Banu's Running Distance: Math Problem Solution

Hey guys! Let's dive into a fun math problem about Banu, who is training for a race. To get ready, Banu runs a certain distance every day. We need to figure out the total distance Banu covers during his training. This is a super practical problem, because it shows us how math helps in everyday situations, especially when we're talking about sports and fitness. Let's break it down step by step so we can really understand how to solve this kind of problem. Get ready to put on your thinking caps and run through this with me!

Understanding the Problem

Alright, let’s get our heads around the problem. The key here is to really understand what's being asked. Banu runs 3/10 km every day. This is the distance Banu covers in a single day. Now, he doesn’t just run one day; Banu runs for 5 days to prepare for his race. So, what we need to find out is: how far does Banu run in total over these 5 days? It’s like figuring out the total mileage when you're planning a road trip! This problem is all about repeated addition, which is really just a fancy way of saying multiplication. Think of it like this: if you do the same thing every day, you can multiply to find the total. So, Banu running the same distance each day means we can use multiplication to find the total distance. Make sense? We're going to take this daily distance and multiply it by the number of days. This is a crucial step because if we don't understand what the problem is asking, we can't solve it correctly. Always make sure you read the problem carefully and identify what information you have and what you need to find. Once we've got this clear in our minds, the math becomes much easier. We're essentially adding 3/10 km five times, but multiplication is a much quicker way to do that. So, let's move on to setting up the equation and solving it!

Setting Up the Equation

Okay, now that we know what we need to find, let’s set up the equation. This is where we turn the words of the problem into a mathematical expression. Remember, Banu runs 3/10 km each day, and he does this for 5 days. To find the total distance, we need to multiply these two numbers. So, the equation looks like this: Total distance = (Distance per day) × (Number of days). In our case, this translates to: Total distance = (3/10 km) × (5 days). This equation is the roadmap to our solution. It tells us exactly what operation we need to perform to get the answer. Setting up the equation correctly is super important because it ensures we’re doing the right math. It’s like having the right recipe before you start baking; if you don't have the correct ingredients and instructions, the cake won't turn out right! Think of the equation as the recipe for solving the problem. Now, we’ve got our equation all set up, we’re ready for the next step, which is solving it. We'll take 3/10 and multiply it by 5. This will give us the total distance Banu runs in preparation for his race. So, let’s move on and crunch those numbers!

Solving the Equation

Alright, let's get down to solving the equation! We've already figured out that the equation is: Total distance = (3/10 km) × (5 days). Now, we need to actually do the multiplication. When we multiply a fraction by a whole number, we can think of the whole number as a fraction with a denominator of 1. So, 5 can be written as 5/1. This makes our equation look like this: Total distance = (3/10) × (5/1) km. To multiply fractions, we multiply the numerators (the top numbers) and the denominators (the bottom numbers). So, we multiply 3 by 5 to get the new numerator, and we multiply 10 by 1 to get the new denominator. This gives us: Total distance = (3 × 5) / (10 × 1) km. Now, let's do those multiplications: 3 multiplied by 5 is 15, and 10 multiplied by 1 is 10. So, we have: Total distance = 15/10 km. We're not quite done yet, though! We have a fraction, 15/10, which we can simplify. Both 15 and 10 are divisible by 5. If we divide both the numerator and the denominator by 5, we get: Total distance = (15 ÷ 5) / (10 ÷ 5) km. This simplifies to: Total distance = 3/2 km. We can also express this as a mixed number. 3/2 is the same as 1 and 1/2. So, Banu runs a total of 1 and 1/2 kilometers. See how we broke it down step by step? We turned the word problem into an equation, then multiplied the fractions, and finally, we simplified the answer. That’s how you solve it like a pro!

Converting to Decimal (Optional)

Okay, guys, let's take it a step further! While we've already found the answer as a fraction (3/2 km) and a mixed number (1 and 1/2 km), sometimes it's helpful to see the answer as a decimal too. Converting to a decimal can give us a slightly different perspective on the distance. To convert the fraction 3/2 to a decimal, we simply divide the numerator (3) by the denominator (2). So, we're doing 3 divided by 2. When you divide 3 by 2, you get 1.5. This means that 3/2 is the same as 1.5. Therefore, Banu runs a total of 1.5 kilometers. Seeing the answer as 1.5 km can be really intuitive because we often talk about distances in decimals in our daily lives. For example, if you're using a fitness app or a GPS, distances are usually displayed in decimal form. So, knowing how to convert fractions to decimals can be super useful. Plus, it gives us another way to check our work. We already knew the answer was 1 and 1/2 km, and 1.5 km is just another way of saying the same thing. This step is optional, but it's a great way to reinforce your understanding and practice your math skills. Plus, it shows how different forms of the same number can be used in different situations. So, whether you prefer fractions, mixed numbers, or decimals, you've got the tools to understand Banu's total running distance!

Final Answer

Alright, we've reached the finish line! After working through the problem step by step, we've got our final answer. Let’s recap what we did. We started by understanding the problem, which was figuring out the total distance Banu ran while training for a race. Banu runs 3/10 km every day, and he runs for 5 days. We set up the equation: Total distance = (3/10 km) × (5 days). Then, we solved the equation by multiplying the fractions, which gave us 15/10 km. We simplified the fraction to 3/2 km, which is the same as 1 and 1/2 km. And just for good measure, we also converted it to a decimal, which is 1.5 km. So, the final answer is: Banu runs a total of 1 and 1/2 kilometers (or 1.5 km) during his 5 days of training. This means Banu covered a significant distance preparing for his race! This problem shows us how fractions and multiplication work together in a real-world situation. We took a seemingly complex question and broke it down into manageable steps. We identified the information we had, set up an equation, solved it, and even simplified the answer. That’s some serious math power! Remember, practice makes perfect, so keep tackling these kinds of problems, and you'll become a math whiz in no time. Great job, everyone! We nailed it!