Evaluate The Expression For The Given Value Of The Variables. 0.9g - 2.1h G = 15, H=2
Understanding how to evaluate algebraic expressions with given variable values is a fundamental skill in mathematics. This process involves substituting specific numerical values for variables within an expression or equation and computing the result accordingly. In this article, we will explore step-by-step how to evaluate the expression 0.9g - 2.1h given the values G = 15 and H = 2. We will also discuss important concepts related to algebraic expressions, variable substitution, and the importance of accurate calculations.
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Understanding the Expression: 0.9g - 2.1h
Before diving into the evaluation process, it is essential to understand the structure of the expression and the roles played by each variable.
Breaking Down the Expression
The expression 0.9g - 2.1h consists of two terms:
- 0.9g: The first term, which involves the variable g multiplied by 0.9.
- - 2.1h: The second term, which involves the variable h multiplied by 2.1, with a subtraction sign preceding it.
This expression is linear, meaning it involves variables raised to the first power and no products of variables or exponents.
Understanding the Variables G and H
The variables G and H are placeholders for numerical values. In this context:
- G = 15
- H = 2
These are specific values assigned to the variables, which allows us to compute the value of the entire expression.
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Step-by-Step Evaluation Process
Evaluating an algebraic expression involves systematic substitution and calculation. Let's outline the steps:
Step 1: Write Down the Expression
The original expression is:
```plaintext
0.9g - 2.1h
```
Step 2: Substitute the Given Values
Replace g with 15 and h with 2:
```plaintext
0.9 15 - 2.1 2
```
Step 3: Perform the Multiplications
Calculate each term separately:
- 0.9 15:
\[
0.9 \times 15 = (0.9 \times 10) + (0.9 \times 5) = 9 + 4.5 = 13.5
\]
- 2.1 2:
\[
2.1 \times 2 = 4.2
\]
Step 4: Combine the Results
Subtract the second product from the first:
```plaintext
13.5 - 4.2 = 9.3
```
Thus, the evaluated value of the expression when G = 15 and H = 2 is 9.3.
---
Additional Concepts Related to Evaluating Expressions
Understanding the process of evaluating expressions extends beyond this specific example. Here are some key concepts and tips to deepen your understanding.
Variables and Constants
- Variables are symbols (like g and h) that represent unknown or changing values.
- Constants are fixed numerical values, such as 0.9 and 2.1 in the expression.
Substitution and Evaluation
- Substitution involves replacing variables with their numerical values.
- Proper substitution ensures accurate calculations and understanding of the expression's value.
Order of Operations
When evaluating expressions, adhere to the order of operations (PEMDAS/BODMAS):
- Parentheses
- Exponents
- Multiplication and Division (left to right)
- Addition and Subtraction (left to right)
In this case, only multiplication and subtraction are involved, so perform multiplications first, then subtraction.
Handling Negative Signs
- Negative signs before terms indicate subtraction.
- Be cautious to maintain the correct sign during calculations.
Practical Applications of Evaluating Expressions
Evaluating expressions with given variable values is a critical skill across various fields:
- Physics: Calculating force, velocity, or energy based on variables.
- Economics: Determining profit or cost based on quantities and rates.
- Engineering: Computing stress, strain, or other parameters in systems.
- Statistics: Calculating expected values or probabilities.
In real-world scenarios, you often need to evaluate expressions to make informed decisions or predictions.
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Common Mistakes to Avoid When Evaluating Expressions
While evaluating algebraic expressions, it's easy to make errors. Here are some common pitfalls and how to avoid them:
1. Incorrect Substitution
- Always double-check that you've replaced each variable with the correct value.
- Use brackets if necessary to clarify the order of operations.
2. Ignoring the Sign of Terms
- Keep track of positive and negative signs.
- Remember that subtraction signs affect the entire term following them.
3. Miscalculations in Multiplication
- Perform multiplications carefully, possibly using a calculator for complex numbers.
- Break down complex multiplications into smaller steps if needed.
4. Neglecting the Order of Operations
- Follow the standard rules to ensure accurate results.
Extending the Concept: Evaluating More Complex Expressions
Once comfortable with simple expressions, you can explore more complex ones involving:
- Multiple variables
- Exponents
- Fractions
- Parentheses
For example, if the expression was (0.9g - 2.1h) / (g + h), you would follow similar substitution steps, perform numerator and denominator calculations separately, then divide.
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Summary
In summary, evaluating the expression 0.9g - 2.1h for G = 15 and H = 2 involves:
- Substituting the given values into the expression.
- Performing the multiplication operations.
- Combining the results through subtraction.
The final result is 9.3, illustrating the importance of systematic calculation and understanding the underlying concepts of algebra.
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Conclusion
Mastering the skill of evaluating algebraic expressions is crucial for students and professionals alike. It enhances problem-solving abilities and provides a foundation for advanced mathematical concepts. By carefully substituting values, following the order of operations, and performing calculations accurately, you can confidently evaluate complex expressions in various contexts. Remember, practice makes perfect—so keep working through different problems to strengthen your understanding and proficiency in algebra.
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