Dividing 91 By 7: A Step-by-Step Guide

by Alex Johnson 39 views

Hey there! Ever found yourself staring at a division problem and feeling a bit puzzled? Don't worry, we've all been there. Today, we're going to break down a classic division problem: 91 divided by 7. It might seem intimidating at first, but trust me, with a step-by-step approach, it's totally manageable. So, grab your pencil and paper, and let's dive into the world of division!

Understanding Division

Before we jump into the specific problem, let's quickly recap what division is all about. At its core, division is simply splitting a larger number into equal groups. Think of it as the opposite of multiplication. When we see a problem like 91 ÷ 7, we're essentially asking, "How many groups of 7 can we make from 91?" or "If we divide 91 into 7 equal groups, how many will be in each group?" This understanding will help us as we work through the problem.

Now, let's get started with the division process. The standard method we often use is called long division. It might look a bit like a puzzle at first, but once you get the hang of the steps, you'll be solving division problems like a pro. We'll break down 91 ÷ 7 into smaller, more manageable steps. First, we set up the problem using the long division symbol, which looks like a little roof over the number we're dividing (the dividend) and the number we're dividing by (the divisor) sitting outside. So, we write 7 outside the division symbol and 91 underneath it.

The next step is to look at the first digit of the dividend (91), which is 9. We ask ourselves, "How many times does 7 go into 9?" Well, 7 goes into 9 once. So, we write 1 above the 9 in the quotient area (the space above the division symbol). Now, we multiply this 1 by the divisor (7), which gives us 7. We write this 7 below the 9 in the dividend. This step helps us keep track of how much of the dividend we've accounted for so far. The next step is subtraction. We subtract the 7 we just wrote from the 9 above it. 9 minus 7 equals 2. We write this 2 below the 7. This tells us how much of the first part of the dividend is left over after dividing by 7 once.

After subtraction, we bring down the next digit from the dividend, which is 1. We write this 1 next to the 2, forming the number 21. Now, we have a new number to work with. We ask ourselves again, "How many times does 7 go into 21?" If you know your multiplication tables, you'll recognize that 7 goes into 21 exactly 3 times. So, we write 3 next to the 1 in the quotient area. This tells us that 7 goes into 21 three times. Next, we multiply the 3 we just wrote by the divisor (7), which gives us 21. We write this 21 below the 21 we already have. The final step is another subtraction. We subtract the 21 we just wrote from the 21 above it. 21 minus 21 equals 0. We write this 0 below the 21. This is a key moment! The fact that we have 0 as a remainder tells us that 7 divides into 91 perfectly, with no leftover. Now, let's put it all together. Looking at the quotient area (the space above the division symbol), we see the number 13. This is our answer! So, 91 divided by 7 equals 13. Congratulations, you've just solved a division problem using long division!

Breaking Down the Steps

Let's break down the steps of dividing 91 by 7 into a more digestible format:

  1. Set up the problem: Write 91 inside the division symbol and 7 outside.
  2. Divide the first digit: 7 goes into 9 one time. Write 1 above the 9.
  3. Multiply: 1 multiplied by 7 is 7. Write 7 below the 9.
  4. Subtract: 9 minus 7 is 2. Write 2 below the 7.
  5. Bring down: Bring down the next digit (1) to form 21.
  6. Divide: 7 goes into 21 three times. Write 3 next to the 1 above the division symbol.
  7. Multiply: 3 multiplied by 7 is 21. Write 21 below the 21.
  8. Subtract: 21 minus 21 is 0. Write 0 below the 21.
  9. Read the quotient: The answer is 13.

Step 1: Setting Up the Problem

First things first, let's get our problem set up correctly. This is a crucial step because a well-organized setup makes the whole process smoother. Imagine you're building a house; a solid foundation is key! Similarly, in long division, a neat setup helps prevent errors and keeps your work clear. Write the dividend (the number being divided, which is 91 in our case) inside the division symbol. This symbol looks like a little roof or a curved line with a horizontal line extending from the top. Now, place the divisor (the number we're dividing by, which is 7) outside the division symbol, to the left. This setup visually represents the question we're asking: "How many times does 7 fit into 91?" or "If we split 91 into groups of 7, how many groups will we have?"

Think of it like this: 91 is the total number of items we have, and 7 is the size of each group we want to make. By setting up the problem in this way, we create a clear framework for our calculations. It's like having a roadmap before a journey; it guides us through the steps and helps us reach our destination – the correct answer. A neatly set-up problem also makes it easier to check your work later. If your numbers are aligned and clear, you can quickly spot any potential mistakes. So, take your time with this first step, and make sure everything is in its place. A little bit of preparation here can save you from headaches down the road!

Step 2: Divide the First Digit

Now that we've got our problem neatly set up, it's time to start the division process. We're going to tackle the dividend (91) digit by digit, starting with the leftmost digit, which is 9. Our question now is: "How many times does the divisor (7) go into this first digit (9)?" Think of it like figuring out how many whole groups of 7 we can make from 9 items. If you know your multiplication facts, you might already have an idea. 7 times 1 is 7, and 7 times 2 is 14. Since 14 is larger than 9, 7 can only go into 9 one time completely.

So, we write the number 1 above the 9 in the quotient area (the space above the division symbol where our answer will appear). This 1 represents the number of times 7 fits into 9. It's important to place this digit correctly, as it forms part of our final answer. Think of this step as the first piece of our puzzle falling into place. We've determined that 7 goes into the first part of our dividend once. But we're not done yet! This is just the first step in the process. We've accounted for one group of 7, but we still have more of the dividend to consider. This initial step is like starting a journey; we've taken the first step, but we have more ground to cover. The key is to break down the problem into smaller, manageable chunks, and this step is a perfect example of that. By focusing on just the first digit, we make the problem less daunting and more approachable. So, we've successfully divided the first digit; now, let's move on to the next step and see what comes next!

Step 3: Multiply

Great job on getting through the first division step! Now, we move on to multiplication, which is a crucial part of the long division process. This step helps us figure out how much of the dividend we've accounted for so far. Remember the 1 we wrote above the 9 in the quotient area? We're going to use that now. We multiply this number (1) by the divisor (7). So, 1 multiplied by 7 equals 7. This calculation tells us that one group of 7 is equal to 7. We then write this 7 below the 9 in the dividend. It's important to align the numbers correctly, as this helps keep our work organized and prevents mistakes.

Think of this step as checking our progress. We've determined that 7 goes into 9 once, and now we're calculating exactly how much of the 9 that accounts for. The multiplication step bridges the gap between division and subtraction, which is the next step we'll take. It's like building a bridge across a river; it connects two different points and allows us to move forward. By multiplying, we're essentially reversing the division process to see how much of the original number we've used up. This step is also a good way to double-check our initial division. If the product (the result of the multiplication) is larger than the digit we're working with in the dividend, it means we might have chosen the wrong number in the division step. So, multiplication not only helps us move forward but also provides a way to catch potential errors early on. We've multiplied and found out how much of the dividend our first division accounts for. Now, let's move on to the next step and see what we have left!

Step 4: Subtract

Alright, we've divided and multiplied; now it's time to subtract! Subtraction in long division helps us determine the remainder after the initial division. Remember, we wrote 7 below the 9 in the dividend. Now, we subtract this 7 from the 9. So, 9 minus 7 equals 2. We write this 2 below the 7. This 2 represents the amount left over after we've taken out one group of 7 from 9. It's like having 9 apples and taking away 7; you're left with 2. This remainder is crucial because it tells us how much we still have to divide. Think of this step as taking stock. We started with 9, we've accounted for 7, and now we know we have 2 left to deal with. This subtraction step is essential for keeping track of our progress and ensuring we don't over-divide or under-divide. It's like balancing a checkbook; you need to subtract the expenses to know how much money you have remaining.

The subtraction step also sets us up for the next part of the problem. The remainder we've calculated will be combined with the next digit in the dividend, creating a new number to divide. This is where long division becomes a step-by-step process, each step building on the previous one. Subtraction is a key operation in many areas of math, and it plays a vital role in long division. It helps us break down a larger problem into smaller, more manageable parts. We've subtracted and found our remainder. Now, let's move on to the next step and see how we can use this remainder to continue solving the problem!

Step 5: Bring Down

Excellent work so far! We've divided, multiplied, and subtracted. Now, we have a remainder of 2, and it's time to bring down the next digit from the dividend. This step is like calling in reinforcements; we're bringing in the next digit to help us continue the division. Look at the original dividend, 91. We've already worked with the 9, and now we need to bring down the 1. We write this 1 next to the remainder 2, forming the number 21. This new number, 21, is what we'll be dividing in the next step.

Think of this step as combining leftovers. We had a remainder of 2, and we're adding the next digit, 1, to create a new quantity to work with. This process of bringing down digits is what makes long division a step-by-step method. It allows us to break down a large division problem into smaller, more manageable chunks. The "bring down" step is also visually important. It helps keep our work organized and ensures we don't miss any digits in the dividend. By bringing down the digits one at a time, we maintain a clear and structured approach to the problem. This step is like gathering ingredients for a recipe; we're bringing together the necessary components to move forward. We've brought down the next digit and formed a new number to divide. Now, let's head back to the division step and see how many times 7 goes into 21!

Step 6: Divide (Again!)

Here we are again, back to the division step! This time, we're working with the number 21, which we formed by bringing down the next digit. Our question now is: "How many times does the divisor (7) go into 21?" This is where knowing your multiplication facts comes in handy. Think about the multiples of 7: 7, 14, 21... Aha! 7 times 3 equals 21. So, 7 goes into 21 exactly 3 times. We write this 3 next to the 1 in the quotient area (above the division symbol). This 3 is a crucial part of our final answer, so it's important to place it correctly. Think of this step as solving a mini-division problem within the larger one. We've isolated a smaller chunk (21) and figured out how many times our divisor (7) fits into it. This step reinforces the idea that long division is a process of breaking down a problem into smaller, more manageable steps. Each time we divide, we're getting closer to the final answer. This step is like finding the right key for a lock; it unlocks the next part of the problem and allows us to move forward. We've divided and found out how many times 7 goes into 21. Now, let's move on to the multiplication step and see how much of the 21 we've accounted for!

Step 7: Multiply (Again!)

We've divided, and now it's time for another round of multiplication! This step is similar to the first multiplication step, but this time we're working with the new digit we just placed in the quotient (3). We multiply this 3 by the divisor (7). So, 3 multiplied by 7 equals 21. We write this 21 below the 21 we already have (the one we formed by bringing down the digit). It's crucial to align these numbers carefully to avoid any confusion in the next step. Think of this step as verifying our previous division. We determined that 7 goes into 21 three times, and now we're confirming that three groups of 7 do indeed equal 21. This multiplication step is a way of double-checking our work and ensuring accuracy. It's like measuring ingredients when you're baking; you want to make sure you have the right amount to get the desired result.

By multiplying, we're also preparing for the next subtraction step. The product (21) will be subtracted from the number above it (also 21), which will help us determine the remainder. This step-by-step process of divide, multiply, and subtract is the heart of long division. Each step builds upon the previous one, leading us closer to the final answer. This step is like fitting puzzle pieces together; each piece we place helps reveal the bigger picture. We've multiplied and confirmed our division. Now, let's move on to the next subtraction step and see what we have left!

Step 8: Subtract (One Last Time!)

We're almost there! We've divided, multiplied, and now it's time for the final subtraction step. This step will tell us if we have any remainder left over after our division. We subtract the 21 we just calculated from the 21 above it. So, 21 minus 21 equals 0. We write this 0 below the 21. This 0 is the remainder, and it's a very important number. A remainder of 0 means that 7 divides into 91 perfectly, with no leftover. Think of this step as the final check. We've accounted for all parts of the dividend, and we're confirming that there's nothing left over. This subtraction step is the culmination of all our previous work. It's like reaching the finish line in a race; we've put in the effort, and now we're seeing the result.

The remainder is also a key indicator of whether our division is accurate. If we had a remainder other than 0, it would mean that 7 doesn't divide into 91 evenly, and we might need to double-check our calculations. But in this case, a remainder of 0 is a great sign! It confirms that we've found the correct quotient. This step is like signing off on a completed project; we've verified that everything is in order and the task is complete. We've subtracted and found a remainder of 0. Now, let's move on to the final step and read our answer!

Step 9: Read the Quotient

Congratulations! You've made it to the final step: reading the quotient. The quotient is the answer to our division problem, and it's located in the space above the division symbol. In our case, if you look above the 91, you'll see the numbers 1 and 3. We combine these digits to form the number 13. So, 13 is the quotient, which means that 91 divided by 7 equals 13. Pat yourself on the back; you've successfully solved a long division problem! Think of this step as revealing the treasure. After all our hard work, we're finally seeing the answer we've been searching for. The quotient is the solution to the puzzle, the destination of our journey. Reading the quotient is also a moment of validation. It confirms that our step-by-step process has led us to the correct answer. It's like reaching the summit of a mountain; we can look back and see the path we've taken to get there.

But the learning doesn't stop here! Understanding how to read the quotient is not just about getting the right answer; it's also about understanding what the answer means. In this case, 13 represents the number of groups of 7 that can be made from 91, or the number you get if you divide 91 into 7 equal groups. This final step is like understanding the meaning of a story; it's not just about reading the words, but also about grasping the message. We've read the quotient and found our answer. You've now completed a long division problem from start to finish! Remember, practice makes perfect, so keep working on these types of problems, and you'll become a division master in no time.

Tips for Mastering Division

Mastering division takes practice, but here are a few tips to help you along the way:

  • Know your multiplication facts: Division is closely related to multiplication, so knowing your multiplication tables will make division much easier.
  • Practice regularly: The more you practice, the more comfortable you'll become with the process.
  • Break it down: Divide the problem into smaller steps to make it less overwhelming.
  • Check your work: Use multiplication to check your answer. For example, if 91 ÷ 7 = 13, then 13 x 7 should equal 91.
  • Use visual aids: Draw diagrams or use manipulatives to help visualize the division process.

Real-World Applications of Division

Division isn't just a math concept; it's a skill we use in everyday life. Think about these scenarios:

  • Sharing: If you have 20 candies and want to share them equally among 5 friends, you'll use division (20 ÷ 5 = 4 candies each).
  • Cooking: If a recipe calls for 2 cups of flour and you want to make half the recipe, you'll use division (2 ÷ 2 = 1 cup of flour).
  • Travel: If you're driving 300 miles and want to know how long it will take at 60 miles per hour, you'll use division (300 ÷ 60 = 5 hours).
  • Finance: If you earn $100 and want to divide it equally among your savings, expenses, and fun money, you'll use division.

Conclusion

Dividing 91 by 7 might have seemed daunting at first, but by breaking it down into clear, manageable steps, we've shown that it's totally achievable. Long division is a powerful tool, and with a little practice, you can master it too. Remember, math is like a muscle; the more you use it, the stronger it gets. So, keep practicing, keep exploring, and keep challenging yourself. You've got this!

For further learning and practice on division and other math topics, consider exploring resources like Khan Academy, which offers comprehensive math lessons and exercises for all levels. Happy dividing!