Calculating The Difference In Buko Juice Purchases A Math Problem

In this mathematical problem, we delve into the world of Hanz and his love for buko juice. Hanz, a buko juice enthusiast, made two separate purchases of this refreshing beverage over two weeks. Last week, he acquired a certain amount, and this week, he increased his stock. Our task is to determine exactly how much more buko juice Hanz bought this week compared to the previous one. This is a classic problem that involves working with mixed fractions and finding the difference between two quantities. To solve this, we'll need to convert the mixed fractions into improper fractions, find a common denominator, and then subtract the quantities to find the difference. Understanding these steps is crucial not only for solving this specific problem but also for tackling various mathematical problems involving fractions.

The ability to solve this kind of problem is an essential skill in mathematics. It requires a solid understanding of fractions, mixed numbers, and how to perform arithmetic operations with them. This isn't just an abstract exercise; it mirrors real-life situations where we need to compare quantities, such as volumes, weights, or amounts of money. By mastering these skills, we build a foundation for more advanced mathematical concepts and problem-solving techniques. Let's embark on this mathematical journey and unravel the solution to Hanz's buko juice dilemma, reinforcing our understanding of fractions and their applications in everyday contexts.

To accurately determine how much more buko juice Hanz purchased this week, we'll meticulously dissect the problem into manageable steps. Our primary objective is to find the difference between the amount of buko juice he bought this week and the amount he bought last week. This involves a series of mathematical operations, starting with understanding the given quantities and culminating in a clear, concise answer. Let's begin by revisiting the information provided in the problem statement:

• Last week, Hanz purchased $5 \frac{5}{9}$ liters of buko juice.
• This week, Hanz purchased $6 \frac{1}{3}$ liters of buko juice.

Our mission is to calculate the difference between these two quantities. To do so, we will follow these steps:

1. Converting Mixed Fractions to Improper Fractions: Mixed fractions can be tricky to work with directly, especially when performing subtraction. Therefore, the first step is to transform both mixed fractions into improper fractions. This involves multiplying the whole number part by the denominator of the fractional part and adding the numerator. The result becomes the new numerator, while the denominator remains the same.

   • For last week's purchase, we convert $5 \frac{5}{9}$ to an improper fraction:
     • Multiply the whole number (5) by the denominator (9): $5 * 9 = 45$
     • Add the numerator (5): $45 + 5 = 50$
     • The improper fraction is $\frac{50}{9}$ liters.
   • Similarly, for this week's purchase, we convert $6 \frac{1}{3}$ to an improper fraction:
     • Multiply the whole number (6) by the denominator (3): $6 * 3 = 18$
     • Add the numerator (1): $18 + 1 = 19$
     • The improper fraction is $\frac{19}{3}$ liters.

2. Finding a Common Denominator: To subtract fractions, they must have the same denominator. This common denominator allows us to accurately compare and subtract the quantities. We need to find the least common multiple (LCM) of the denominators 9 and 3. The LCM of 9 and 3 is 9. This means we only need to adjust the fraction $\frac{19}{3}$ so that it has a denominator of 9.

   • To convert $\frac{19}{3}$ to an equivalent fraction with a denominator of 9, we multiply both the numerator and the denominator by 3:
     • $\frac{19}{3} * \frac{3}{3} = \frac{19 * 3}{3 * 3} = \frac{57}{9}$ liters.

3. Subtracting the Fractions: Now that both fractions have the same denominator, we can subtract the amount of buko juice Hanz bought last week from the amount he bought this week. This will give us the difference, which is the answer we're looking for.

   • Subtract $\frac{50}{9}$ from $\frac{57}{9}$:
     • $\frac{57}{9} - \frac{50}{9} = \frac{57 - 50}{9} = \frac{7}{9}$ liters.

4. Simplifying the Result: The result, $\frac{7}{9}$ liters, is already in its simplest form because 7 and 9 have no common factors other than 1. This means we don't need to further reduce the fraction.

5. Comparing with the Given Options: Finally, we compare our calculated difference with the options provided in the problem.

By methodically working through these steps, we've transformed the problem into a series of manageable tasks. Now, we're ready to present the final answer and confirm our solution aligns with one of the provided choices.

Having meticulously worked through each step of the problem, we've arrived at a solution. We converted mixed fractions to improper fractions, found a common denominator, subtracted the fractions, and simplified the result. Now, let's consolidate our findings and state the answer clearly.

We determined that Hanz bought $\frac{7}{9}$ liters more buko juice this week than last week. Now, let's compare this result with the multiple-choice options provided in the problem:

A. $\frac{1}{3}$ B. $\frac{1}{5}$ C. $\frac{2}{3}$ D. $\frac{2}{5}$

Upon comparing our calculated difference, $\frac{7}{9}$ liters, with the given options, we realize that none of the options match our result. This might indicate a discrepancy in the provided options or a potential error in the problem statement itself. However, based on our calculations, the correct answer should be $\frac{7}{9}$ liters.

It's crucial to emphasize the importance of double-checking our work to ensure accuracy. We've carefully reviewed each step, from converting mixed fractions to subtracting and simplifying, and we're confident in our calculations. Therefore, the most accurate conclusion we can draw is that Hanz bought $\frac{7}{9}$ liters more buko juice this week compared to last week. It is possible there was a mistake when creating the multiple-choice options. In the real world, this highlights the need to be thorough when solving problems and to double-check the givens.

In conclusion, by meticulously working through the problem, we've successfully calculated the difference in the amount of buko juice Hanz purchased over two weeks. Our journey involved converting mixed fractions to improper fractions, finding a common denominator, performing subtraction, and simplifying the result. We found that Hanz bought $\frac{7}{9}$ liters more buko juice this week than last week.

This problem underscores the significance of several key mathematical concepts:

• Fractions and Mixed Numbers: This problem highlighted the importance of converting mixed numbers to improper fractions for ease of calculation. We saw how this conversion allows for straightforward subtraction.
• Finding a Common Denominator: The ability to find a common denominator is a cornerstone of fraction arithmetic. It enables us to compare and perform operations on fractions with different denominators.
• Subtraction of Fractions: Subtracting fractions with a common denominator is a fundamental skill in mathematics. This problem reinforced the process of subtracting numerators while keeping the denominator constant.
• Problem-Solving Strategies: Breaking down a complex problem into smaller, manageable steps is a crucial problem-solving strategy. We saw how this approach made the problem less daunting and more approachable.

Furthermore, this exercise demonstrated the importance of accuracy in mathematical calculations. We meticulously checked each step to ensure the correctness of our solution. It also highlighted the real-world relevance of mathematical skills. This type of problem mirrors everyday situations where we need to compare quantities and find differences.

While our calculated answer, $\frac{7}{9}$ liters, did not match any of the provided options, this underscores the importance of critical thinking and verifying results. It's a reminder that errors can occur, whether in problem statements or multiple-choice options, and it's crucial to rely on our understanding of the underlying mathematical principles to arrive at the correct solution. Ultimately, this exercise reinforced our understanding of fractions and honed our problem-solving skills, which are invaluable in mathematics and beyond.