Evaluate 4-0.25g+0.5h Given G=10 And H=5 A Step-by-Step Guide

Introduction

In this article, we will walk through the process of evaluating the algebraic expression $4-0.25g+0.5h$ given specific values for the variables $g$ and $h$. This type of problem is a fundamental concept in algebra, serving as a cornerstone for more complex mathematical operations. Understanding how to substitute values into an expression and simplify it is crucial for success in mathematics. We will demonstrate a step-by-step approach to solving this problem, ensuring clarity and comprehension for readers of all levels. This includes careful substitution, performing the arithmetic operations in the correct order, and arriving at the final result. Mastery of these skills is essential for tackling more advanced algebraic problems and real-world applications. The expression we will be evaluating is a linear expression, which is a simple yet important type of algebraic expression. It involves constants, variables, and arithmetic operations such as addition, subtraction, and multiplication. By understanding how to evaluate this expression, we lay the foundation for understanding more complex expressions and equations. The ability to evaluate expressions accurately is not just a mathematical skill; it is also a valuable life skill. From budgeting finances to calculating measurements in construction, the principles of evaluating expressions apply in various practical situations. Therefore, this article aims to provide not only a solution to the specific problem but also a broader understanding of the underlying concepts and their relevance.

Understanding the Expression

The expression we are tasked with evaluating is $4 - 0.25g + 0.5h$. This is a linear algebraic expression, which means it involves variables raised to the power of 1, constants, and arithmetic operations. Let's break down the components of the expression to better understand its structure. The expression consists of three terms: a constant term (4), a term involving the variable $g$ (-0.25g), and a term involving the variable $h$ (0.5h). Each term is separated by either a plus or a minus sign, indicating addition or subtraction. The constant term 4 is a fixed value that does not change regardless of the values of the variables. The term -0.25g represents the product of the constant -0.25 and the variable $g$. This means that the value of this term will change depending on the value of $g$. Similarly, the term 0.5h represents the product of the constant 0.5 and the variable $h$. Its value will change depending on the value of $h$. To evaluate the expression, we need to substitute the given values for the variables $g$ and $h$ and then perform the arithmetic operations in the correct order. It's crucial to understand the order of operations (often remembered by the acronym PEMDAS/BODMAS) to arrive at the correct result. This expression is a simple example of the many algebraic expressions we encounter in mathematics and real-world applications. Understanding how to break down and analyze such expressions is a crucial skill for problem-solving and critical thinking. By mastering the fundamentals of algebraic expressions, we can build a strong foundation for more advanced mathematical concepts.

Substituting the Values

Now, let's substitute the given values for the variables $g$ and $h$ into the expression. We are given that $g = 10$ and $h = 5$. This means we will replace every instance of $g$ with 10 and every instance of $h$ with 5 in the expression $4 - 0.25g + 0.5h$. Substituting $g = 10$ into the term $-0.25g$ gives us $-0.25 imes 10$. Substituting $h = 5$ into the term $0.5h$ gives us $0.5 imes 5$. After the substitution, the expression becomes: $4 - 0.25(10) + 0.5(5)$. This new expression no longer contains the variables $g$ and $h$; instead, it consists only of numerical values and arithmetic operations. The next step is to simplify this numerical expression by performing the operations in the correct order. It is essential to pay close attention to the signs (positive and negative) and to the order of operations to avoid errors. Substitution is a fundamental skill in algebra and is used extensively in solving equations, simplifying expressions, and evaluating functions. The ability to accurately substitute values for variables is crucial for success in mathematics and related fields. In this case, we have substituted numerical values for variables, but the same principle applies when substituting algebraic expressions for variables. The key is to replace the variable with the given value or expression, taking care to maintain the correct mathematical structure.

Performing the Calculations

With the values substituted, we now have the expression $4 - 0.25(10) + 0.5(5)$. To simplify this, we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). In this expression, we have multiplication, subtraction, and addition. According to the order of operations, we perform multiplication before addition and subtraction. First, we calculate $-0.25 imes 10$, which equals $-2.5$. Next, we calculate $0.5 imes 5$, which equals $2.5$. Now our expression becomes: $4 - 2.5 + 2.5$. Next, we perform the addition and subtraction from left to right. Subtracting 2.5 from 4 gives us 1.5, so the expression becomes: $1.5 + 2.5$. Finally, adding 1.5 and 2.5 gives us 4. Therefore, the value of the expression $4 - 0.25g + 0.5h$ when $g = 10$ and $h = 5$ is 4. It is important to perform each operation carefully and double-check your work to ensure accuracy. Errors in calculation can lead to incorrect results. Understanding and applying the order of operations is a critical skill in mathematics, and it is essential for solving a wide range of problems. By following the correct order, we can ensure that we arrive at the correct answer. This step-by-step approach helps to minimize errors and makes the process more manageable.

The Final Result

After performing the substitution and calculations, we have arrived at the final result. The expression $4 - 0.25g + 0.5h$, when evaluated at $g = 10$ and $h = 5$, equals 4. This means that when we replace $g$ with 10 and $h$ with 5 in the expression and simplify it according to the order of operations, the resulting value is 4. This result is a single numerical value, representing the value of the expression under the given conditions. The final result is the culmination of all the steps we have taken, from understanding the expression to substituting the values and performing the calculations. It is the answer to the problem we set out to solve. The process of arriving at this result has demonstrated the importance of accurate substitution, adherence to the order of operations, and careful calculation. These skills are essential for success in algebra and other areas of mathematics. The final result of 4 represents a specific value for the expression under the given conditions. It is a constant value, meaning it does not change as long as the values of $g$ and $h$ remain 10 and 5, respectively. Understanding how to arrive at a final result like this is crucial for solving more complex problems in algebra and beyond. It provides a concrete answer to a mathematical question and demonstrates the power of algebraic manipulation. The ability to evaluate expressions and arrive at final results is a fundamental skill that has applications in various fields, from science and engineering to finance and economics. By mastering these skills, we can confidently tackle a wide range of mathematical challenges.

Conclusion

In conclusion, we have successfully evaluated the expression $4 - 0.25g + 0.5h$ when $g = 10$ and $h = 5$. We found that the expression evaluates to 4. This process involved understanding the expression, substituting the given values for the variables, and performing the arithmetic operations in the correct order. We emphasized the importance of following the order of operations (PEMDAS/BODMAS) to ensure accuracy. The key steps in this process were: 1. Understanding the expression: Identifying the terms, variables, and constants. 2. Substituting the values: Replacing the variables $g$ and $h$ with their given values. 3. Performing the calculations: Multiplying, subtracting, and adding in the correct order. 4. Arriving at the final result: Obtaining the value of the expression, which in this case was 4. This example illustrates a fundamental concept in algebra: the ability to evaluate expressions by substituting values for variables. This skill is essential for solving equations, simplifying expressions, and tackling more complex mathematical problems. The principles demonstrated in this article can be applied to a wide range of algebraic expressions and equations. By practicing these skills, students can build a strong foundation in mathematics and gain confidence in their problem-solving abilities. The ability to evaluate expressions accurately is not only a valuable mathematical skill but also a crucial life skill. It is used in various everyday situations, such as calculating costs, measuring ingredients in cooking, and planning budgets. Therefore, mastering this skill is beneficial for both academic and practical purposes. We hope this step-by-step guide has provided a clear and comprehensive understanding of how to evaluate algebraic expressions. By following the principles outlined in this article, readers can confidently tackle similar problems and continue to develop their mathematical skills.