Calculating Ali's Walk: A Step-by-Step Guide

Hey guys! Let's dive into a fun little math problem together. We've got Ali, who's out for a walk, and we need to figure out how far he actually walked. Sounds easy, right? Well, it is! We'll break it down step by step so you can follow along and understand how to solve it. The question states that Ali ran $\frac{3}{8}$ of a 32 km route, and the rest he walked. So, how far did Ali walk? Let's crack this problem! This is a classic example of a fraction problem that's super common in algebra. Understanding how to solve this kind of problem is a great foundation for more complex math later on. It's all about understanding fractions, multiplication, and a little bit of subtraction. Don't worry if you're not a math whiz – we'll take it slow and make sure you get it. By the end of this, you'll be able to solve similar problems with confidence! This problem is straightforward, and we can solve it by first figuring out how many kilometers Ali ran and then subtracting that distance from the total distance. This approach helps to visualize the problem in a clear manner, making it easier to solve.

First, let's get the lowdown on fractions. A fraction like $\frac{3}{8}$ represents a part of a whole. In this case, the whole is Ali's 32 km walk. The fraction $\frac{3}{8}$ tells us that Ali ran 3 out of every 8 parts of the walk. To find out how far he ran, we need to calculate $\frac{3}{8}$ of 32 km. This means we need to multiply the fraction by the total distance. We'll convert the fraction to a decimal so that it's easy to calculate and understand. To do this, we will divide the numerator (3) by the denominator (8). This should leave us with a decimal representing the fraction. Once we have the decimal, we can use it to compute the distance that Ali ran. This is a pretty standard way to approach such problems, and it can come in handy in many different situations, such as calculating distances, measuring ingredients, or understanding proportions in general. After doing this, we can proceed to the second phase, which is finding out how far Ali walked, which is very easy once we have the distance he ran.

Let's break down the problem step-by-step so it's super clear. The problem gives us all the information we need, so the first step is to identify the important information. We know the total distance of the walk is 32 km. We know Ali ran $\frac{3}{8}$ of the total distance and walked the rest. We need to find out how far Ali walked. This is the ultimate goal. The most important thing is to remember the question. So, what is the question? The question is, "How many kilometers did Ali walk?" The problem is quite easy when you break it down. This is what we are going to do. First, we will determine how many kilometers Ali ran. Second, we'll take the result from step one and subtract it from the total distance (32 km) to find the distance Ali walked. Understanding the question is the foundation, ensuring you're solving the right problem, not just crunching numbers randomly. Now that we know exactly what we need to find, we can move forward with confidence. If you are feeling stuck, always try to rephrase the question in your own words. This is the best way to understand the problem. A well-defined problem makes it much easier to find a solution, and that's what we are going to do.

Step-by-Step Solution

Okay, let's get to the good part – actually solving the problem! Remember, we're trying to find out how many kilometers Ali walked. Here's how we'll do it:

1. Calculate the distance Ali ran: We know Ali ran $\frac{3}{8}$ of the 32 km. To find this distance, we'll multiply the fraction by the total distance: $(\frac{3}{8}) \times 32 ext{ km}$. To multiply a fraction by a whole number, multiply the numerator (top number) of the fraction by the whole number, and then divide by the denominator (bottom number). This helps you know how many kilometers he ran. So, multiplying 3 by 32, we get 96. Then, we divide 96 by 8, and we get 12 km. So Ali ran 12 km. That makes Ali the running champion, right?

2. Calculate the distance Ali walked: Now that we know Ali ran 12 km, we can find out how far he walked. We know the total distance is 32 km. To find the distance walked, subtract the distance ran from the total distance: $32 ext{ km} - 12 ext{ km} = 20 ext{ km}$.

Therefore, Ali walked 20 km. This kind of problem helps you practice your fractions and understand how they relate to real-world scenarios. It's like learning how to build a house - you start with the foundation (understanding the question and the basic math), then you build the walls (calculating each part), and finally, you have a complete structure (the answer!). We successfully found out how much Ali walked by knowing how much he ran. This strategy is applicable to many similar problems.

Visualizing the Solution

It is always a good idea to visualize the problem. This can make it easier to understand and remember. Imagine the whole journey as a straight line 32 km long. Now, divide that line into 8 equal parts. Ali ran $\frac{3}{8}$ of the way, which means he covered 3 of those 8 parts. We found out that this equals 12 km. The remaining 5 parts represent the distance Ali walked. As we have calculated, 5 parts are equal to 20 km. If you draw a picture, you will easily understand what the problem is about. Visualizing the problem can also help you check your work, making sure your answer makes sense in the context of the problem. By visualizing, you're making the math more tangible and less abstract. It's another way to make sure you fully grasp what's going on. In this case, the visualization reinforces the relationship between the fraction, the total distance, and the portions Ali ran and walked.

Conclusion

Alright, folks, we did it! We successfully solved the problem and found out how far Ali walked. Ali walked 20 km. This was a great exercise in fractions, multiplication, and subtraction. We broke down the problem step by step, making it easy to understand and solve. By learning how to approach these problems methodically, you're building a strong foundation for more complex math. Remember, the key is to break down the problem, understand what's being asked, and then apply the correct mathematical operations. You can also visualize the problem to make it easier to understand and check your work. Keep practicing, and you'll become a math pro in no time! Now, you're well-equipped to handle similar problems, and you can even start helping your friends with their math homework. Keep up the great work, and never be afraid to ask for help. Math can be fun, and it's all about practice and understanding the basic concepts. Keep practicing and exploring, and you'll see how quickly you improve! Keep an eye out for more fun math challenges and keep your brain active and engaged. That is all for now, and I hope you enjoyed the lesson!