Evaluate The Expression With Its Given Values: 3 X Y \frac{3x}{y} Y 3 X ; Where X = 4 X = 4 X = 4 And Y = 12 Y = 12 Y = 12 A. 9 B. 3 C. 4 D. 1

Mar 13, 2025 by ADMIN 148 views

**Evaluating Algebraic Expressions: A Step-by-Step Guide**

Introduction

Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill for students to master. In this article, we will focus on evaluating the expression $\frac{3x}{y}$ , where $x = 4$ and $y = 12$ . We will break down the steps involved in evaluating this expression and provide a clear explanation of the process.

Understanding the Expression

The given expression is $\frac{3x}{y}$ . This is a simple algebraic expression that involves a fraction. The numerator is $3x$ , and the denominator is $y$ . To evaluate this expression, we need to substitute the given values of $x$ and $y$ into the expression.

Substituting Values

The given values are $x = 4$ and $y = 12$ . We will substitute these values into the expression $\frac{3x}{y}$ .

x = 4
y = 12
expression = (3 * x) / y

Evaluating the Expression

Now that we have substituted the values into the expression, we can evaluate it. To do this, we need to follow the order of operations (PEMDAS):

Multiply 3 and x: $3 \times 4 = 12$
Divide 12 by y: $12 \div 12 = 1$

Therefore, the value of the expression $\frac{3x}{y}$ , where $x = 4$ and $y = 12$ , is 1.

Conclusion

Evaluating algebraic expressions is an essential skill for students to master. By following the steps outlined in this article, we can evaluate the expression $\frac{3x}{y}$ , where $x = 4$ and $y = 12$ . The value of the expression is 1.

Common Mistakes to Avoid

When evaluating algebraic expressions, there are several common mistakes to avoid:

Not following the order of operations (PEMDAS)
Not substituting values into the expression correctly
Not simplifying the expression before evaluating it

By avoiding these common mistakes, we can ensure that we evaluate algebraic expressions correctly and accurately.

Real-World Applications

Evaluating algebraic expressions has numerous real-world applications. For example:

In science, algebraic expressions are used to model real-world phenomena, such as the motion of objects or the growth of populations.
In finance, algebraic expressions are used to calculate interest rates, investment returns, and other financial metrics.
In engineering, algebraic expressions are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Practice Problems

To practice evaluating algebraic expressions, try the following problems:

Evaluate the expression $\frac{2x}{y}$ , where $x = 5$ and $y = 10$ .
Evaluate the expression $\frac{4x}{y}$ , where $x = 3$ and $y = 8$ .
Evaluate the expression $\frac{6x}{y}$ , where $x = 2$ and $y = 6$ .

Answer Key

$\frac{2 \times 5}{10} = \frac{10}{10} = 1$
$\frac{4 \times 3}{8} = \frac{12}{8} = \frac{3}{2}$
$\frac{6 \times 2}{6} = \frac{12}{6} = 2$

Introduction

Evaluating algebraic expressions is a crucial skill for students to master. In our previous article, we provided a step-by-step guide on how to evaluate the expression $\frac{3x}{y}$ , where $x = 4$ and $y = 12$ . In this article, we will answer some frequently asked questions (FAQs) related to evaluating algebraic expressions.

Q&A

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when evaluating an algebraic expression. The acronym PEMDAS stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any 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 evaluate an algebraic expression with multiple variables?

A: To evaluate an algebraic expression with multiple variables, you need to substitute the values of each variable into the expression and then simplify the expression. For example, if you have the expression $2x + 3y$ , where $x = 4$ and $y = 5$ , you would substitute the values of $x$ and $y$ into the expression and get $2(4) + 3(5) = 8 + 15 = 23$ .

Q: What is the difference between an equation and an expression?

A: An equation is a statement that says two expressions are equal, while an expression is a mathematical statement that contains variables, constants, and mathematical operations. For example, $2x + 3 = 5$ is an equation, while $2x + 3$ is an expression.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary operations. For example, if you have the expression $2x + 3x + 4$ , you would combine the like terms $2x$ and $3x$ to get $5x + 4$ .

Q: What are some common mistakes to avoid when evaluating algebraic expressions?

A: Some common mistakes to avoid when evaluating algebraic expressions include:

Not following the order of operations (PEMDAS)
Not substituting values into the expression correctly
Not simplifying the expression before evaluating it
Not checking for any errors or typos in the expression

Practice Problems

To practice evaluating algebraic expressions, try the following problems:

Evaluate the expression $\frac{2x}{y}$ , where $x = 5$ and $y = 10$ .
Evaluate the expression $\frac{4x}{y}$ , where $x = 3$ and $y = 8$ .
Evaluate the expression $\frac{6x}{y}$ , where $x = 2$ and $y = 6$ .

Answer Key

$\frac{2 \times 5}{10} = \frac{10}{10} = 1$
$\frac{4 \times 3}{8} = \frac{12}{8} = \frac{3}{2}$
$\frac{6 \times 2}{6} = \frac{12}{6} = 2$

By practicing these problems, you can improve your skills in evaluating algebraic expressions and apply them to real-world situations.

Real-World Applications

Evaluating algebraic expressions has numerous real-world applications. For example:

In science, algebraic expressions are used to model real-world phenomena, such as the motion of objects or the growth of populations.
In finance, algebraic expressions are used to calculate interest rates, investment returns, and other financial metrics.
In engineering, algebraic expressions are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Conclusion

Evaluating algebraic expressions is a crucial skill for students to master. By following the steps outlined in this article and practicing the problems provided, you can improve your skills in evaluating algebraic expressions and apply them to real-world situations. Remember to always follow the order of operations (PEMDAS) and simplify the expression before evaluating it.