How To Solve 15000 Divided By 12 A Step-by-Step Guide

Hey guys! Today, we’re diving into a common math problem: 15000 divided by 12. It might seem intimidating at first, but don’t worry! We’re going to break it down into simple, easy-to-follow steps. Whether you’re a student tackling homework or just brushing up on your math skills, this guide will help you master long division and understand the process behind it. So, let’s get started and make math a little less scary and a lot more fun!

Understanding Division Basics

Before we jump into solving 15000 divided by 12, let’s quickly review the basics of division. Division, at its heart, is all about splitting a whole into equal parts. Think of it as sharing a big bag of candy among your friends. You have a certain number of candies (the dividend), and you want to divide them equally among a certain number of friends (the divisor). The result you get is how many candies each friend receives (the quotient), and sometimes, you might have a few candies left over (the remainder).

In our problem, 15000 is the dividend – the total amount we’re starting with. The number 12 is the divisor – the number we’re dividing by. Our goal is to find the quotient, which is the result of this division. Understanding these terms is crucial because they help us set up the problem correctly and interpret the answer we get.

Division is one of the four basic arithmetic operations, alongside addition, subtraction, and multiplication. It's the inverse operation of multiplication, meaning that if you multiply the quotient by the divisor, you should get the dividend (plus any remainder). This relationship is a great way to check your work and make sure you’ve solved the problem correctly.

Mastering division is essential for many real-life situations. From calculating how to split a bill with friends to figuring out how many items you can buy within a budget, division is a practical skill that comes in handy all the time. So, let’s get comfortable with the process, and you’ll find that these types of calculations become much easier over time. Now that we’ve refreshed our understanding of the basics, let’s move on to the step-by-step guide for solving 15000 divided by 12. We'll tackle it using the long division method, which is a systematic way to break down larger division problems into smaller, more manageable steps. Stick with me, and you’ll see how straightforward it can be!

Step 1: Setting Up the Long Division

The first step in tackling 15000 divided by 12 using long division is setting up the problem correctly. This visual organization is key to keeping track of your calculations and avoiding mistakes. Think of it as building the foundation for a sturdy structure – if the foundation is solid, the rest will follow smoothly.

To set up the long division, you'll draw a division symbol, which looks like a sideways L with a horizontal line extending from the top. The dividend, which is 15000 in our case, goes inside the “house” formed by the division symbol. The divisor, which is 12, goes outside, to the left of the vertical part of the division symbol. This setup visually represents the problem: how many times does 12 fit into 15000?

It’s crucial to align the numbers properly. Make sure each digit of the dividend is lined up in its place value column (ones, tens, hundreds, thousands, etc.). This alignment will help you keep track of which part of the dividend you’re working with at each step. A neat setup also makes it easier to spot any errors in your calculations as you go along.

Once you’ve set up the problem, take a moment to double-check that everything is in the correct place. This simple step can save you a lot of frustration later on. If the numbers are misplaced, the entire calculation will be off. So, a quick check now ensures a smoother process moving forward.

Think of this setup as the blueprint for solving the division problem. It provides a clear roadmap for the steps you’ll take next. With the problem set up correctly, we’re ready to start the actual division process. In the next step, we'll begin dividing 12 into the first few digits of 15000, working our way from left to right. So, let’s move on and see how it’s done!

Step 2: Dividing the First Digits

Now that we have 15000 divided by 12 set up using long division, it’s time to start dividing! We begin by looking at the first digit (or digits) of the dividend, 15000, and comparing it to the divisor, 12. The goal here is to figure out how many times 12 can fit into the first part of 15000.

We start by considering the first digit of 15000, which is 1. Can 12 fit into 1? No, it can’t, because 1 is smaller than 12. So, we move on to the first two digits, which form the number 15. Now, we ask ourselves: how many times does 12 fit into 15?

The answer is 1 time, because 12 multiplied by 1 is 12, which is less than 15, but 12 multiplied by 2 is 24, which is greater than 15. So, we write the number 1 above the 5 in 15000, because we’re dividing 12 into 15. This 1 represents the first digit of our quotient – the answer to the division problem.

Next, we multiply the divisor, 12, by the number we just wrote above (which is 1). 12 multiplied by 1 is 12. We write this 12 below the 15 in the dividend. This step is important because it sets us up for the next part of the process, which is subtraction.

Remember, each step in long division builds upon the previous one. By carefully considering how many times the divisor fits into the current part of the dividend, we’re slowly chipping away at the problem, making it more manageable. This methodical approach is what makes long division so effective for solving larger division problems. Now that we’ve divided into the first part of the dividend and multiplied, we’re ready to move on to the next step: subtracting to see what’s left over.

Step 3: Subtracting and Bringing Down

After figuring out how many times the divisor, 12, fits into the first part of the dividend (15) in 15000 divided by 12, and multiplying, we move on to the subtraction step. This step helps us determine the remainder after the initial division, which we’ll then use for the next part of the problem. Think of it as taking away what we’ve already accounted for to see what’s still left to divide.

We subtract the 12 (which we got from multiplying 12 by 1) from the 15 in the dividend. 15 minus 12 equals 3. So, we write 3 below the 12. This 3 is the remainder after dividing 12 into 15 once. It's important to perform the subtraction accurately, as any error here will affect the rest of the calculation.

Now comes the “bringing down” part. We bring down the next digit from the dividend, which is 0 in this case, and write it next to the 3. This forms the new number 30. Bringing down a digit essentially means we’re now focusing on the next part of the dividend. It’s like moving to the next group of “candies” to divide.

The number 30 is what we’ll be working with in the next round of division. We’re now asking ourselves: how many times does 12 fit into 30? This process of subtracting and bringing down is repeated throughout long division until we’ve used all the digits in the dividend.

Bringing down the digits one by one allows us to break down a large division problem into a series of smaller, more manageable divisions. It’s a systematic way of working through the problem, ensuring we don’t miss any parts of the dividend. So, with our new number 30, we’re ready to repeat the division process. In the next step, we’ll divide 12 into 30 and continue the cycle of dividing, multiplying, subtracting, and bringing down until we reach the end of the problem.

Step 4: Repeating the Process

With the number 30 formed after subtracting and bringing down in 15000 divided by 12, we’re now ready to repeat the division process. This is where the cyclical nature of long division becomes apparent. We’ll continue dividing, multiplying, subtracting, and bringing down until we’ve used all the digits in the dividend.

First, we ask ourselves: how many times does 12 fit into 30? We know that 12 multiplied by 2 is 24, and 12 multiplied by 3 is 36. Since 36 is greater than 30, 12 can fit into 30 only 2 times. So, we write the number 2 above the 0 in 15000, next to the 1 we wrote earlier. This 2 becomes the next digit in our quotient.

Next, we multiply the divisor, 12, by the number we just wrote above (which is 2). 12 multiplied by 2 is 24. We write this 24 below the 30. Now, we subtract 24 from 30. 30 minus 24 equals 6. So, we write 6 below the 24. This 6 is the remainder after dividing 12 into 30.

We then bring down the next digit from the dividend, which is another 0. We write this 0 next to the 6, forming the new number 60. Now, we ask ourselves: how many times does 12 fit into 60? This is a bit easier because we might recognize that 12 multiplied by 5 is exactly 60.

So, we write the number 5 above the next 0 in 15000, making it the next digit in our quotient. We multiply 12 by 5, which is 60, and write this 60 below the 60 we have. Subtracting 60 from 60 gives us 0. This means there’s no remainder in this step, and we’ve successfully divided 12 into 60.

But we’re not quite done yet! We still have one more digit to bring down, which is the last 0 in 15000. Bringing down this 0 gives us 0. Now, we need to divide 12 into 0. How many times does 12 fit into 0? Zero times, of course! So, we write a 0 as the last digit in our quotient.

The process of repeating these steps is what makes long division work for dividends of any size. By breaking the problem down into smaller parts and systematically working through each step, we can find the quotient and any remainder. In the next and final step, we’ll look at interpreting the results and understanding what our answer means.

Step 5: Interpreting the Result

After completing the long division process for 15000 divided by 12, we arrive at our final step: interpreting the result. This is where we make sense of the numbers we’ve calculated and understand the answer to our original problem. Think of it as translating the mathematical steps into a meaningful solution.

Looking at our long division work, we see the quotient written above the dividend. In this case, the quotient is 1250. This means that 15000 divided by 12 equals 1250. There’s no remainder in this division, which means 12 fits perfectly into 15000 exactly 1250 times.

To double-check our answer, we can use the inverse operation of division, which is multiplication. If we multiply the quotient (1250) by the divisor (12), we should get the dividend (15000). Let’s try it: 1250 multiplied by 12 is indeed 15000. This confirms that our division is correct!

Understanding the result in context is also important. If we were, for example, dividing 15000 candies among 12 friends, each friend would get 1250 candies, and there would be no candies left over. This practical interpretation helps us see how division can be applied in real-life situations.

The ability to interpret the result is a crucial part of problem-solving in mathematics. It’s not just about crunching the numbers; it’s about understanding what those numbers mean. So, taking the time to review your work and make sure the answer makes sense is always a worthwhile step.

Congratulations! You’ve successfully solved 15000 divided by 12 using long division. By breaking the problem down into smaller steps – setting up, dividing, subtracting, bringing down, repeating, and interpreting – you’ve mastered a valuable mathematical skill. Keep practicing, and you’ll become even more confident in your division abilities. Now you can tackle similar problems with ease and apply this knowledge to various real-world scenarios. Great job, guys!