Divide 647 By 5: Long Division Explained

by Kenji Nakamura 41 views

Hey guys! Ever stumbled upon a division problem that looks a little intimidating? Don't worry, we've all been there. Today, we're going to break down the problem of dividing 647 by 5. It might seem tricky at first, but with a step-by-step approach, you'll be a pro in no time. We'll not only solve it but also understand the logic behind each step, making sure you can tackle similar problems with confidence.

Understanding Division

Before we dive into the main problem, let's quickly recap what division actually means. In simple terms, division is splitting a number into equal groups. When we say 647 divided by 5, we're essentially asking: how many groups of 5 can we make from 647, and what's left over? The number we're dividing (647) is called the dividend, the number we're dividing by (5) is the divisor, the result is the quotient, and any leftover amount is the remainder. Knowing these terms will help us understand the process better. Think of it like sharing 647 cookies among 5 friends – how many cookies does each friend get, and how many are left?

Long Division: The Method We'll Use

For larger numbers, we typically use a method called long division. It's a systematic way to break down the problem into smaller, more manageable steps. Long division might look a bit daunting with all its symbols and steps, but it's really just a series of repeated steps: divide, multiply, subtract, and bring down. We'll go through each of these steps in detail as we solve our problem. The key is to stay organized and follow the steps carefully. Remember, practice makes perfect, so don't be discouraged if it doesn't click right away. We are trying to make something that could be hard easy. We’ll get you through it!

Step-by-Step Solution: 647 ÷ 5

Okay, let's get to the heart of the matter: solving 647 divided by 5. We'll go through each step slowly and explain the reasoning behind it. Grab a pen and paper, and feel free to follow along! This will help you understand the process much better. Trust me, seeing it in action makes a big difference.

Step 1: Setting Up the Problem

First, we write the problem in the long division format. This looks like a little 'house' with the dividend (647) inside and the divisor (5) outside to the left. This setup helps us keep track of the steps and stay organized. It's like setting up your workspace before starting a big project – everything in its place makes the task much smoother. The visual structure of long division is designed to help us break down the problem into smaller, more digestible parts.

Step 2: Dividing the First Digit

Now, we look at the first digit of the dividend, which is 6. We ask ourselves: how many times does 5 go into 6? Well, 5 goes into 6 one time. So, we write '1' above the 6 in our quotient (the answer). This '1' represents the hundreds place in our final answer. Think of it as distributing the largest possible groups of 5 first. It's like tackling the biggest part of a job first to make the rest feel easier. We're essentially saying, "We can make one group of 5 from the hundreds place in 647."

Step 3: Multiplying and Subtracting

Next, we multiply the quotient digit we just wrote (1) by the divisor (5). 1 multiplied by 5 is 5. We write this '5' below the '6' in the dividend. Then, we subtract 5 from 6, which gives us 1. This subtraction tells us how much is left over after taking out one group of 5 from the hundreds place. It's like figuring out how many cookies are left in the jar after you've taken some out. This step is crucial because it sets up the next part of the division.

Step 4: Bringing Down the Next Digit

Now, we bring down the next digit from the dividend, which is 4. We write this '4' next to the remainder '1', forming the number 14. This is like adding more cookies to the jar so you can continue sharing. Bringing down the digit allows us to continue the division process with the next place value. We're essentially saying, "Okay, now we have 14 to work with in the tens place."

Step 5: Repeating the Process

We repeat the process: how many times does 5 go into 14? It goes in 2 times. We write '2' next to the '1' in the quotient, above the '4' in the dividend. This '2' represents the tens place in our final answer. Then, we multiply 2 by 5, which is 10. We write '10' below the '14' and subtract. 14 minus 10 is 4. So, we have 4 left over after taking out two groups of 5 from the tens place. This repetition is the heart of long division – we keep dividing, multiplying, and subtracting until we can't divide anymore. This systematic approach is what makes long division so effective.

Step 6: Bringing Down the Last Digit

We bring down the last digit, which is 7. We write it next to the remainder 4, forming the number 47. We're now working with the units place. We've broken down the problem into manageable chunks, and we're almost there!

Step 7: Final Division and Remainder

How many times does 5 go into 47? It goes in 9 times. We write '9' next to the '2' in the quotient, above the '7' in the dividend. This '9' represents the units place in our final answer. Then, we multiply 9 by 5, which is 45. We write '45' below '47' and subtract. 47 minus 45 is 2. This means we have 2 left over, which is our remainder. We've divided as much as we can, and we have a remainder – the leftover cookies that couldn't be evenly distributed.

The Answer

So, 647 divided by 5 is 129 with a remainder of 2. We can write this as 129 R 2. This means that 5 goes into 647 a total of 129 times, with 2 left over. We've successfully navigated the long division process! Give yourself a pat on the back!

Checking Our Work

It's always a good idea to check our work to make sure we didn't make any mistakes. We can do this by multiplying the quotient (129) by the divisor (5) and then adding the remainder (2). If we did it correctly, we should get the original dividend (647).

Let's do it: 129 * 5 = 645. Then, 645 + 2 = 647. Hooray! Our answer is correct. Checking our work gives us confidence in our solution and reinforces the relationship between division, multiplication, and remainders.

Why This Matters: Real-World Applications

Now, you might be wondering, why does this even matter? Well, division is a fundamental math skill that we use in everyday life. From splitting a bill with friends to calculating ingredients for a recipe, division is everywhere. Understanding long division helps us solve more complex problems and develop strong problem-solving skills. Think about it – any time you need to share something equally or figure out how many groups you can make, you're using division! It's a skill that empowers you in various situations, both big and small.

Tips for Mastering Long Division

Long division can seem tricky at first, but with practice, it becomes much easier. Here are a few tips to help you master it:

  • Practice Regularly: The more you practice, the more comfortable you'll become with the steps.
  • Stay Organized: Keep your work neat and tidy to avoid mistakes.
  • Know Your Multiplication Facts: Knowing your times tables will make the division process much faster.
  • Break It Down: If a problem seems overwhelming, break it down into smaller steps.
  • Check Your Work: Always check your answer to make sure you didn't make any errors.

Remember, everyone learns at their own pace. Don't get discouraged if you don't get it right away. Keep practicing, and you'll get there!

Conclusion

So, we've successfully divided 647 by 5 using long division. We broke down the problem step-by-step, understood the logic behind each step, and even checked our work. You've now added another tool to your math toolkit! Remember, math is like building blocks – each skill builds upon the previous one. By mastering long division, you're setting yourself up for success in more advanced math topics. Keep practicing, stay curious, and most importantly, have fun with it!

If you have any questions or want to try more examples, feel free to ask. We're here to help you on your math journey. You've got this, guys!