Step-by-Step Guide To Solve 168 Divided By 3

Hey guys! Ever found yourself staring at a division problem and feeling a bit lost? Don't worry, we've all been there! Today, we're going to break down a common problem: 168 divided by 3. We'll go through it step-by-step, making sure you understand not just the answer, but why it's the answer. So, grab your pencil and paper (or your favorite notes app) and let's dive in!

Understanding the Basics of Division

Before we jump into solving 168 divided by 3, let's quickly refresh our understanding of division itself. At its core, division is simply splitting a larger number into equal groups. Think of it like sharing a bag of candies among your friends. The total number of candies is the number you're dividing (the dividend), the number of friends is the number you're dividing by (the divisor), and the number of candies each friend gets is the answer (the quotient).

In the problem 168 divided by 3, 168 is the dividend, 3 is the divisor, and we're trying to find the quotient. So, we're essentially asking: "How many groups of 3 can we make from 168?" or "If we split 168 into 3 equal groups, how big will each group be?" Understanding this fundamental concept is crucial because it lays the foundation for tackling more complex division problems down the road. Division isn't just about memorizing a process; it's about understanding the relationship between numbers and how they can be broken down and shared. When you grasp this, the steps we'll cover next will make a lot more sense, and you'll feel much more confident in your ability to solve similar problems. Remember, math is like building with LEGOs—each piece (or concept) builds upon the previous one, and a solid foundation is key to creating something amazing! So, let’s move forward with this strong base and conquer the challenge of dividing 168 by 3, one step at a time. We're going to break it down so simply that you'll wonder why you ever felt intimidated by division in the first place. Let's get started and demystify the magic of dividing numbers!

Step 1: Setting Up the Problem

Okay, so how do we actually write out 168 divided by 3? We'll use the long division format, which might seem a little intimidating at first, but trust me, it's super organized and helps keep everything clear. The dividend (168) goes inside the "division house," and the divisor (3) goes outside, to the left. Think of the division house as a shelter for the number being divided, while the divisor is the one doing the splitting. Setting it up correctly is half the battle, guys! This visual representation makes the whole process much more manageable. You can actually see how the numbers interact, which is way more helpful than just trying to imagine it in your head. It's like having a map to guide you through the problem. Without the correct setup, you might get lost in the numbers and make unnecessary mistakes. So, let's make sure we nail this first step. Get your dividend cozy inside the division house and put the divisor in its rightful place. With this clear visual in place, we're ready to move on to the real dividing action. This methodical approach is what makes long division so powerful – it breaks down a potentially tricky problem into a series of smaller, much more manageable steps. It’s like chopping a big log into smaller pieces that are easier to lift. So, take a deep breath, pat yourself on the back for getting the setup perfect, and let's get ready to divide and conquer!

Step 2: Dividing the First Digit

Now, let's focus on the first digit of our dividend, which is 1. Can we divide 1 by 3? In other words, how many whole times does 3 fit into 1? Well, it doesn't! 3 is bigger than 1, so it doesn't fit even once. We write a 0 above the 1 in the quotient (the answer area). This is a crucial step because it acknowledges that we can't make any whole groups of 3 from just the hundreds digit of 168. It's like trying to share three cookies among more than three friends – you can't give everyone a whole cookie. This zero acts as a placeholder and keeps our place values aligned as we work through the problem. Ignoring this step or skipping it can lead to errors in the final answer, so it’s super important to get it right. Think of it as setting the stage for the rest of the division process. We've acknowledged that the hundreds place isn't going to give us a whole number, and that's perfectly okay. It just means we need to look at more digits together to find our quotient. So, don’t feel discouraged by that zero – it’s a necessary part of the process. It’s like saying, “Okay, the hundreds place alone isn’t enough, let’s see what we can do with the next digit.” With that zero in place, we’re ready to move on to the next phase of the division, feeling confident and prepared. Let's keep this momentum going and crack this problem wide open!

Step 3: Dividing the First Two Digits

Since 3 doesn't go into 1, we need to consider the first two digits of 168 together, which is 16. Now we ask ourselves: How many times does 3 go into 16? Think of your multiplication facts! 3 times 5 is 15, which is close to 16 without going over. 3 times 6 is 18, which is too big. So, 3 goes into 16 five times. We write the 5 above the 6 in the quotient. This is where your times tables really come in handy, guys. Knowing your multiplication facts makes division so much faster and easier. When you're fluent with your times tables, you can quickly see the relationship between numbers and determine how many times one number fits into another. This step is like fitting puzzle pieces together. We're figuring out the biggest chunk of 168 that we can divide by 3 at this stage. We've identified that 5 is the magic number, because 5 groups of 3 get us as close as possible to 16 without exceeding it. This is key to the long division process – we want to find the largest whole number that works at each step. It ensures we're being as efficient as possible and not leaving too much behind for later. So, with that 5 securely placed in our quotient, we’ve made a significant leap forward in solving our problem. We've successfully divided a portion of the dividend by the divisor and are well on our way to finding the final answer. Let’s keep this momentum going and move on to the next step, where we’ll continue to break down 168 into manageable pieces.

Step 4: Multiplying and Subtracting

Now, we multiply the 5 (from the quotient) by the divisor, which is 3. 5 times 3 is 15. We write this 15 below the 16. This step is like checking our work from the previous step. We figured out that 3 goes into 16 five times, and now we're confirming exactly how much of the 16 that accounts for. Multiplying the quotient digit (5) by the divisor (3) gives us the total amount that we're taking away from the dividend at this stage. Writing the 15 below the 16 sets us up for the next crucial operation: subtraction. This is where we see how much is “left over” after we’ve taken out those 5 groups of 3. The multiplication step is a bridge between division and subtraction, connecting the quotient we’ve found back to the original dividend. It’s a fundamental part of the long division algorithm, ensuring that we’re accurately accounting for each part of the division process. So, with that 15 neatly written below the 16, we’re perfectly positioned to subtract and reveal the remainder, which will guide us to the next digit we need to consider. Now, we subtract 15 from 16. 16 minus 15 is 1. We write the 1 below the 15. This subtraction tells us how much is left over after we've taken out those 5 groups of 3. In this case, we have 1 remaining. This remainder is super important because it carries over to the next digit of the dividend, helping us to continue the division process. It’s like saying, “Okay, we’ve divided as much as we can from these digits, but we still have a little bit left, so let’s see how it combines with the next digit.” The subtraction step is where we see the true impact of our division. It reveals the portion of the dividend that hasn’t yet been divided, guiding us towards the next stage of the solution. It’s a crucial checkpoint in the process, ensuring that we’re staying on track and accurately accounting for every part of the number we’re dividing. With that remainder of 1 clearly displayed, we’re ready to bring down the next digit and keep the division train rolling!

Step 5: Bring Down the Next Digit

We have a remainder of 1, and we still have one more digit in the dividend (168) that we haven't used yet: the 8. So, we bring down the 8 next to the 1, making the new number 18. Bringing down the next digit is like adding a new piece to the puzzle. We've dealt with the first part of the dividend, and now we're incorporating the next digit to see how it fits into the division. This step is crucial for ensuring that we account for every part of the dividend in our calculation. It's like saying, “Okay, we’ve handled this much of the number, now let’s bring in the next part and see what we can do.” The act of bringing down the digit transforms the remainder into a new, larger number that we can divide. In this case, the remainder of 1 combines with the brought-down 8 to create 18. This new number represents the total amount we still need to divide by our divisor (3). This step keeps the division process flowing smoothly and ensures that we don't leave any part of the dividend behind. It’s like making sure you use all the ingredients in your recipe – you wouldn’t want to leave anything out! With the 8 brought down and our new number of 18 formed, we’re ready to repeat the division process with this new value. We’ve successfully extended our division to the next level, and we’re one step closer to finding the final answer. Let’s keep this momentum going and tackle the division of 18 by 3 with confidence!

Step 6: Divide Again

Now we have 18. How many times does 3 go into 18? If you know your multiplication tables, you'll know that 3 times 6 is exactly 18! So, 3 goes into 18 six times. We write the 6 above the 8 in the quotient. This is a satisfying moment in the division process, guys! We’ve found a perfect fit – a number that divides evenly into the value we’re working with. Knowing that 3 goes into 18 exactly 6 times means we’re on the right track to a clean and accurate answer. This step highlights the importance of mastering your multiplication facts. When you have your times tables memorized, these division steps become much quicker and more intuitive. You can instantly recognize the relationships between numbers and confidently determine how many times one number fits into another. This division step is like finding the missing piece of a jigsaw puzzle. We’ve identified the exact number of groups of 3 that can be made from 18, and that knowledge allows us to complete this stage of the division process. We’ve successfully divided another portion of the dividend, and we’re getting closer and closer to the final quotient. With that 6 securely placed in our quotient, we’re ready to move on to the final steps of multiplication and subtraction, where we’ll confirm our result and see if we have any remainder left over. Let’s keep up the great work and bring this division problem to a triumphant conclusion!

Step 7: Multiply and Subtract (Again)

We multiply the 6 (from the quotient) by the divisor, which is 3. 6 times 3 is 18. We write this 18 below the 18 we already have. Just like before, this multiplication step is a confirmation of our division. We determined that 3 goes into 18 six times, and now we’re verifying exactly how much that accounts for. Multiplying the quotient digit (6) by the divisor (3) gives us the total amount we’re taking away from the current value (18). This step sets us up for the final subtraction, which will reveal whether we have a remainder or if we’ve divided perfectly. It’s a crucial part of the process, ensuring that we’re accurately accounting for each group of 3 within the dividend. Think of it as a double-check to make sure our calculations are spot-on. With that 18 neatly written below the other 18, we’re ready to perform the subtraction and see the result. This step is like the final piece of the puzzle, bringing us closer to the complete picture. Now, we subtract 18 from 18. 18 minus 18 is 0. We write the 0 below the 18. A remainder of 0 means that 3 divides into 168 perfectly! There's nothing left over. This is the moment of truth in our division journey, guys! A remainder of zero is the best possible outcome – it means we’ve divided the dividend completely and evenly by the divisor. It’s like reaching the summit of a mountain after a long climb, or finishing a race with a burst of energy. Seeing that zero confirms that our calculations have been accurate and that we’ve found the exact quotient. This step is a testament to the power of the long division process, which allows us to break down complex problems into manageable steps and arrive at a clear and satisfying answer. With that zero proudly displayed as our remainder, we can confidently declare that we’ve solved the division problem and found the final quotient. Let’s celebrate this victory and move on to the final step, where we’ll state our answer clearly and reflect on the process we’ve used.

Step 8: State the Answer

Since we have a remainder of 0, the answer to 168 divided by 3 is simply the number we have in the quotient, which is 56. So, 168 / 3 = 56. There you have it! We've successfully navigated the steps of long division and arrived at our answer. Clearly stating the answer is the final flourish in our mathematical journey. It’s like signing your name on a work of art, or putting the period at the end of a sentence. It’s the definitive statement of our solution, making it clear and unambiguous for anyone who’s following our work. This step also provides a sense of closure and accomplishment. After all the calculations and careful steps, we’ve reached our destination, and now we’re proudly announcing our findings. Stating the answer is also a good practice for clear communication in mathematics. It demonstrates that we understand the problem, we’ve applied the correct methods, and we’ve arrived at a logical and well-defined solution. It’s like presenting your case in a courtroom – you want to make sure your conclusion is clear, concise, and convincing. So, with our answer of 56 declared loud and proud, we’ve completed the division process and successfully solved the problem. Let’s take a moment to pat ourselves on the back for a job well done, and then we can reflect on the steps we’ve taken and the insights we’ve gained along the way.

Conclusion

And there you have it, guys! We've successfully solved 168 divided by 3 using long division. Remember, practice makes perfect, so the more you work on these types of problems, the easier they'll become. Don't be afraid to break down complex problems into smaller steps. You've got this! We've reached the end of our division adventure, and it’s a great time to pause and reflect on what we’ve accomplished. We started with a seemingly complex problem – 168 divided by 3 – and we broke it down into a series of manageable steps. We set up the problem, divided digit by digit, multiplied, subtracted, and brought down numbers until we arrived at our final answer. This step-by-step approach is the key to success in mathematics, and it’s a valuable skill that can be applied to many different types of problems. Remember that math isn't just about memorizing formulas and procedures; it's about understanding the underlying concepts and applying them in a logical and systematic way. We learned that division is essentially splitting a larger number into equal groups, and that long division is a powerful tool for organizing and executing this process. We also saw the importance of knowing our multiplication facts, as they make division much faster and easier. So, as you continue your mathematical journey, remember to embrace the process, break down challenges into smaller steps, and celebrate your successes along the way. You have the power to conquer any mathematical mountain, one step at a time. Keep practicing, keep exploring, and keep that mathematical spirit burning bright! You've got this, guys!