Calculating Maria's Running Time A Step By Step Guide

Introduction

Hey guys! Let's dive into a fun math problem today. We're going to figure out how long Maria spends running each Saturday. This is a classic example of a word problem that combines fractions and a bit of real-life scenario, making it super practical. Word problems like these help us understand how math applies to our daily lives. So, grab your thinking caps, and let's get started! This kind of problem is fantastic for honing our skills with fractions, which are crucial in many areas, from cooking to construction. Let’s break down the problem step by step to make sure we understand exactly what's going on. Understanding word problems involves not just the math but also the comprehension of the situation presented. We need to identify the key information and what the problem is asking us to find. In this case, we know Maria exercises for a certain amount of time, and a fraction of that time is spent running. Our goal is to calculate that specific duration. This involves converting mixed numbers to improper fractions, multiplying fractions, and simplifying the result. By mastering these skills, we build a strong foundation for more advanced mathematical concepts. So, let's tackle this problem together and see how we can solve it efficiently and accurately.

Problem Breakdown

The problem states that Maria exercises for 1 5/6 hours every Saturday. Of this time, 3/4 is spent running. We need to calculate the actual hours Maria spends running. To solve this, we'll need to multiply the total exercise time by the fraction representing the running time. This involves a few key steps: first, converting the mixed number (1 5/6) into an improper fraction, then multiplying the fractions, and finally, simplifying the result back into a mixed number if necessary. Breaking down the problem into these smaller, manageable steps makes it easier to understand and solve. Remember, the key to solving word problems is to identify the relevant information and translate the words into mathematical operations. In this case, “of that time” indicates multiplication. By carefully following each step, we can accurately determine how many hours Maria runs each Saturday. This exercise not only strengthens our math skills but also enhances our problem-solving abilities, which are valuable in many real-world situations.

Step-by-Step Solution

1. Convert the Mixed Number to an Improper Fraction: First, we need to convert 1 5/6 into an improper fraction. To do this, we multiply the whole number (1) by the denominator (6) and add the numerator (5). This gives us (1 * 6) + 5 = 11. We then place this result over the original denominator, resulting in 11/6. Converting mixed numbers to improper fractions is a crucial step because it allows us to perform multiplication more easily. Improper fractions represent the total quantity as a single fraction, making calculations smoother and more straightforward. This conversion ensures that we are working with consistent units, allowing us to accurately determine the fraction of time Maria spends running. By mastering this conversion, we lay a solid foundation for tackling more complex fraction-related problems.
2. Multiply the Fractions: Next, we multiply the improper fraction (11/6) by the fraction representing the running time (3/4). To multiply fractions, we multiply the numerators (11 * 3) and the denominators (6 * 4). This gives us 33/24. The multiplication of fractions is a fundamental operation in many mathematical contexts. It allows us to determine parts of parts, which is essential in various real-life scenarios, from dividing recipes to calculating proportions. By understanding how to multiply fractions, we gain a powerful tool for solving a wide range of problems. In this case, multiplying 11/6 by 3/4 helps us pinpoint the exact fraction of an hour Maria spends running, making our solution more precise and meaningful.
3. Simplify the Fraction: Now, we simplify the fraction 33/24. Both 33 and 24 are divisible by 3. Dividing both the numerator and the denominator by 3 gives us 11/8. Simplifying fractions is a crucial step in mathematics as it helps us represent the answer in its most concise and understandable form. By reducing the fraction to its lowest terms, we make it easier to compare and interpret the result. In this case, simplifying 33/24 to 11/8 allows us to see the fraction in a more manageable form, which is essential for converting it back into a mixed number if needed. Mastering simplification techniques not only enhances our mathematical proficiency but also improves our ability to communicate mathematical concepts effectively.
4. Convert Back to a Mixed Number: Finally, we convert the improper fraction 11/8 back to a mixed number. We divide 11 by 8, which gives us 1 with a remainder of 3. This means the mixed number is 1 3/8. Converting improper fractions back to mixed numbers is often necessary to provide the answer in a more intuitive and relatable format. Mixed numbers combine a whole number and a fraction, making it easier to visualize the quantity. In this case, converting 11/8 to 1 3/8 hours helps us understand that Maria runs for one full hour and an additional 3/8 of an hour. This step ensures that our answer is not only mathematically correct but also practically meaningful. By mastering this conversion, we demonstrate a comprehensive understanding of fractions and their applications.

Answer

Maria runs for 1 3/8 hours each Saturday. So, the correct answer is C. 1 3/8.

Conclusion

Great job, guys! We've successfully solved the problem by breaking it down into manageable steps. Remember, practice makes perfect, so keep tackling those math problems. Understanding how to work with fractions is super useful in everyday life, from cooking to budgeting. By mastering these skills, you’re not just learning math; you’re building a foundation for problem-solving in all areas of life. Keep up the great work, and you'll be math whizzes in no time! Remember, every math problem is a puzzle waiting to be solved, and with the right approach, you can crack it. So, keep practicing, keep learning, and most importantly, keep having fun with math!