Select The Correct Answer.If $g=8$, What Is The Value Of The Expression $\frac{g}{2+3}$?A. $ 8 5 \frac{8}{5} 5 8 [/tex] B. $\frac{11}{2}$ C. 7 D. 19
Introduction
In this article, we will delve into the world of mathematics and focus on solving a specific expression involving a variable. The expression in question is $\frac{g}{2+3}$, where $g=8$. Our goal is to determine the value of this expression by substituting the given value of $g$ and simplifying the resulting expression.
Understanding the Expression
Before we proceed with the solution, let's break down the expression and understand its components. The expression is a fraction, where the numerator is the variable $g$ and the denominator is the sum of two constants, $2$ and $3$. We are given that $g=8$, so we can substitute this value into the expression.
Substituting the Value of g
Now that we have the value of $g$, we can substitute it into the expression. This gives us:
Simplifying the Expression
The next step is to simplify the expression by evaluating the denominator. The denominator is the sum of $2$ and $3$, which equals $5$. Therefore, the expression becomes:
Conclusion
In conclusion, by substituting the value of $g$ into the expression and simplifying the resulting fraction, we have determined that the value of the expression $\frac{g}{2+3}$ is $\frac{8}{5}$.
Answer
The correct answer is:
- A. $\frac{8}{5}$
Discussion
This problem requires a basic understanding of algebra and fraction simplification. The key concept here is to substitute the given value of $g$ into the expression and then simplify the resulting fraction. This problem is a great example of how to apply algebraic concepts to solve real-world problems.
Tips and Tricks
When solving expressions involving variables, it's essential to follow the order of operations (PEMDAS):
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
By following this order of operations, you can ensure that you simplify expressions correctly and arrive at the correct solution.
Common Mistakes
When solving expressions involving variables, some common mistakes to avoid include:
- Failing to substitute the given value of the variable into the expression.
- Not simplifying the resulting fraction correctly.
- Not following the order of operations (PEMDAS).
By being aware of these common mistakes, you can avoid them and arrive at the correct solution.
Real-World Applications
This problem has real-world applications in various fields, such as:
- Science: When working with variables and expressions in scientific equations, it's essential to simplify expressions correctly to arrive at accurate results.
- Engineering: In engineering, expressions involving variables are used to model real-world systems and make predictions about their behavior.
- Finance: In finance, expressions involving variables are used to calculate interest rates, investment returns, and other financial metrics.
Introduction
In our previous article, we explored how to solve expressions involving variables by substituting the given value of the variable into the expression and simplifying the resulting fraction. In this article, we will provide a Q&A section to help you better understand the concepts and address any questions you may have.
Q: What is the order of operations (PEMDAS)?
A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying expressions. The acronym PEMDAS stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I simplify a fraction?
A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD is the largest number that divides both the numerator and denominator without leaving a remainder. Once you have found the GCD, you can divide both the numerator and denominator by the GCD to simplify the fraction.
Q: What is the difference between a variable and a constant?
A: A variable is a letter or symbol that represents a value that can change. A constant, on the other hand, is a value that does not change. In the expression $\frac{g}{2+3}$, $g$ is a variable because its value can change, while $2$ and $3$ are constants because their values do not change.
Q: How do I evaluate an expression with multiple variables?
A: To evaluate an expression with multiple variables, you need to substitute the given values of each variable into the expression and then simplify the resulting expression. For example, if you have the expression $\frac{g}{2+3} + \frac{h}{4+5}$, you would substitute the given values of $g$ and $h$ into the expression and then simplify the resulting expression.
Q: What is the importance of following the order of operations?
A: Following the order of operations is crucial when simplifying expressions because it ensures that you perform the operations in the correct order. If you do not follow the order of operations, you may arrive at an incorrect solution.
Q: Can you provide an example of a real-world application of solving expressions involving variables?
A: Yes, here is an example of a real-world application of solving expressions involving variables:
Suppose you are a manager at a company and you want to calculate the total cost of producing a certain number of units of a product. The cost of producing each unit is represented by the variable $c$, and the number of units produced is represented by the variable $n$. The total cost of producing $n$ units is given by the expression $\frac{c}{2+3} \times n$. To calculate the total cost, you would substitute the given values of $c$ and $n$ into the expression and then simplify the resulting expression.
Q: What are some common mistakes to avoid when solving expressions involving variables?
A: Some common mistakes to avoid when solving expressions involving variables include:
- Failing to substitute the given value of the variable into the expression.
- Not simplifying the resulting fraction correctly.
- Not following the order of operations (PEMDAS).
- Not considering the units of the variables when simplifying the expression.
By being aware of these common mistakes, you can avoid them and arrive at the correct solution.
Conclusion
In this article, we have provided a Q&A section to help you better understand the concepts of solving expressions involving variables. We have covered topics such as the order of operations (PEMDAS), simplifying fractions, and real-world applications of solving expressions involving variables. By following the tips and avoiding the common mistakes, you can become proficient in solving expressions involving variables and apply this knowledge to real-world problems.