Luana's Pool: Calculating Remaining Water Fraction

Hey guys! Let's dive into a fun math problem involving Luana's swimming pool. This is a classic example of a fraction problem, and it's super easy to visualize. We'll break it down step-by-step so you can totally nail it. The original problem is: 'A piscina da casa de Luana estava com 3/4 da capacidade total de água, mas em uma manhã ela conseguiu tirar 1/2 da água que havia. Qual fração da água que havia ainda?' Which translates to: Luana's pool was 3/4 full, but she removed 1/2 of the water that was there. How much water is left?

Understanding the Initial State: The Pool's Capacity

Okay, so the problem tells us that Luana's pool initially had 3/4 of its total capacity filled with water. Think of the pool as a whole, like a pizza. The whole pizza represents the full capacity of the pool. Now, we're told that 3/4 of this pizza is covered with water. This means the pool isn't completely full; there's some space left. This initial fraction, 3/4, is our starting point. It's crucial to understand this because it sets the stage for everything that follows. Imagine the pool divided into four equal parts. Three of those parts are filled with water. This visual can really help grasp the concept. Remember, fractions are just parts of a whole. In this case, the whole is the pool's maximum capacity. The water currently in the pool is a portion of that whole. Before Luana removes any water, the pool is at 75% capacity because 3/4 is equivalent to 75/100, which is the same as 75%. That 25% of the pool is empty and has room for more water. Understanding the starting point is critical before proceeding to the water removal phase.

Now, let's look at it practically. Suppose the pool can hold 1000 liters of water. If it's 3/4 full, it currently has (3/4) * 1000 = 750 liters of water. This gives you a clear sense of the amount of water we're dealing with. Knowing the initial amount helps us keep track of what's happening. The fraction 3/4 describes the initial amount of water in the pool relative to its maximum capacity. Before we introduce any changes, like Luana removing water, the pool is at the 3/4 mark. The concept of initial state is critical to solving the entire problem; otherwise, you will get it wrong.

Visualize the Water Level

Visualize a swimming pool; now, imagine that the water level reaches up to the 3/4 mark. You can almost see the water sloshing around. This visual image helps in understanding and solving the problem; it also sets a good foundation before moving on. What happens when some water is removed from it? We will find this out in the next section.

Removing the Water: Calculating the Amount Removed

Alright, so Luana decides to remove some water. The problem states she removes 1/2 of the water that was there. This part is super important. We're not removing 1/2 of the entire pool's capacity, but rather 1/2 of the water already present. Remember, the pool started with 3/4 full. So, we need to calculate 1/2 of 3/4. This is where a little bit of multiplication comes in. To find 1/2 of 3/4, we multiply the two fractions together: (1/2) * (3/4) = 3/8. So, Luana removed 3/8 of the pool's total capacity. This means that 3/8 of the entire pool's volume was taken out. Going back to our pizza analogy, she took away half of the pizza slices that were covered with water.

It's easy to get confused at this stage, but let's break it down further. Luana removed half of the water that was in the pool. If there were 750 liters initially, then she removed half of that amount. Which is (1/2) * 750 = 375 liters. From the initial 750 liters, 375 liters have been removed. This means the pool went down significantly and the water level also dropped. To recap, Luana removed 3/8 of the total volume of the pool. When we calculated the total amount of water left in the pool, we used this new fraction as the key element. Keep in mind that when we're dealing with fractions, multiplication is our friend. And when we are removing portions, we are subtracting. These two operations are essential in solving these types of problems.

The impact of removing water

When water is removed, the water level goes down. Removing the water has a direct impact on the fraction of water remaining in the pool. It is critical to calculate the new fraction.

Calculating the Remaining Water: Finding the Final Fraction

Now comes the final step: determining how much water is still in the pool. We know that the pool initially had 3/4 of its capacity filled, and we've figured out that Luana removed 3/8 of the total capacity. To find out what's left, we need to subtract the amount removed (3/8) from the initial amount (3/4). However, we can't directly subtract these fractions because they have different denominators (the bottom numbers). We need to find a common denominator. The smallest common denominator for 4 and 8 is 8. So, we'll convert 3/4 to an equivalent fraction with a denominator of 8. To do this, we multiply both the numerator (top number) and the denominator by 2: (3/4) * (2/2) = 6/8. Now, we have 6/8 representing the initial amount of water. We can now subtract the amount removed (3/8) from the initial amount (6/8): 6/8 - 3/8 = 3/8. Therefore, after Luana removed water, 3/8 of the pool's capacity remained filled with water. That means the pool is not completely empty; it has some water left.

Now, let's go back to our practical example. We calculated that Luana removed 375 liters. The pool initially had 750 liters. If we subtract the amount removed from the initial amount, we get the quantity of water remaining: 750 - 375 = 375 liters. If the pool has a 1000-liter capacity, then the remaining 375 liters represent 37.5% of the pool's volume. So, our final answer is that 3/8 of the pool's volume is filled with water. Also, to reiterate, it is essential to have common denominators when subtracting fractions. If you don't do this, you won't get the correct solution. And finally, when you subtract the water removed, you get the amount of water remaining.

Checking our answer

To ensure our answer is correct, we can also think about the amount of water Luana removed. She removed 3/8 of the water, so we know that she had 3/8 of the original capacity, and she removed another 3/8. Therefore, there is 3/8 of the water still in the pool. If you have any doubts, consider recalculating to see the results.

Conclusion: Summarizing the Solution

Let's wrap it up, guys! We started with a pool that was 3/4 full. Luana removed 1/2 of the water that was there. We calculated that this meant she removed 3/8 of the pool's total capacity. Then, by subtracting the amount removed (3/8) from the initial amount (6/8), we found that 3/8 of the pool's capacity remained filled with water. So, to answer the question, 3/8 of the pool's capacity still has water. Remember, breaking down the problem step-by-step, understanding the fractions, and using visuals can make these types of problems a breeze. Good job! Keep practicing, and you'll become a fraction whiz in no time. If you have any questions, just let me know!