How To Divide 91 By 7 Using Long Division Step-by-Step

Hey guys! Ever wondered how to solve 91 ÷ 7 using long division? It might seem tricky at first, but I promise it's super manageable once you break it down. In this guide, we'll go through each step together, so you'll be a long division pro in no time. Long division might seem like a daunting task, especially when you're faced with numbers that don't immediately reveal their factors. However, it's a fundamental skill in mathematics that can unlock the solutions to many division problems. The beauty of long division lies in its systematic approach, breaking down the dividend into smaller, more manageable parts. This step-by-step method not only helps you find the quotient but also enhances your understanding of how numbers interact with each other. Think of it as a journey, where each step brings you closer to the final answer. The ability to perform long division is not just about getting the correct answer; it's about developing a logical and methodical approach to problem-solving, a skill that extends far beyond the realm of mathematics. So, let's dive in and demystify this powerful tool together!

Setting Up the Problem

First things first, let's set up our problem. We're dividing 91 (the dividend) by 7 (the divisor). Write it out in the long division format – the 91 goes inside the "house," and the 7 goes outside. Setting up the problem correctly is the first crucial step in solving any long division problem. It's like laying the foundation for a building; if the foundation is shaky, the entire structure could be unstable. The dividend, which is the number being divided (in this case, 91), is placed inside the division symbol, often referred to as the "house." The divisor, the number by which we are dividing (7), sits outside the house. This arrangement visually represents the division problem and guides us through the subsequent steps. A clear and organized setup prevents confusion and helps to streamline the process. It allows you to focus on the arithmetic without getting bogged down by visual clutter. So, take a moment to ensure everything is properly aligned before moving on – it's a small investment of time that pays dividends in accuracy and efficiency.

Dividing the First Digit

Now, let’s look at the first digit of the dividend, which is 9. How many times does 7 go into 9? It goes in once, right? So, we write a "1" above the 9. This is where the actual division process begins. We start by examining the leftmost digit of the dividend, which in this case is 9. We ask ourselves, "How many times does the divisor (7) fit into this digit?" In other words, what's the largest multiple of 7 that is less than or equal to 9? The answer is 1, since 7 multiplied by 1 equals 7, which is less than 9. We then write this quotient (1) above the 9 in the dividend. This placement is crucial as it signifies the beginning of our quotient, the result of the division. This step is not just about finding a number; it's about understanding the relationship between the divisor and the dividend. It sets the stage for the subsequent steps, where we will continue to break down the dividend into smaller parts. The accuracy of this first step is paramount, as it influences the rest of the calculation. So, take your time, double-check your work, and ensure you've found the correct quotient before proceeding.

Multiplying and Subtracting

Next, we multiply the 1 (that we just wrote above) by the divisor, 7. 1 times 7 is 7. Write that 7 below the 9. Then, subtract 7 from 9, which gives us 2. This step involves two key operations: multiplication and subtraction. We first multiply the quotient we just obtained (1) by the divisor (7). This gives us 7, which we write directly below the digit we were working with in the dividend (9). This multiplication step helps us determine how much of the dividend we have accounted for so far. Next, we subtract this product (7) from the corresponding digit in the dividend (9). This subtraction tells us the remainder, the amount "left over" after we've divided as much as possible. In this case, 9 minus 7 equals 2. This remainder is crucial because it becomes the starting point for the next step in the long division process. It represents the portion of the dividend that we still need to divide. The accuracy of both the multiplication and subtraction is essential for maintaining the integrity of the calculation. A mistake in either step can throw off the entire process. So, take your time, be meticulous, and double-check your work to ensure you're on the right track.

Bringing Down the Next Digit

Now, bring down the next digit from the dividend (which is 1) and write it next to the 2. We now have 21. Bringing down the next digit is a crucial step in the long division process. It allows us to continue dividing even when the previous digit has been fully divided. In this case, we bring down the 1 from the dividend and place it next to the remainder we calculated in the previous step, which was 2. This combines the remainder with the next digit, forming a new number to divide (21). Think of it as replenishing our "stock" of numbers to divide. Without bringing down the next digit, we would be stuck with the remainder and unable to proceed further. This step ensures that we consider all digits of the dividend in our calculation. It also highlights the iterative nature of long division, where we repeat the same steps (divide, multiply, subtract, bring down) until we have reached the end of the dividend. The act of bringing down the digit also emphasizes the place value of each digit in the dividend. It reinforces the understanding that each digit represents a different power of ten and contributes to the overall value of the number.

Dividing Again

How many times does 7 go into 21? It goes in exactly 3 times! Write the 3 above the 1 in the dividend. We've now come to the stage where we need to divide the new number we formed (21) by the divisor (7). This step is similar to the initial division step, but now we're working with a larger number. We ask ourselves, "How many times does 7 fit into 21?" The answer is 3, since 7 multiplied by 3 equals 21. We write this quotient (3) above the 1 in the dividend, carefully aligning it with the place value. This placement is crucial for keeping track of our quotient and ensuring we arrive at the correct final answer. This division step is a key part of the iterative process of long division. We're essentially repeating the same process we started with, but with a new number. This repetition helps to solidify our understanding of the division process and build our confidence in tackling more complex problems. The accuracy of this step is paramount, as it directly impacts the final result. So, take your time, double-check your multiplication facts, and ensure you've found the correct quotient before moving on.

Final Steps: Multiplying and Subtracting Again

Multiply the 3 by the divisor, 7. 3 times 7 is 21. Write that below the 21 we already have. Subtract 21 from 21, and you get 0. We're in the final stretch now! We multiply the quotient we just obtained (3) by the divisor (7). This gives us 21, which we write directly below the 21 we were working with. This multiplication step helps us determine how much of the number we're dividing (21) we have accounted for. Next, we subtract this product (21) from the number above it (21). This subtraction tells us the remainder, the amount "left over" after we've divided as much as possible. In this case, 21 minus 21 equals 0. A remainder of 0 indicates that the division is exact, meaning that the divisor divides evenly into the dividend. This is a satisfying outcome, as it confirms that we have successfully divided the numbers without any leftovers. The accuracy of both the multiplication and subtraction is crucial for arriving at the correct final answer. A mistake in either step can lead to an incorrect remainder and ultimately an incorrect quotient. So, take your time, be meticulous, and double-check your work to ensure you've completed these final steps accurately.

The Answer

Since we have a remainder of 0, our division is complete! The answer, or the quotient, is the number we wrote above the "house," which is 13. Voila! We've reached the end of our long division journey! The remainder of 0 signifies that the division is complete and that the divisor (7) divides evenly into the dividend (91). This is a clear indication that we have found the exact quotient. The quotient, the final answer to our division problem, is the number we wrote above the "house," carefully aligned with the digits of the dividend. In this case, the quotient is 13. This means that 91 divided by 7 equals 13. This final step is not just about stating the answer; it's about reflecting on the entire process and confirming that we have arrived at the correct solution. It's a moment of satisfaction, knowing that we have successfully tackled a long division problem using a systematic and methodical approach. The ability to arrive at the correct answer through long division is a testament to our understanding of the relationship between numbers and our ability to apply mathematical principles. So, celebrate your success and take pride in your accomplishment!

Conclusion

There you have it! 91 ÷ 7 = 13. Long division might seem tough at first, but with practice, you’ll get the hang of it. Keep practicing, and you'll be solving even more complex problems in no time! So, there you have it, guys! We've successfully navigated the world of long division and conquered the problem of 91 divided by 7. It might have seemed like a daunting task at the beginning, but we've broken it down step by step, demystified the process, and arrived at the correct answer: 13. Long division, like any mathematical skill, might feel challenging at first. But with consistent practice and a methodical approach, it becomes much more manageable. The key is to break down the problem into smaller, more digestible steps, focusing on accuracy and understanding at each stage. The more you practice, the more confident you'll become in your ability to tackle even the most complex division problems. Remember, mathematics is not just about memorizing formulas and procedures; it's about developing logical thinking, problem-solving skills, and a deep understanding of the relationships between numbers. So, keep practicing, keep exploring, and keep challenging yourself. The world of mathematics is vast and fascinating, and the more you delve into it, the more rewarding it becomes. So, go forth and conquer those mathematical challenges!