A Polytank Has 4500 Liters Of Water. 1/5 Is Used For Cleaning. (i) How Much Water Was Used? (ii) What Percent Of Water Remains?
In this article, we will explore a practical problem involving water usage from a polytank and percentage calculations. We'll break down the steps to find the volume of water used for cleaning and determine the percentage of water remaining in the tank. This exercise is not only a mathematical problem but also a real-world scenario that highlights the importance of resource management and understanding proportions. Let's dive into the details and solve this problem together.
H2: (i) Finding the Volume of Water Used for Cleaning
To determine the volume of water used for cleaning, we need to calculate the fraction of the total water volume that was utilized. The problem states that the polytank initially contains 4500 liters of water, and 1/5 of this water is used for cleaning purposes. This is a classic problem involving fractions and proportions, a fundamental concept in mathematics with wide-ranging applications in daily life. Understanding how to work with fractions is crucial for various calculations, from cooking recipes to managing finances. Now, let's delve into the calculation process.
H3: Step-by-Step Calculation
The key to solving this problem lies in understanding that finding a fraction of a whole involves multiplication. In this case, we need to find 1/5 of 4500 liters. Mathematically, this can be expressed as:
(1/5) * 4500 liters
To perform this multiplication, we can simply divide 4500 by 5. This is because multiplying by a fraction like 1/5 is the same as dividing by its denominator, which is 5 in this case. Let's perform the division:
4500 liters / 5 = 900 liters
Therefore, the volume of water used for cleaning is 900 liters. This straightforward calculation demonstrates how fractions can be used to determine portions of a whole. It is a crucial skill for various real-world applications, such as calculating discounts, understanding proportions in recipes, and managing budgets. This problem provides a practical context for understanding the importance of fractions in everyday life.
H3: Practical Implications
Understanding how to calculate the volume of water used is essential for managing water resources effectively. In households and industries, knowing the amount of water consumed for different purposes helps in planning and conservation efforts. For example, if a household uses 900 liters of water for cleaning from a 4500-liter tank, they can estimate how frequently they need to refill the tank and adjust their water usage habits accordingly. This simple calculation can lead to significant water savings and a more sustainable lifestyle. Furthermore, in industrial settings, accurate water usage calculations are critical for cost management and environmental compliance. By understanding and applying these basic mathematical principles, we can make informed decisions about resource consumption and contribute to a more sustainable future.
H2: (ii) Calculating the Percentage of Water Left in the Tank
Now, let's determine the percentage of water remaining in the polytank after the cleaning process. This involves a few steps, including calculating the remaining water volume and then expressing that volume as a percentage of the original amount. Understanding percentages is crucial in many aspects of life, from financial calculations to understanding statistical data. This problem provides a practical application of percentage calculations in the context of water management.
H3: Step-by-Step Calculation
First, we need to calculate the amount of water left in the tank. We know that the tank initially contained 4500 liters, and 900 liters were used for cleaning. To find the remaining volume, we subtract the used amount from the initial amount:
4500 liters - 900 liters = 3600 liters
So, there are 3600 liters of water remaining in the tank. Now, we need to express this remaining volume as a percentage of the original volume. To do this, we use the following formula:
Percentage = (Remaining Volume / Original Volume) * 100%
Plugging in the values, we get:
Percentage = (3600 liters / 4500 liters) * 100%
Now, let's simplify the fraction:
3600 / 4500 = 36 / 45 = 4 / 5
So, the fraction simplifies to 4/5. Now, we multiply this fraction by 100%:
(4/5) * 100% = 0.8 * 100% = 80%
Therefore, 80% of the water is left in the tank. This calculation demonstrates how to convert a fraction or a ratio into a percentage, a valuable skill in various real-world scenarios. Understanding percentages allows us to easily compare proportions and make informed decisions.
H3: Significance of Percentage Calculations
Percentage calculations are fundamental in many areas of life, including finance, statistics, and everyday decision-making. In the context of water management, knowing the percentage of water remaining in a tank helps in assessing the available water resources and planning for future needs. For instance, if a tank is only 20% full, it indicates a need for refilling or conserving water. In business, percentages are used to calculate profit margins, discounts, and growth rates. In statistics, percentages help in understanding data distributions and making comparisons. By mastering percentage calculations, individuals can improve their financial literacy, data analysis skills, and overall decision-making abilities. This problem highlights the practical relevance of percentages in managing resources and making informed choices.
H2: Conclusion: Practical Application of Mathematical Concepts
In conclusion, this exercise demonstrated how basic mathematical concepts, such as fractions and percentages, can be applied to solve real-world problems. By calculating the volume of water used for cleaning and the percentage of water remaining in the polytank, we gained insights into practical water management. These calculations are not only mathematically sound but also relevant to everyday situations where resource management is crucial. Understanding these concepts empowers us to make informed decisions about water usage and contribute to sustainable practices. The ability to work with fractions and percentages is a valuable skill that extends beyond the classroom and into various aspects of life, from managing household resources to making financial decisions. This exercise underscores the importance of mathematical literacy in navigating the complexities of the modern world.