Fabiana's Walk: A Metric Conversion Problem

Hey guys! Let's dive into a fun math problem today. We're going to help Fabiana figure out how much further she needs to walk to reach her daily goal. This is a great example of how we use math in our everyday lives, and it's a fantastic way to practice converting between different units of measurement. So, grab your thinking caps, and let's get started!

The Problem: Fabiana's 4 km Journey

Our main problem revolves around Fabiana's daily walk, which is a solid 4 kilometers. That's her target, her daily quest! But she's already covered some ground. She's walked 5 hectometers, 9 decameters, and 125 meters. The big question is: How many meters does Fabiana still need to walk to hit that 4 km goal? To nail this, we need to become unit conversion wizards. We have to make sure all our distances are in the same unit, and the easiest way to do that here is to convert everything to meters. Why meters? Because the final question asks for the remaining distance in meters. This makes our lives way simpler and avoids extra steps later on. Think of it like this: we're turning a slightly confusing puzzle into a clear, step-by-step path to the answer. So, we'll tackle each part of Fabiana's walk, converting those hectometers and decameters into good old meters, and then we'll be ready to do some simple subtraction to find out the final distance.

First things first, let's break down what we know:

• Fabiana's total distance: 4 kilometers (km)
• Distance already walked: 5 hectometers (hm) + 9 decameters (dam) + 125 meters (m)

Now, let's convert everything to meters. This is where our unit conversion skills come into play. Remember, converting units is like changing the language you're using to describe the same thing. The distance doesn't magically change, we're just expressing it differently.

Converting Kilometers to Meters

Let's kick things off by converting kilometers to meters. This is crucial because Fabiana's total daily distance is given in kilometers, and we need to work with meters to solve the problem. So, how do we do it? The key is knowing the relationship between kilometers and meters: 1 kilometer is equal to 1000 meters. This is a fundamental conversion factor that's super important to remember. It's like having a secret code that unlocks the solution. Now, to convert 4 kilometers into meters, we simply multiply 4 by 1000. This is because each kilometer contains 1000 meters, so 4 kilometers will contain 4 times that amount. The calculation is straightforward: 4 km * 1000 meters/km = 4000 meters. And there you have it! We've successfully converted Fabiana's total daily distance into meters. This is a big step forward because now we have a clear target of 4000 meters that Fabiana needs to reach. This conversion is the foundation upon which we'll build the rest of our solution, so it's vital that we get it right. It's like laying the first brick in a wall – a solid foundation ensures the rest of the structure will stand strong. Now that we know the total distance in meters, we can move on to converting the other parts of Fabiana's walk into meters as well, bringing us closer and closer to solving the puzzle.

Converting Hectometers to Meters

Next up, we tackle converting hectometers to meters. Fabiana has already walked 5 hectometers, and we need to know how many meters that represents. Again, we need a conversion factor, that magic key that unlocks the relationship between hectometers and meters. In this case, 1 hectometer is equal to 100 meters. This is another important conversion to memorize, as it's frequently used in various measurement problems. Think of it as adding another tool to your math toolbox – the more conversion factors you know, the better equipped you'll be to tackle these kinds of challenges. Now, to convert 5 hectometers into meters, we multiply 5 by 100. Just like with the kilometers, we're scaling up the distance based on how many meters are in each hectometer. The math is simple and elegant: 5 hm * 100 meters/hm = 500 meters. So, 5 hectometers is equivalent to a solid 500 meters. We're making great progress here! We've converted the kilometers and now the hectometers into meters, bringing us closer to a unified measurement system for the entire problem. This step-by-step approach is key to solving complex problems – break them down into smaller, manageable chunks, and each piece becomes much easier to handle. With the hectometers converted, we're ready to move on to the next unit, the decameters, and continue our conversion journey.

Converting Decameters to Meters

Alright, let's keep the ball rolling by converting decameters to meters. Fabiana has walked 9 decameters, and our mission is to figure out how many meters that is. You guessed it – we need another conversion factor! This time, the magic number is: 1 decameter is equal to 10 meters. See how these units are all related? It's like a staircase, each step connecting one unit to another. Knowing these relationships makes conversions much less intimidating. Now, just like before, we'll multiply the number of decameters by the conversion factor to get the equivalent distance in meters. So, 9 decameters * 10 meters/dam = 90 meters. There we have it! 9 decameters is the same as 90 meters. We're really on a roll now! We've successfully converted kilometers, hectometers, and decameters into meters. This is a huge accomplishment because it means we can finally compare all the distances on the same scale. It's like translating different languages into a common tongue – now we can understand the whole picture. We're just one step away from solving the main problem. We have all the individual distances in meters, and the next step is to combine them to find the total distance Fabiana has already walked.

Calculating Total Distance Walked

Now that we've converted all the distances to meters, we can find out the total distance Fabiana has already walked. This is a crucial step because it allows us to determine how much further she needs to go to reach her goal of 4 kilometers. Remember, we converted 5 hectometers to 500 meters, 9 decameters to 90 meters, and we were already given 125 meters. So, to find the total distance, we simply add these values together. It's like adding up the ingredients in a recipe to see the total amount of food you'll have. The calculation is as follows: 500 meters (from hectometers) + 90 meters (from decameters) + 125 meters = 715 meters. There you have it! Fabiana has already walked a total of 715 meters. This is a significant portion of her 4-kilometer goal, but she still has some distance to cover. This is the heart of solving word problems – breaking them down into smaller steps and then combining the results to get the final answer. We've come a long way, converting different units and adding them together. Now, we're just one step away from the grand finale: figuring out how many more meters Fabiana needs to walk. We've built a solid foundation, and the final calculation will be a breeze.

Finding the Remaining Distance

We're in the home stretch now! The final piece of the puzzle is to find the remaining distance Fabiana needs to walk. We know her total goal is 4000 meters (which we converted from 4 kilometers), and we know she's already walked 715 meters. So, to find the remaining distance, we simply subtract the distance she's walked from her total goal. It's like figuring out how much money you have left after spending some of it. The calculation is straightforward: 4000 meters (total) - 715 meters (walked) = 3285 meters. And there you have it! Fabiana still needs to walk 3285 meters to reach her daily goal. We did it! We successfully solved the problem by breaking it down into smaller, manageable steps. We converted different units of measurement, added them together, and then subtracted to find the remaining distance. This is a fantastic example of how math can be used to solve real-world problems. We can see that understanding unit conversions and basic arithmetic can help us navigate everyday situations. So, the next time you're faced with a math challenge, remember Fabiana's walk and break it down step by step – you'll be surprised at how easily you can find the solution!

Answer

Therefore, Fabiana still needs to walk 3285 meters.