Dividing 60583 By 35: A Step-by-Step Guide

Nov 3, 2025 by Admin 43 views

Hey everyone! Let's dive into a classic math problem: dividing 60583 by 35. Don't worry, it seems intimidating, but we'll break it down into easy-to-follow steps. This guide will walk you through the process, ensuring you grasp the concept of long division. We'll explore each stage, making sure you understand the 'why' behind every move. Ready to become a division whiz? Let's get started!

Step 1: Setting up the Division Problem

First things first, let's set up our long division problem. We're going to place the dividend (the number we're dividing, which is 60583) inside the division symbol, and the divisor (the number we're dividing by, which is 35) outside. Think of it like a little house for the dividend! So, it should look something like this:

      ______
35 | 60583

Now, we've got our problem nicely arranged, and we're ready to start dividing. Understanding this setup is super important because it lays the foundation for all the steps that follow. Remember, the goal is to figure out how many times 35 fits into 60583. It's like asking, "If we have a bunch of groups of 35, how many groups can we make with 60583 items?" This step isn't just about writing numbers; it's about setting the stage for problem-solving. Make sure your numbers are clear and neatly written, so you don't confuse them as you go through the calculations. Proper setup can prevent a lot of common mistakes. And trust me, getting off on the right foot makes the rest of the journey much smoother. So, take your time, and make sure your division house is ready for action!

Step 2: Dividing the First Digits

Alright, let's start dividing! We're going to look at the first digits of the dividend, starting from the left. Does 35 go into 6? Nope, 35 is bigger than 6. So, we'll move on to the next digit, considering the first two digits. Does 35 go into 60? Yes, it does! We need to figure out how many times 35 fits into 60. Well, 35 times 1 is 35, and 35 times 2 is 70. Since 70 is bigger than 60, 35 fits into 60 only once. So, we write a "1" above the "0" in the dividend:

      1_____
35 | 60583

Next, we multiply the 1 (the number we just wrote above) by the divisor (35). 1 times 35 equals 35. We write this 35 under the 60:

      1_____
35 | 60583
     -35

Then, we subtract 35 from 60. 60 minus 35 equals 25:

This first step is all about getting the ball rolling. It might seem small, but it's the foundation for the whole process. Always start from the leftmost digits and work your way across. Keep in mind that you're essentially trying to find the biggest multiple of the divisor (35, in this case) that fits into the current part of the dividend (first 60, then 25). Don't rush; take your time to ensure your multiplication and subtraction are correct. Accurate calculations now will save you headaches down the line. It's like building a strong base for a tall building - if it's shaky, the whole thing will be unstable! So, double-check your work, and you're doing great!

Step 3: Bringing Down the Next Digit

Now, it's time to bring down the next digit from the dividend, which is "5." We place this "5" next to the 25 that we have from the subtraction, forming the number 255:

This step is all about recycling the remaining parts of your original dividend. We bring down the next digit and repeat the cycle of dividing, multiplying, and subtracting. Bringing down the "5" is like adding another piece to our ongoing sum. The new number, 255, is what we will work with for this round of dividing. Think of it as combining what was left from the last step with the next piece of your original number. This stage keeps the process moving forward, expanding your calculations. Remember to bring down only one digit at a time and not to skip any. Doing this guarantees that all of the original digits are factored into the solution. It's like adding another ingredient to the pot; now you have a new combination to work with. Keep up the good work; you're doing great!

Step 4: Dividing Again

Okay, time to divide again! We now have the number 255 to work with. How many times does 35 go into 255? Let's figure it out. We know that 35 times 7 is 245, and 35 times 8 is 280. Since 280 is larger than 255, we'll use 7. Write a "7" next to the "1" in your quotient (the number at the top):

Now, multiply 7 by 35. 7 times 35 is 245. Write 245 under 255:

Then, subtract 245 from 255. 255 minus 245 equals 10:

See, we're making progress. In this stage, we're basically repeating the process from the previous steps. It's like taking a deep breath and doing it all over again, with new numbers. Remember, this step is all about finding the closest multiple of the divisor to the number you're working with. If you're unsure, try a few multiplication problems on the side to find the most accurate number. Make sure your multiplication and subtraction are accurate, because a small error can spread to the rest of the problem. Also, this stage is a testament to the power of repetition - practice makes perfect! So, stay focused, and keep pushing forward; you've got this!

Step 5: Bringing Down Another Digit

Alright, let's bring down the next digit, which is "8," from the dividend. Place the "8" next to the 10, forming the number 108:

Bringing down the "8" adds another dimension to our ongoing calculation. We're getting closer to solving the entire problem. It is the same as the step of the bringing down another digit, the value of the number increases, which will affect the result. It is like another stage of the same game. Each time you bring down a digit, you're getting closer to the final answer. Keep it up! Take a moment to appreciate how the problem is gradually evolving as you bring down each digit. The aim is to include every number from the original dividend. You're doing a fantastic job – keep your focus, and you'll nail it!

Step 6: Dividing Again (Third Time)

Let's get back to dividing. We now have 108. How many times does 35 go into 108? We know 35 times 3 is 105, and 35 times 4 is 140. Since 140 is larger than 108, we will use 3. Write a "3" next to the "7" in the quotient:

Now, multiply 3 by 35. 3 times 35 is 105. Write 105 under 108:

Subtract 105 from 108. 108 minus 105 is 3:

We're now in the final stretch, guys! It is the third round of dividing, like a well-oiled machine at this point. Ensure the numbers are properly placed, like placing the right pieces of a puzzle. Ensure your multiplication and subtraction are correct, since a mistake here can affect the final solution. Take a moment to admire how far you have come from the beginning. You have already completed a number of key stages; celebrate this achievement. You are doing well, and you're almost there! Hold the course; you are doing an awesome job!

Step 7: Bringing Down the Final Digit

Okay, let's bring down the last digit, which is "3," from the dividend. Place the "3" next to the 3, forming the number 33:

This is the last piece of the puzzle! At this stage, you're ready to find the final part of your solution. It is all about incorporating the last digit. We are ready to make the final determination. It represents the last contribution from the dividend. You're just a few steps away from completing the division. You're doing a fantastic job – the end is near! Keep your eyes on the prize, and make sure everything is in its proper place. Great job; you are almost done!

Step 8: The Final Division

Alright, we now have 33. How many times does 35 go into 33? Well, 35 is bigger than 33, so it goes in zero times. We write a "0" next to the "3" in our quotient:

Since 35 doesn't go into 33, our remainder is 33. This means that 60583 divided by 35 equals 1730 with a remainder of 33. Our final answer is:

1730 R 33

This is it - the final step! You have made it to the end. Since the divisor (35) cannot fit into the current number (33), our remainder is 33. Thus, our final solution includes a quotient (1730) and a remainder (33). Remember to express your answer with both the quotient and the remainder, because this provides a full picture of the solution. Great work! You've successfully completed the division problem. It's time to feel pride in all the hard work and effort you have done! Take a moment to recognize the work you have completed. You have made it. Wonderful job!

Conclusion

And there you have it! We've successfully divided 60583 by 35, step-by-step. You've now seen how to handle long division, and you've learned the process. Remember, practice is key. Keep working on these problems, and you'll become a pro in no time! Keep practicing, and don't be afraid to ask for help if you need it. Math may be challenging, but it can be conquered with practice and hard work.