following the division of the first digit in our long division problem of 795 divided by 5, we now proceed to subtraction. We subtract the 5 (the result of multiplying 5 by 1) from the 7 (the first digit of the dividend). This yields a remainder of 2. This remainder represents the portion of the dividend that has not yet been divided by the divisor. Next, we bring down the next digit of the dividend, which is 9, and place it next to the remainder 2, forming the number 29. This step is vital as it combines the remainder with the next digit, allowing us to continue the division process. Bringing down the next digit effectively creates a new dividend (29 in this case) that we can work with. This iterative process of subtracting and bringing down is the heart of long division, enabling us to systematically break down the dividend and determine the quotient. By meticulously performing these steps, we ensure accuracy and avoid errors. With the new dividend formed, we are now ready to repeat the division process.

Step 4: Dividing the New Number

With the new number 29 formed after bringing down the second digit in our long division of 795 divided by 5, we now repeat the division process. We ask ourselves: how many times does 5 fit into 29? The answer is 5, as 5 multiplied by 5 equals 25, which is the largest multiple of 5 that is less than 29. We write this '5' next to the '1' in the quotient space, effectively building the quotient digit by digit. Next, we multiply the divisor (5) by the new quotient digit (5), which gives us 25. We write this '25' directly below the 29. This step is crucial for determining the portion of the new dividend that is accounted for by the divisor. By carefully aligning the numbers, we ensure clarity and prevent potential errors in subsequent steps. This process of dividing and multiplying is a fundamental part of long division, and it allows us to systematically determine the quotient. With this step completed, we move on to the next phase, where we subtract to determine the remaining portion of the new dividend.

Step 5: Subtracting Again and Bringing Down the Last Digit

Continuing our long division of 795 divided by 5, we now subtract the 25 (the result of multiplying 5 by 5) from the 29. This subtraction yields a remainder of 4. This remainder represents the portion of the new dividend that has not yet been divided by the divisor. Next, we bring down the last digit of the dividend, which is 5, and place it next to the remainder 4, forming the number 45. This step is crucial as it combines the remainder with the final digit, allowing us to complete the division process. Bringing down the last digit effectively creates the final dividend (45 in this case) that we need to divide. This iterative process of subtracting and bringing down is the essence of long division, enabling us to systematically break down the dividend and determine the quotient. By meticulously performing these steps, we ensure accuracy and avoid errors. With the final dividend formed, we are now ready for the last division.

Step 6: Final Division and Finding the Remainder

Having brought down the last digit and formed the number 45 in our long division problem of 795 divided by 5, we now perform the final division. We ask ourselves: how many times does 5 fit into 45? The answer is 9, as 5 multiplied by 9 equals 45. We write this '9' next to the '15' in the quotient space, completing the quotient. Next, we multiply the divisor (5) by the final quotient digit (9), which gives us 45. We write this '45' directly below the 45. Subtracting 45 from 45, we get a remainder of 0. This indicates that 5 divides evenly into 795, and there is no remainder. The fact that the remainder is 0 signifies a clean division, where the divisor fits perfectly into the dividend. This final step confirms our quotient and completes the long division process. With the quotient and remainder determined, we have successfully solved the problem.

Step 7: The Answer

After meticulously performing the steps of long division for 795 divided by 5, we have arrived at the solution. The quotient, which is the result of the division, is 159. The remainder is 0, indicating that 5 divides evenly into 795. Therefore, 795 ÷ 5 = 159. This answer represents the number of times 5 fits into 795, and it is the culmination of our step-by-step calculations. The quotient provides a clear and concise answer to the division problem, and the remainder confirms the completeness of the division. In summary, our journey through the long division process has not only yielded the numerical answer but also provided a deeper understanding of the underlying principles. This knowledge empowers us to tackle similar division problems with confidence and accuracy.

Conclusion: Long Division Mastery

In conclusion, we have successfully navigated the process of long division for 795 divided by 5, arriving at the quotient of 159 with a remainder of 0. This step-by-step guide has demonstrated the importance of setting up the problem correctly, dividing each digit systematically, subtracting, and bringing down the next digit until the division is complete. By understanding the logic behind each step, you can confidently tackle a wide range of division problems. Long division is a fundamental skill in mathematics, and mastering it opens doors to more advanced concepts. Remember, practice is key to proficiency. The more you practice long division, the more comfortable and efficient you will become. So, take on new challenges, apply the principles you've learned, and continue to expand your mathematical horizons. With dedication and perseverance, you can achieve mastery in long division and beyond. Keep exploring the fascinating world of mathematics, and let the power of numbers guide your way.