Calculating Total Gallons Of Paint And Thinner For Brigada Eskwela

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Introduction

In preparation for the Brigada Eskwela, a dedicated stakeholder generously volunteered their time and resources to paint the PAGCOR building for Grade Six students. This act of community involvement highlights the importance of creating a conducive learning environment for students. To accomplish this task, the stakeholder brought a variety of painting supplies, including different colors and paint thinner. Specifically, they brought 5 1/3 gallons of white paint, 3 1/2 gallons of green paint, 3/4 gallon of brown paint, and 2 gallons of paint thinner. The main question we aim to answer is: What is the total volume, in gallons, of all the liquids brought by the stakeholder? This involves adding mixed numbers and fractions, a fundamental skill in mathematics. Understanding how to calculate the total volume of paint and thinner is crucial for planning and executing painting projects efficiently. This calculation not only helps in ensuring that there is enough material for the task but also aids in budgeting and resource allocation. By accurately determining the total volume, we can appreciate the stakeholder’s contribution and ensure that the painting project proceeds smoothly. The process involves converting mixed numbers to improper fractions, finding a common denominator, and adding the fractions. This exercise provides a practical application of arithmetic skills, demonstrating how mathematical concepts are relevant in real-world scenarios. Moreover, it highlights the importance of attention to detail and accuracy in calculations, which are essential in various fields, including construction, interior design, and project management. Therefore, understanding this calculation is not just an academic exercise but a practical skill that can be applied in numerous contexts. The stakeholder's contribution to the Brigada Eskwela initiative exemplifies community spirit and commitment to education, emphasizing the importance of collective effort in improving school facilities. Through this detailed calculation, we not only solve a mathematical problem but also appreciate the practical implications of such contributions to community projects. The involvement of stakeholders in school activities plays a vital role in fostering a sense of ownership and pride among community members, further enhancing the learning environment for students.

Breaking Down the Problem

Before we dive into the calculations, let’s break down the problem. We need to find the total volume of all the liquids the stakeholder brought. This includes:

  • 5 1/3 gallons of white paint
  • 3 1/2 gallons of green paint
  • 3/4 gallon of brown paint
  • 2 gallons of paint thinner

To find the total volume, we need to add these quantities together. The challenge here is that we have mixed numbers (like 5 1/3 and 3 1/2) and a fraction (3/4). To add these together, it's easiest to convert the mixed numbers into improper fractions. This conversion simplifies the addition process and ensures accurate results. Converting mixed numbers to improper fractions involves multiplying the whole number by the denominator of the fraction and adding the numerator. The result becomes the new numerator, while the denominator remains the same. For instance, 5 1/3 can be converted to an improper fraction by multiplying 5 by 3 (which equals 15) and adding 1, resulting in 16. The improper fraction is then 16/3. Similarly, 3 1/2 can be converted by multiplying 3 by 2 (which equals 6) and adding 1, resulting in 7. The improper fraction is 7/2. Once we have all the quantities expressed as fractions, including the whole number 2 (which can be written as 2/1), we can proceed with finding a common denominator. A common denominator is a number that all the denominators can divide into evenly. This allows us to add the fractions together by simply adding their numerators. This process not only simplifies the calculation but also reduces the risk of errors. Breaking down the problem into smaller, manageable steps is a crucial strategy in problem-solving. It allows us to focus on each component individually and ensures a systematic approach to finding the solution. In this case, converting mixed numbers to improper fractions and then finding a common denominator are key steps in accurately determining the total volume of liquids brought by the stakeholder. By carefully addressing each step, we can confidently arrive at the correct answer and appreciate the mathematical principles involved in this practical scenario. The stakeholder's thoughtful contribution highlights the value of community support in enhancing educational facilities, demonstrating how such efforts can make a significant difference in creating a positive learning environment for students.

Step 1: Converting Mixed Numbers to Improper Fractions

First, let's convert the mixed numbers to improper fractions. This makes it easier to add them together. We have two mixed numbers:

  • 5 1/3 gallons of white paint
  • 3 1/2 gallons of green paint

To convert a mixed number to an improper fraction, we use the formula:

(Whole number × Denominator) + Numerator / Denominator

For 5 1/3:

(5 × 3) + 1 / 3 = 15 + 1 / 3 = 16/3 gallons

So, 5 1/3 gallons is equal to 16/3 gallons.

For 3 1/2:

(3 × 2) + 1 / 2 = 6 + 1 / 2 = 7/2 gallons

Thus, 3 1/2 gallons is equal to 7/2 gallons. Converting mixed numbers into improper fractions is a crucial step because it allows us to perform addition and subtraction with greater ease and accuracy. Mixed numbers combine a whole number and a fraction, which can complicate calculations if not properly converted. By transforming them into improper fractions, where the numerator is greater than or equal to the denominator, we express the quantity as a single fractional value. This simplifies the process of finding a common denominator and adding the fractions together. For example, when dealing with the volume of paint, converting mixed numbers to improper fractions provides a more precise representation of the quantity. In the context of the Brigada Eskwela, where a stakeholder has contributed various amounts of paint, this conversion ensures that we accurately calculate the total volume, which is essential for planning the painting project. The process of converting 5 1/3 gallons to 16/3 gallons and 3 1/2 gallons to 7/2 gallons demonstrates the practical application of this mathematical skill. These improper fractions represent the total number of thirds and halves, respectively, making it easier to combine them with other fractional amounts. Moreover, this conversion step highlights the importance of understanding fraction concepts in real-world scenarios. Whether it's measuring ingredients for a recipe, calculating distances, or determining the quantity of materials for a project, the ability to convert mixed numbers to improper fractions is a valuable skill. Therefore, this step is not just a mathematical exercise but a practical tool for solving problems in various contexts. The stakeholder's contribution to the school exemplifies the community's commitment to supporting education, and accurate calculations, such as these, ensure that resources are utilized effectively.

Step 2: Identifying All Fractions

Now that we've converted the mixed numbers, let's list all the fractions we need to add:

  • 16/3 gallons (white paint)
  • 7/2 gallons (green paint)
  • 3/4 gallon (brown paint)
  • 2 gallons of paint thinner

We can write the 2 gallons of paint thinner as a fraction by putting it over 1, so it becomes 2/1 gallons. Identifying all the fractions is a pivotal step in calculating the total volume of liquids, as it sets the stage for finding a common denominator and adding the quantities together. This step involves compiling all the fractional amounts, ensuring that no component is overlooked. In this scenario, we have the volume of white paint, green paint, brown paint, and paint thinner, each expressed as a fraction. The white paint contributes 16/3 gallons, the green paint contributes 7/2 gallons, and the brown paint contributes 3/4 gallon. The paint thinner, which is 2 gallons, is also expressed as a fraction by writing it as 2/1. This representation ensures that all quantities are in a consistent fractional format, which is essential for the subsequent steps in the calculation. By explicitly listing all the fractions, we create a clear picture of the components that need to be added. This systematic approach minimizes the risk of error and allows us to focus on the next step: finding a common denominator. The importance of this step extends beyond the specific mathematical problem. In many real-world scenarios, such as project planning, resource allocation, or even cooking, identifying and listing all the components is crucial for accurate calculations and successful outcomes. Whether it's the volume of different liquids, the quantities of ingredients in a recipe, or the amount of materials needed for a construction project, a comprehensive list ensures that nothing is missed. The stakeholder's contribution to the Brigada Eskwela highlights the value of community involvement in supporting education. Accurate calculations, facilitated by steps like this, ensure that resources are used effectively and the painting project is completed successfully. This detailed approach not only solves a mathematical problem but also emphasizes the importance of precision and thoroughness in practical tasks, demonstrating how mathematical skills are relevant in various contexts.

Step 3: Finding the Least Common Denominator (LCD)

To add fractions, we need a common denominator. The denominators we have are 3, 2, 4, and 1. The least common denominator (LCD) is the smallest number that all these denominators can divide into evenly.

  • Multiples of 3: 3, 6, 9, 12, 15...
  • Multiples of 2: 2, 4, 6, 8, 10, 12...
  • Multiples of 4: 4, 8, 12, 16...
  • Multiples of 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12...

The least common multiple (LCM) of 3, 2, 4, and 1 is 12. Therefore, the LCD is 12. Finding the Least Common Denominator (LCD) is a crucial step in adding fractions, as it provides a common basis for combining different fractional quantities. The LCD is the smallest number that is a multiple of all the denominators involved, ensuring that each fraction can be converted to an equivalent form with the same denominator. In this scenario, we need to add fractions with denominators of 3, 2, 4, and 1. To find the LCD, we identify the multiples of each denominator and determine the smallest multiple that is common to all. The multiples of 3 are 3, 6, 9, 12, and so on. The multiples of 2 are 2, 4, 6, 8, 10, 12, and so on. The multiples of 4 are 4, 8, 12, 16, and so on. And the multiples of 1 are simply all whole numbers, including 12. By examining these multiples, we find that the smallest number that appears in all lists is 12. Therefore, the LCD for 3, 2, 4, and 1 is 12. This LCD allows us to convert each fraction to an equivalent fraction with a denominator of 12. This conversion is essential because fractions can only be added directly if they have the same denominator. Once all fractions have the same denominator, we can add their numerators while keeping the denominator constant. The concept of the LCD extends beyond basic arithmetic and is relevant in various mathematical and practical contexts. For instance, in algebra, finding the LCD is necessary when adding or subtracting rational expressions. In real-world applications, the LCD can be used in tasks such as scheduling events, measuring quantities, and planning projects. The stakeholder's contribution to the Brigada Eskwela highlights the community's dedication to supporting education. By accurately calculating the total volume of paint, we ensure that resources are used efficiently and the painting project is completed successfully. The process of finding the LCD demonstrates how mathematical principles are applied in practical scenarios, reinforcing the importance of mathematical literacy in everyday life.

Step 4: Converting Fractions to Equivalent Fractions with the LCD

Now, we need to convert each fraction to an equivalent fraction with a denominator of 12.

  • 16/3: To get a denominator of 12, we multiply both the numerator and denominator by 4 (since 3 × 4 = 12). So, 16/3 becomes (16 × 4) / (3 × 4) = 64/12.
  • 7/2: To get a denominator of 12, we multiply both the numerator and denominator by 6 (since 2 × 6 = 12). So, 7/2 becomes (7 × 6) / (2 × 6) = 42/12.
  • 3/4: To get a denominator of 12, we multiply both the numerator and denominator by 3 (since 4 × 3 = 12). So, 3/4 becomes (3 × 3) / (4 × 3) = 9/12.
  • 2/1: To get a denominator of 12, we multiply both the numerator and denominator by 12 (since 1 × 12 = 12). So, 2/1 becomes (2 × 12) / (1 × 12) = 24/12.

Now we have the following equivalent fractions:

  • 64/12 gallons
  • 42/12 gallons
  • 9/12 gallon
  • 24/12 gallons

Converting fractions to equivalent fractions with the LCD is a vital step in adding or subtracting fractions, ensuring that all quantities are expressed in a common unit. This process involves multiplying both the numerator and the denominator of each fraction by a specific number, such that the new denominator is equal to the LCD. This maintains the value of the fraction while allowing for straightforward addition or subtraction. In our scenario, having determined that the LCD is 12, we convert each fraction to an equivalent fraction with a denominator of 12. For 16/3, we multiply both the numerator (16) and the denominator (3) by 4, resulting in 64/12. For 7/2, we multiply both the numerator (7) and the denominator (2) by 6, resulting in 42/12. For 3/4, we multiply both the numerator (3) and the denominator (4) by 3, resulting in 9/12. And for 2/1, we multiply both the numerator (2) and the denominator (1) by 12, resulting in 24/12. This conversion ensures that all fractions now have the same denominator, allowing us to add them by simply adding their numerators. The equivalent fractions we obtain are 64/12 gallons, 42/12 gallons, 9/12 gallon, and 24/12 gallons. This step highlights the importance of understanding fraction equivalence. Fractions that look different can represent the same value, and this principle is crucial in various mathematical contexts. Whether it's simplifying expressions, solving equations, or performing calculations in real-world scenarios, the ability to convert fractions to equivalent forms is an essential skill. The stakeholder's contribution to the Brigada Eskwela initiative exemplifies community support for education. By accurately converting fractions, we ensure that the total volume of paint is calculated correctly, enabling effective planning and execution of the painting project. This detailed approach underscores the practicality of mathematical skills in everyday tasks and the significance of precision in problem-solving.

Step 5: Adding the Fractions

Now that all the fractions have the same denominator, we can add them together. To add fractions with the same denominator, we add the numerators and keep the denominator the same.

64/12 + 42/12 + 9/12 + 24/12 = (64 + 42 + 9 + 24) / 12

Add the numerators:

64 + 42 + 9 + 24 = 139

So, the sum is 139/12 gallons. Adding the fractions is the culmination of the previous steps, where we combine all the equivalent fractions to find the total volume of liquids. Since all the fractions now have the same denominator, which is 12, we simply add their numerators while keeping the denominator constant. This process is straightforward and ensures an accurate result. We have the fractions 64/12, 42/12, 9/12, and 24/12. To add them, we add the numerators: 64 + 42 + 9 + 24. Summing these numbers gives us 139. Therefore, the total sum of the fractions is 139/12 gallons. This fraction represents the total volume of white paint, green paint, brown paint, and paint thinner that the stakeholder brought for the Brigada Eskwela project. The process of adding fractions with a common denominator is a fundamental concept in arithmetic and is widely applicable in various contexts. Whether it's calculating the total amount of ingredients in a recipe, determining the combined length of multiple segments, or finding the total volume of liquids, the ability to add fractions is an essential skill. In this scenario, adding the fractions allows us to determine the precise quantity of painting supplies available, which is crucial for planning the project effectively. The result, 139/12 gallons, provides a clear picture of the total resources at hand. This step highlights the importance of accuracy in mathematical calculations. Even a small error in the addition can lead to a significant discrepancy in the final result, which could impact the success of the project. The stakeholder's contribution to the Brigada Eskwela initiative underscores the community's commitment to supporting education. By accurately adding the fractions, we ensure that we have a clear understanding of the resources available, contributing to the smooth execution of the painting project. This demonstrates how mathematical skills are essential for practical tasks and how precision can lead to successful outcomes.

Step 6: Converting the Improper Fraction to a Mixed Number

The result we have, 139/12 gallons, is an improper fraction. To make it easier to understand, let's convert it to a mixed number. To do this, we divide the numerator (139) by the denominator (12).

139 ÷ 12 = 11 with a remainder of 7

So, the whole number part is 11, and the remainder is 7. The mixed number is 11 7/12 gallons. Converting the improper fraction to a mixed number provides a more intuitive understanding of the quantity. An improper fraction, where the numerator is greater than or equal to the denominator, can be difficult to visualize in real-world terms. By converting it to a mixed number, we express the quantity as a whole number and a fraction, making it easier to conceptualize. In this case, we have the improper fraction 139/12 gallons, which represents the total volume of liquids. To convert this to a mixed number, we divide the numerator (139) by the denominator (12). The division results in 11 with a remainder of 7. This means that 139 divided by 12 equals 11 whole units, with 7 units remaining. Therefore, the mixed number is 11 7/12 gallons. This representation is more practical because it clearly indicates that we have 11 full gallons and an additional 7/12 of a gallon. This is easier to visualize than the improper fraction 139/12. The process of converting improper fractions to mixed numbers is a fundamental skill in arithmetic and is useful in various real-world scenarios. Whether it's measuring ingredients for cooking, calculating distances, or determining quantities for a project, mixed numbers provide a more practical and relatable way to express measurements. In the context of the Brigada Eskwela project, knowing that the stakeholder contributed 11 7/12 gallons of liquid provides a clear understanding of the amount of resources available. This can help in planning the painting project more effectively. The stakeholder's contribution to the school highlights the importance of community involvement in education. By accurately converting the improper fraction to a mixed number, we ensure that we have a precise understanding of the resources, contributing to the success of the project. This step underscores the practical application of mathematical skills in everyday tasks and demonstrates how precision in calculations can lead to better outcomes.

Final Answer

The stakeholder brought a total of 11 7/12 gallons of liquids. This includes the white paint, green paint, brown paint, and paint thinner. This calculation helps us understand the total amount of resources available for the Brigada Eskwela painting project. The final answer, 11 7/12 gallons, represents the total volume of liquids contributed by the stakeholder for the Brigada Eskwela painting project. This comprehensive calculation includes the white paint, green paint, brown paint, and paint thinner, providing a clear understanding of the total resources available. This result is crucial for effective project planning, ensuring that there are sufficient materials to complete the task. Expressing the final answer as a mixed number, 11 7/12 gallons, provides a practical and intuitive understanding of the quantity. It is easier to visualize 11 full gallons and an additional 7/12 of a gallon compared to the improper fraction 139/12 gallons. This representation helps in assessing whether the amount is sufficient for the intended purpose and in making informed decisions about resource allocation. This calculation demonstrates the importance of mathematical skills in real-world scenarios. From converting mixed numbers to improper fractions, finding the least common denominator, adding fractions, and converting back to a mixed number, each step is essential for arriving at the correct answer. This process highlights how arithmetic concepts are applied in practical situations, such as project management and resource planning. The stakeholder's generous contribution to the Brigada Eskwela initiative underscores the community's commitment to supporting education. By accurately calculating the total volume of liquids, we ensure that the resources are utilized effectively, contributing to the success of the painting project. This final answer not only solves a mathematical problem but also emphasizes the significance of community involvement in enhancing educational facilities and creating a positive learning environment for students. The dedication and support of stakeholders play a vital role in improving schools and fostering a sense of pride and ownership among community members.