Math Problem: Hose Lengths And Divisions

Hey guys, let's break down this math problem step-by-step. It's all about equal lengths, dividing things up, and figuring out the sizes of the pieces. We'll start with the situation Tarik has with the hoses and then see how to solve it. It is actually a very fun problem when you get to know the concept of it. Problems like these are designed to test your understanding of basic arithmetic operations. The core concept here revolves around the idea that when you divide an object (in this case, a hose) into equal parts, each part represents a fraction of the whole. This is a crucial concept in mathematics, as it lays the foundation for understanding ratios, proportions, and algebraic concepts. Let's start with the first hose. Tarik cuts it into 16 equal pieces. We also know that one of these pieces is 21 meters long. So, the first thing we should think about is how we can determine the original length of the whole hose from this information, since it's the foundation we'll need for the rest of the problem. This initial step involves a simple multiplication. Understanding this helps you see how smaller parts combine to make a whole. Remember, understanding fractions and division is not just about getting the right answer in a math problem; it's also about developing critical thinking skills that can be applied in many other areas of life, like dividing work among team members, splitting costs with friends, and many more. It's a fundamental concept that you'll use time and again. Remember also to be patient. Learning takes time and practice. If you don't understand something at first, that's okay. The key is to keep practicing and asking questions. The more you work through problems like these, the better you'll become at recognizing the patterns and applying the correct methods to solve them. This approach will not only help you to solve the specific problem at hand, but it will also strengthen your problem-solving skills in general, making you more confident in tackling future mathematical challenges.

Finding the Original Length

To find the original length of the hose, we need to multiply the length of one part by the number of parts. This is because all parts are equal, and when you combine them, they make up the whole hose. This is why each part is the same, so we can know that if we multiply it by the number of parts, we'll get the full length. So, if one part is 21 meters long, and there are 16 parts, then the total length of the hose is 21 meters * 16 = 336 meters. This gives us the total length of the original hose.

Think of it like this: if you have 16 identical building blocks and each block is 21 centimeters long, you can find the total length of the structure you create by multiplying the length of one block by the total number of blocks. The underlying principle is the same here. In doing so, we're not only finding the total length of the hose but also reinforcing the concept of multiplication as a way to combine equal groups. This will boost your understanding of the relationship between multiplication and division, which is absolutely fundamental in math. By working through this process, you develop a better grasp of how multiplication can be used to solve real-world problems. This strengthens the understanding and application of multiplication in various mathematical contexts. This understanding is key for more complex mathematical ideas later on. The ability to visualize and understand these numerical relationships is a cornerstone of mathematical fluency, enabling you to approach and solve a wide array of problems with greater ease and confidence.

Now we can know the original length of the hose. Knowing this, we can move forward and solve the second part of the problem.

Solving for the Second Hose

Now, let's look at the second hose. We know that the length of the second hose is also 336 meters, as the problem states they are equal in length. Tarik divides this hose into 4 equal parts. To find the length of one part, we need to divide the total length of the hose by the number of parts. So, we'll do 336 meters / 4 = 84 meters. This means if the hose were divided into 4 equal pieces, each piece would be 84 meters long. This is our answer! By breaking the problem into steps, we've solved it easily. We took a complicated problem and made it into a simple one, and that is what you need to do to solve problems. This way, we can be confident in our answers and avoid any silly mistakes. The method we used to solve the problem helps in building confidence. Remember, practice is essential. The more you solve such problems, the more comfortable you'll become with the process. The process of breaking down the problem, identifying the known information, and applying the correct mathematical operations. It's not just about getting the answer; it's about understanding the underlying principles and improving your problem-solving skills. The key to mastering math is not just memorizing formulas but understanding how they work and when to apply them. It’s also about building confidence and resilience when facing challenges, knowing that every problem you solve makes you stronger and more capable. With each step you take, you are improving your ability to approach, analyze, and solve complex problems.

Final Answer

If Tarik divides the second hose into 4 equal parts, each part will be 84 meters long. This problem is a great example of how you can use basic arithmetic to solve problems. It's all about multiplication and division and how to apply these operations in practical scenarios. Understanding these concepts will also provide a solid foundation for more complex mathematical concepts in the future, helping to develop your critical thinking skills and improve your mathematical skills.