Triathlon Rémi: Calcul De La Fraction Nage Du Parcours

Hey guys! Let's dive into this math problem about Rémi, a 13-year-old athlete, who's tackling a triathlon. This isn't just about numbers; it's about understanding how to break down a problem and solve it step by step. Rémi’s triathlon journey gives us a practical way to think about fractions and how they relate to real-world distances. We will explore how to calculate the fraction of the total distance Rémi swims, which involves combining different fractional parts of the race. This kind of problem-solving is super useful, not just in math class but also in everyday life, where we often need to figure out proportions and parts of a whole. Remember, understanding fractions is a fundamental skill, and this triathlon example makes it both relatable and a bit of fun. So, grab your mental calculators, and let’s get started!

Découvrons le Défi de Rémi

Okay, so Rémi is crushing this triathlon, right? He's doing three parts: running, biking, and swimming. We know he runs 1/3 of the total distance and bikes 20/31 of it. The question we need to crack is: what fraction of the whole race does he swim? To nail this, we've gotta figure out what portion of the race is left after the running and biking legs. This kind of problem is all about piecing things together, kinda like a puzzle. Each part of the race is like a piece, and we need to see how they fit into the whole. The challenge here isn’t just about the math; it’s about visualizing the race and how the different stages combine to make up the entire distance. This approach to problem-solving—breaking it down into smaller parts—is a skill that’s gonna help you way beyond just math class. Think about it: whether you’re planning a trip, managing your time, or even figuring out how much pizza to order, understanding how parts make up a whole is super important. So, let’s use Rémi’s triathlon as our training ground for this essential life skill.

La Clé : Additionner les Fractions de Course et de Vélo

Alright, to figure out the swimming part, first we need to add up the fractions Rémi spends running and biking. That means we gotta combine 1/3 (running) and 20/31 (biking). Now, here’s the math magic: we can't just add fractions willy-nilly; they need to have the same denominator, the bottom number. Think of it like trying to add apples and oranges – you need a common unit to add them together, right? So, we're looking for a common denominator for 3 and 31. The easiest way to find this is usually to multiply the two denominators together: 3 * 31 = 93. This means we need to convert both fractions so they have 93 as their denominator. This step is crucial because it sets us up to accurately combine the distances Rémi covers in the first two parts of the triathlon. Without a common denominator, our calculations would be off, and we wouldn't get the right fraction for the swimming portion. So, let’s focus on this step, make sure we nail it, and then we can move on to figuring out the rest of the problem. It’s like building a solid foundation for a house – get this right, and everything else falls into place!

Trouver un Dénominateur Commun

Okay, let’s break down how to find that common denominator, because it's super important. We've got 1/3 and 20/31, and we figured out that 93 is the magic number we're aiming for. So, how do we get there? For 1/3, we need to think: what do we multiply 3 by to get 93? The answer is 31. But here's the rule: whatever you do to the bottom (the denominator), you gotta do to the top (the numerator). So, we multiply both the top and bottom of 1/3 by 31. That gives us (1 * 31) / (3 * 31) which equals 31/93. Boom! We've converted 1/3 into a fraction with the denominator 93. Now, let’s tackle 20/31. This time, we need to figure out what to multiply 31 by to get 93. We already know it's 3 (because 3 * 31 = 93), so we multiply both the top and bottom of 20/31 by 3. This gives us (20 * 3) / (31 * 3) which equals 60/93. Awesome! We've converted both fractions to have the same denominator: 31/93 and 60/93. Now they’re speaking the same language, and we can finally add them together. Remember, this step is all about making sure we’re comparing apples to apples. With the same denominator, we can accurately see how much of the total distance Rémi has covered in running and biking.

Additionner les Fractions

Now that we’ve got our fractions singing the same tune with a common denominator of 93, we can finally add them together! We have 31/93 (the running part) and 60/93 (the biking part). Adding fractions with the same denominator is actually pretty straightforward – you just add the numerators (the top numbers) and keep the denominator the same. So, we’re doing 31 + 60. What does that give us? 91! So, 31/93 + 60/93 = 91/93. This means that Rémi has covered 91/93 of the total triathlon distance by running and biking. That’s a big chunk of the race already done! This fraction, 91/93, tells us exactly how much of the race is accounted for by these two legs. It’s like we’re piecing together a puzzle, and we’ve just figured out a major section. But, we’re not done yet. We still need to figure out how much of the race is left for swimming. Knowing that running and biking take up 91/93 of the race is a huge step, because it sets us up perfectly to calculate the remaining fraction. So, let’s keep going and see how we can use this information to find out the swimming portion.

Calculer la Fraction du Parcours Effectuée à la Nage

Okay, so we know Rémi has covered 91/93 of the race by running and biking. Now, to find out the fraction he swims, we need to figure out what's left over. Think of the entire race distance as one whole, or 1/1. If we subtract the fraction he's already done (91/93) from the whole race (1/1), we'll find out the fraction he swims. The math trick here is to rewrite 1/1 with the same denominator as our other fraction, which is 93. So, 1/1 becomes 93/93. Now we can easily subtract: 93/93 (the whole race) minus 91/93 (running and biking). What does that give us? To subtract fractions with the same denominator, you just subtract the numerators and keep the denominator the same. So, we have 93 - 91 = 2. That means 93/93 - 91/93 = 2/93. And there you have it! Rémi swims 2/93 of the total triathlon distance. This fraction represents the final piece of the puzzle, showing us exactly how much of the race is dedicated to swimming. It’s a small fraction compared to the running and biking, but every part is crucial in a triathlon!

Visualiser la Solution

Let’s take a step back and visualize the solution, because sometimes seeing it differently can really help it click. Imagine the entire triathlon distance as a long line divided into 93 equal parts (because our common denominator is 93). Rémi runs 31 of those parts (31/93), bikes 60 parts (60/93), and then swims the remaining 2 parts (2/93). If you picture this in your head, you can see how the fractions fit together to make up the whole race. This kind of mental picture is super useful for understanding fractions and proportions in general. It’s like having a visual aid that makes the math less abstract and more real. You can also think of it like a pie chart, where the whole pie represents the entire race, and each slice represents a different part. The running slice would be a bit smaller than the biking slice, and the swimming slice would be the smallest of them all. Visualizing the problem like this can also help you double-check your answer. Does it make sense that swimming is a small fraction of the total distance? In a triathlon, it usually is. So, by picturing the fractions and how they relate to each other, you can build a stronger understanding of the problem and the solution.

Réponse Finale

Alright, guys, we did it! We figured out that Rémi swims 2/93 of the total triathlon distance. This wasn’t just about crunching numbers; it was about breaking down a problem, finding common ground (literally, with the common denominator!), and piecing together the solution step by step. We started with a fraction for running (1/3) and another for biking (20/31), and we needed to find the swimming fraction. To do that, we had to get those fractions talking the same language by finding a common denominator. We added the running and biking fractions together, and then we subtracted that total from the whole race to find out what was left for swimming. This kind of problem-solving is a fantastic skill to have, not just for math class, but for all sorts of situations in life. Whether you’re planning a project, managing your time, or even figuring out a recipe, the ability to break things down and work with parts of a whole is super valuable. So, give yourselves a pat on the back for tackling this triathlon problem with Rémi. You've not only solved a math question, but you've also sharpened your problem-solving skills!