Babitas Ribbon Collection Solving A Mixed Number Problem

In this article, we will delve into a fascinating mathematical problem involving Babita and her vibrant collection of blue and red ribbons. This exercise is not just about crunching numbers; it's about understanding fractions, applying addition, and visualizing real-world scenarios. So, let's unravel the problem and discover the colorful solution together.

The Ribbon Puzzle: Unveiling Babita's Collection

Babita's ribbon collection presents a classic word problem that requires us to combine mixed numbers. The problem states that Babita has 2 1/3 meters of blue ribbon and 3 1/2 meters of red ribbon. The core question is: How much blue and red ribbon does she have in total? To solve this, we need to add the lengths of the blue and red ribbons. This involves understanding how to add mixed numbers, which are numbers composed of a whole number and a fraction. The key to tackling this problem lies in converting these mixed numbers into improper fractions, finding a common denominator, adding the fractions, and then converting the result back into a mixed number, if necessary. This methodical approach will not only give us the answer but also enhance our understanding of fraction operations. Understanding fractions is crucial in various aspects of life, from cooking and baking to measuring and construction. By solving this problem, we reinforce our grasp of these fundamental mathematical concepts. It's also a great way to illustrate how math problems can be derived from everyday situations, making learning more relatable and engaging. This problem is a perfect example of how mathematical skills can be applied practically. As we work through the solution, we'll break down each step, ensuring clarity and comprehension. This problem is designed to test and improve your ability to work with fractions, a skill that is essential in many areas of mathematics and real-life applications. So, let's dive into the steps and solve the mystery of Babita's ribbon collection!

Breaking Down the Mixed Numbers

Mixed numbers can sometimes seem daunting, but they are quite manageable once you understand their components and how to manipulate them. In Babita's case, we have 2 1/3 meters of blue ribbon and 3 1/2 meters of red ribbon. The first step in solving this problem is to convert these mixed numbers into improper fractions. An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). This conversion is necessary because it makes addition much simpler. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator of the fraction and then add the numerator. This result becomes the new numerator, and the denominator remains the same. For the blue ribbon (2 1/3 meters), we multiply 2 (the whole number) by 3 (the denominator), which gives us 6. Then, we add 1 (the numerator) to get 7. So, 2 1/3 is equivalent to 7/3 as an improper fraction. Similarly, for the red ribbon (3 1/2 meters), we multiply 3 by 2, which equals 6. Adding the numerator 1 gives us 7. Thus, 3 1/2 is equivalent to 7/2 as an improper fraction. Now that we've converted the mixed numbers into improper fractions (7/3 and 7/2), we're one step closer to finding the total length of the ribbons. This conversion is a crucial step in simplifying the addition process. It allows us to work with fractions that have a clear numerator and denominator, making the next steps more straightforward. The ability to convert mixed numbers to improper fractions is a foundational skill in mathematics, particularly when dealing with fractions and mixed numbers in various operations. It's a skill that will be beneficial in more complex mathematical problems and real-life applications.

Finding the Common Denominator

Once the mixed numbers are converted into improper fractions, the next critical step in adding fractions is to find a common denominator. A common denominator is a number that can be divided evenly by both denominators of the fractions we want to add. In our problem, we have the fractions 7/3 and 7/2, representing the lengths of the blue and red ribbons, respectively. The denominators are 3 and 2. To find the common denominator, we need to identify the least common multiple (LCM) of these two numbers. The least common multiple is the smallest number that is a multiple of both denominators. For 3 and 2, the LCM is 6. This means 6 is the smallest number that both 3 and 2 can divide into without leaving a remainder. Now that we've identified the common denominator as 6, we need to convert both fractions so that they have this denominator. To convert 7/3 to an equivalent fraction with a denominator of 6, we multiply both the numerator and the denominator by the same number. In this case, we multiply both by 2 (since 3 multiplied by 2 equals 6). So, 7/3 becomes (7 * 2) / (3 * 2) = 14/6. Similarly, to convert 7/2 to an equivalent fraction with a denominator of 6, we multiply both the numerator and the denominator by 3 (since 2 multiplied by 3 equals 6). So, 7/2 becomes (7 * 3) / (2 * 3) = 21/6. Now we have two fractions, 14/6 and 21/6, both with the same denominator. This makes adding the fractions much simpler. Finding a common denominator is a crucial step in adding fractions, as it ensures that we are adding like terms. Without a common denominator, it would be like trying to add apples and oranges – the quantities cannot be directly combined. This step lays the groundwork for the final addition and allows us to find the total length of the ribbons accurately.

Adding the Fractions

With a common denominator in place, the process of adding fractions becomes straightforward. We now have the fractions 14/6 and 21/6, which represent the lengths of the blue and red ribbons, respectively, in terms of a common unit. To add these fractions, we simply add the numerators (the top numbers) while keeping the denominator (the bottom number) the same. So, we add 14 and 21, which gives us 35. The denominator remains 6. Therefore, the sum of the fractions is 35/6. This fraction represents the total length of the ribbons, but it's an improper fraction, meaning the numerator is larger than the denominator. While 35/6 is a correct answer, it's often more helpful to convert it back into a mixed number to better understand the total length. To convert an improper fraction to a mixed number, we divide the numerator by the denominator. The quotient (the whole number result of the division) becomes the whole number part of the mixed number, the remainder becomes the new numerator, and the denominator stays the same. When we divide 35 by 6, we get a quotient of 5 and a remainder of 5. This means that 35/6 is equivalent to the mixed number 5 5/6. So, Babita has a total of 5 5/6 meters of ribbon. This result gives us a clear understanding of the total length, with 5 meters being the whole number part and 5/6 of a meter being the fractional part. Adding fractions is a fundamental skill in mathematics, and this example demonstrates how it's applied in practical scenarios. By converting to a common denominator and adding the numerators, we can easily find the total of fractional quantities. The ability to work with fractions is essential in various real-life situations, from measuring ingredients in cooking to calculating distances in travel.

The Colorful Conclusion: Babita's Total Ribbon Length

After carefully working through each step of the problem, we've arrived at the conclusion: Babita has a total of 5 5/6 meters of ribbon. This answer represents the combined length of her blue and red ribbons. To recap, we started with the mixed numbers 2 1/3 meters (blue ribbon) and 3 1/2 meters (red ribbon). We converted these mixed numbers into improper fractions (7/3 and 7/2), found a common denominator (6), added the fractions (14/6 + 21/6 = 35/6), and then converted the improper fraction back into a mixed number (5 5/6). This process illustrates the importance of understanding fractions and mixed numbers in problem-solving. It also highlights the practical application of mathematical concepts in everyday situations. The ability to add fractions and mixed numbers is a valuable skill that extends beyond the classroom. It's used in various fields, such as construction, cooking, and finance. Understanding how to work with fractions allows us to accurately measure, calculate, and compare quantities. In Babita's case, knowing she has 5 5/6 meters of ribbon gives us a clear picture of her total collection. We can visualize this length and compare it to other measurements. This problem is a great example of how mathematics helps us quantify and understand the world around us. By breaking down the problem into smaller steps, we were able to solve it methodically and confidently. This approach is applicable to many mathematical problems and can help build problem-solving skills. So, next time you encounter a problem involving fractions or mixed numbers, remember the steps we've discussed, and you'll be well-equipped to find the solution. Babita's ribbon collection serves as a colorful reminder of the power and relevance of mathematics in our lives.