Math Problem: Find The Number Divided By 12

Hey guys! Let's dive into a cool math problem that many students find tricky but is actually super straightforward once you get the hang of it. We're going to figure out how to find a natural number that, when you divide it by 12, gives you a quotient of 6 and a remainder of 5. Sounds like a puzzle, right? Well, let's break it down step by step. Understanding the relationship between the dividend, divisor, quotient, and remainder is key here. Once you grasp that, these types of problems become a piece of cake! So, grab your thinking caps, and let's get started!

Understanding the Basics of Division

Before we tackle the specific problem, let's quickly revisit the fundamental concepts of division. In any division problem, you have four main components:

• Dividend: This is the number being divided.
• Divisor: This is the number by which the dividend is divided.
• Quotient: This is the result of the division (the whole number part).
• Remainder: This is the amount left over when the dividend cannot be divided evenly by the divisor.

The relationship between these components can be expressed using the following formula:

Dividend = (Divisor × Quotient) + Remainder

This formula is the foundation for solving problems involving division and remainders. Think of it like this: if you multiply the divisor by the quotient, you get a number close to the dividend. The remainder is just the extra bit you need to add to reach the exact dividend. Grasping this relationship will make solving our original problem much easier. It's like having a secret code to unlock the answer!

For example, if we divide 27 by 5, we get a quotient of 5 and a remainder of 2. Using the formula:

27 = (5 × 5) + 2

See how it works? Now, let's apply this knowledge to solve the problem at hand!

Solving the Problem: Finding the Natural Number

Alright, now that we've refreshed our understanding of division, let's get back to the original question: What natural number, when divided by 12, gives a quotient of 6 and a remainder of 5? We know the following:

• Divisor = 12
• Quotient = 6
• Remainder = 5

We need to find the dividend (the natural number). Using the formula we discussed earlier:

Dividend = (Divisor × Quotient) + Remainder

Plug in the values:

Dividend = (12 × 6) + 5

Now, let's do the math:

Dividend = 72 + 5

Dividend = 77

Therefore, the natural number is 77. Easy peasy, right? This means that when you divide 77 by 12, you get a quotient of 6 and a remainder of 5. You can check this by performing the division: 77 ÷ 12 = 6 with a remainder of 5. Understanding and applying the formula is the key to cracking these types of problems. Keep practicing, and you'll become a pro in no time!

Real-World Applications of Division with Remainders

You might be wondering, "Okay, this is cool, but where would I ever use this in real life?" Well, the concept of division with remainders pops up in many everyday situations! Let's explore some practical examples.

• Distributing Items: Imagine you have 50 candies and want to distribute them equally among 7 kids. How many candies does each kid get, and how many are left over? This is a division with remainders problem! 50 ÷ 7 = 7 with a remainder of 1. Each kid gets 7 candies, and there's 1 candy left. Knowing this helps in fair distribution and managing resources.
• Scheduling Tasks: Suppose you need to complete 23 tasks, and you can complete 4 tasks per day. How many days will it take to finish all the tasks, and how many tasks will you complete on the last day? 23 ÷ 4 = 5 with a remainder of 3. It will take 5 full days, and on the 6th day, you'll complete the remaining 3 tasks. This is useful for project management and time estimation.
• Packaging Products: A factory produces 100 items and packs them into boxes of 9. How many full boxes can they make, and how many items will be left over? 100 ÷ 9 = 11 with a remainder of 1. They can make 11 full boxes, and 1 item will be left over. This is crucial for inventory management and logistics.
• Calculating Time: If you have 200 minutes and want to know how many hours and minutes that is, you divide 200 by 60 (minutes in an hour). 200 ÷ 60 = 3 with a remainder of 20. That's 3 hours and 20 minutes. This is handy for planning your day and managing appointments.

As you can see, division with remainders isn't just a math concept; it's a practical tool that helps us solve everyday problems. Recognizing these situations and applying the division formula can make your life a lot easier!

Tips and Tricks for Solving Similar Problems

Want to become a master at solving division problems with remainders? Here are some tips and tricks that can help you ace them every time!

• Understand the Question: Read the problem carefully and identify what you need to find. Are you looking for the dividend, divisor, quotient, or remainder? Knowing this from the start will guide your approach.
• Write Down the Given Information: List all the known values (divisor, quotient, remainder) clearly. This helps you organize your thoughts and avoid confusion.
• Use the Formula: Remember the formula: Dividend = (Divisor × Quotient) + Remainder. This is your go-to equation for solving these problems. Practice using it until it becomes second nature.
• Check Your Answer: After finding the solution, plug it back into the original problem to see if it makes sense. Does the division result in the given quotient and remainder? If not, double-check your calculations.
• Practice Regularly: The more you practice, the better you'll become. Try solving various problems with different numbers and scenarios. This will help you develop your problem-solving skills and build confidence.
• Draw Diagrams: Sometimes, visualizing the problem can help. Draw a simple diagram or use objects to represent the division process. This can make the concept more concrete and easier to understand.
• Break Down Complex Problems: If the problem seems complicated, break it down into smaller, more manageable steps. Solve each step individually and then combine the results to find the final answer.
• Use Real-World Examples: Relate the problems to real-life situations. This will make the concept more relatable and easier to remember. Think about distributing items, scheduling tasks, or packaging products.

By following these tips and tricks, you'll be well-equipped to tackle any division problem with remainders that comes your way. Keep practicing, and you'll become a math whiz in no time!

Conclusion: Mastering Division with Remainders

So there you have it, folks! We've successfully tackled the problem of finding the natural number that, when divided by 12, gives a quotient of 6 and a remainder of 5. The answer, as we discovered, is 77. But more importantly, we've explored the underlying concepts and techniques that make solving these types of problems a breeze.

Remember, the key is to understand the relationship between the dividend, divisor, quotient, and remainder. The formula Dividend = (Divisor × Quotient) + Remainder is your best friend in these situations. Practice applying this formula to various problems, and you'll quickly become proficient in solving division problems with remainders.

We also discussed real-world applications of this concept, from distributing items and scheduling tasks to packaging products and calculating time. Recognizing these practical uses can make math more engaging and relevant to your everyday life.

And finally, we shared some valuable tips and tricks to help you ace these problems every time. From understanding the question and writing down the given information to checking your answer and practicing regularly, these strategies will set you on the path to success.

So, keep practicing, stay curious, and remember that math is not just about numbers and formulas; it's about problem-solving, critical thinking, and making sense of the world around us. Keep up the great work, and you'll be a math master in no time!