Calculating Jessica's Walking Distance: A Math Problem

Hey Plastik Magazine readers! Let's dive into a fun little math problem. We're going to figure out how far Jessica walked in total. This is a classic example of adding fractions, a fundamental concept in mathematics. Don't worry, it's not as scary as it sounds! We'll break it down step by step, so even if math isn't your favorite subject, you'll be able to follow along. This problem is perfect for anyone looking to brush up on their basic math skills or help a younger sibling with their homework. The key here is understanding how to add fractions with different denominators. This skill is super useful in everyday life, whether you're baking a cake or figuring out how far you need to drive. So, grab your pencils and let's get started!

Understanding the Problem: Jessica's Journey

The Problem: Jessica walks a certain distance to the post office and then continues walking to the library. We know the distances she walked for each part of her journey. Our mission? To calculate the total distance she covered. This is a simple addition problem disguised as a real-world scenario. The problem is stated as: Jessica walks $\frac{1}{3}$ mile to the post office and then $\frac{2}{5}$ mile to the library. How far did Jessica walk altogether? Let's clarify what the problem is asking. The question is straightforward: what is the sum of the two distances? This means we need to add the fraction $\frac{1}{3}$ to the fraction $\frac{2}{5}$.

To solve this, we'll use the principles of fraction addition. Remember, you can only add fractions if they have the same denominator, which is the bottom number of the fraction. If the denominators are different, as they are in this problem (3 and 5), we need to find a common denominator. The common denominator is a number that both 3 and 5 can divide into evenly. The most common approach is to find the least common multiple (LCM) of the denominators. In this case, the LCM of 3 and 5 is 15. Once we've found the common denominator, we'll convert both fractions to equivalent fractions with that denominator. This involves multiplying the numerator (the top number) and the denominator of each fraction by a number that results in the common denominator. Finally, we'll add the numerators of the equivalent fractions and keep the common denominator. The resulting fraction will be the answer to the problem, representing the total distance Jessica walked. So, are you ready to unlock this mystery? Let's take the first step towards the solution by finding the common denominator!

Finding the Common Denominator: The Key Step

Alright, guys and gals, let's get down to the nitty-gritty and find that common denominator! Remember, the common denominator is the foundation upon which we'll build our solution. It's the key to unlocking our ability to add these fractions. We need to find the least common multiple (LCM) of 3 and 5. The LCM is the smallest number that both 3 and 5 can divide into without any remainders. There are a few ways to find the LCM, but here’s a simple method. List out the multiples of each number until you find a number that appears in both lists:

• Multiples of 3: 3, 6, 9, 12, 15, 18, 21…
• Multiples of 5: 5, 10, 15, 20, 25…

See that? The smallest number that appears in both lists is 15. Therefore, the least common multiple of 3 and 5 is 15. This means our common denominator will be 15. Now that we've found our common denominator, we need to convert our original fractions, $\frac{1}{3}$ and $\frac{2}{5}$, into equivalent fractions that have a denominator of 15. To do this, we'll multiply the numerator and the denominator of each fraction by a number that results in a denominator of 15. Let’s start with $\frac{1}{3}$. We need to multiply the denominator (3) by 5 to get 15. But we can't just change the denominator; we must also multiply the numerator (1) by 5 to keep the fraction equivalent. So, $\frac{1}{3}$ becomes $\frac{1*5}{3*5} = \frac{5}{15}$. Next up is $\frac{2}{5}$. To get a denominator of 15, we need to multiply the denominator (5) by 3. Again, we multiply the numerator (2) by 3 as well. So, $\frac{2}{5}$ becomes $\frac{2*3}{5*3} = \frac{6}{15}$. Excellent! We've successfully converted both fractions to equivalent fractions with a common denominator. We're now ready for the final step: adding the fractions!

Adding the Fractions: The Final Calculation

We're in the home stretch, folks! Now that we have our fractions with a common denominator, we can finally add them together. Remember, our original problem was to find the total distance Jessica walked, which means we need to add $\frac{1}{3} + \frac{2}{5}$. We've already converted these fractions to equivalent fractions with a common denominator of 15. We found that $\frac{1}{3} = \frac{5}{15}$ and $\frac{2}{5} = \frac{6}{15}$. So, our addition problem now becomes $\frac{5}{15} + \frac{6}{15}$. Adding fractions with the same denominator is super easy. You simply add the numerators and keep the denominator the same. Therefore, $5 + 6 = 11$. Keeping the denominator of 15, our final answer is $\frac{11}{15}$. This means that Jessica walked a total of $\frac{11}{15}$ mile.

So, there you have it! We've successfully solved the problem and found the total distance Jessica walked. We started with a word problem, broke it down into smaller, manageable steps, and used our knowledge of fractions to arrive at the correct answer. You guys did amazing! You have conquered this mathematical challenge. Remember, practice is key when it comes to math. The more you practice, the more comfortable and confident you'll become. So, keep practicing, keep learning, and keep exploring the wonderful world of mathematics! Feel free to revisit this problem and try similar ones. Remember, it's always fun to sharpen your skills.

Conclusion: The Answer and Beyond

So, after all our hard work, we've determined that Jessica walked a total of $\frac{11}{15}$ mile. Therefore, the correct answer to the question is C. $\frac{11}{15}$ mile. Now you know how to add fractions and solve a word problem involving distances. This skill is useful in various real-life scenarios, from calculating travel distances to measuring ingredients while cooking. The principles used here can also be applied to other fraction-related problems. You can use these methods to solve other questions and real-world problems. Keep practicing and applying these concepts, and you will become even better at math. Keep learning, and always be curious!

Final Answer: C. $\frac{11}{15}$ mile