Leon Evaluated The Expression − 1 2 ( − 4 A − 6 ) + A 2 -\frac{1}{2}(-4a-6)+a^2 − 2 1 ( − 4 A − 6 ) + A 2 For A = 8 A=8 A = 8 .1. $-\frac{1}{2}(-4(8)-6)+8^2$2. $-\frac{1}{2}(-32-6)+8^2$3. $-\frac{1}{2}(-38)+8^2$4. $-\frac{1}{2}(-38)+16$5. $-19+16$6.

Mar 13, 2025 by ADMIN 252 views

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

Introduction

In mathematics, evaluating expressions is a crucial skill that helps us simplify complex mathematical statements. It involves applying the order of operations (PEMDAS) to simplify the expression and arrive at a final value. In this article, we will evaluate the expression $-\frac{1}{2}(-4a-6)+a^2$ for $a=8$ .

Step 1: Substitute the Value of a

The first step in evaluating the expression is to substitute the value of $a$ into the expression. In this case, we are given that $a=8$ . So, we will replace $a$ with $8$ in the expression.

-\frac{1}{2}(-4(8)-6)+8^2

Step 2: Apply the Order of Operations

The next step is to apply the order of operations (PEMDAS) to simplify the expression. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. In this expression, we have parentheses and exponents.

-\frac{1}{2}(-4(8)-6)+8^2

First, we will evaluate the expression inside the parentheses: $-4(8)-6$ . This simplifies to $-32-6$ , which is equal to $-38$ .

-\frac{1}{2}(-38)+8^2

Next, we will evaluate the exponent: $8^2$ . This simplifies to $64$ .

-\frac{1}{2}(-38)+64

Step 3: Simplify the Expression

Now that we have simplified the expression, we can combine the terms. We will start by simplifying the fraction: $-\frac{1}{2}(-38)$ . This simplifies to $19$ .

19+64

Finally, we will add the two terms together: $19+64$ . This simplifies to $83$ .

Conclusion

In this article, we evaluated the expression $-\frac{1}{2}(-4a-6)+a^2$ for $a=8$ . We applied the order of operations (PEMDAS) to simplify the expression and arrived at a final value of $83$ . This demonstrates the importance of following the order of operations when evaluating expressions.

Discussion

Evaluating expressions is a crucial skill in mathematics that helps us simplify complex mathematical statements. By following the order of operations (PEMDAS), we can simplify expressions and arrive at a final value. In this article, we evaluated the expression $-\frac{1}{2}(-4a-6)+a^2$ for $a=8$ and arrived at a final value of $83$ .

Common Mistakes

When evaluating expressions, it is easy to make mistakes. Some common mistakes include:

Not following the order of operations (PEMDAS)
Not simplifying expressions inside parentheses
Not evaluating exponents correctly
Not combining terms correctly

Tips and Tricks

When evaluating expressions, here are some tips and tricks to keep in mind:

Always follow the order of operations (PEMDAS)
Simplify expressions inside parentheses first
Evaluate exponents next
Combine terms last
Check your work by plugging in a value for the variable

Real-World Applications

Evaluating expressions has many real-world applications. For example:

In science, we use expressions to model real-world phenomena, such as the motion of objects or the growth of populations.
In finance, we use expressions to calculate interest rates or investment returns.
In engineering, we use expressions to design and optimize systems, such as bridges or buildings.

Conclusion

Introduction

In our previous article, we evaluated the expression $-\frac{1}{2}(-4a-6)+a^2$ for $a=8$ . We applied the order of operations (PEMDAS) to simplify the expression and arrived at a final value of $83$ . In this article, we will answer some frequently asked questions about evaluating expressions.

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 expression. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is important because it ensures that we evaluate expressions correctly. If we don't follow the order of operations, we may get incorrect results.

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

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

Not following the order of operations (PEMDAS)
Not simplifying expressions inside parentheses
Not evaluating exponents correctly
Not combining terms correctly

Q: How do I simplify expressions inside parentheses?

A: To simplify expressions inside parentheses, we need to follow the order of operations (PEMDAS). We will start by evaluating any expressions inside the parentheses, then evaluate any exponents, and finally combine any terms.

Q: What is the difference between an exponent and a power?

A: An exponent is a small number that is raised to a power. For example, in the expression $2^3$ , the 3 is an exponent and the 2 is the base.

Q: How do I evaluate expressions with fractions?

A: To evaluate expressions with fractions, we need to follow the order of operations (PEMDAS). We will start by simplifying any fractions inside the expression, then evaluate any exponents, and finally combine any terms.

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 is a value that does not change.

Q: How do I evaluate expressions with variables?

A: To evaluate expressions with variables, we need to substitute the value of the variable into the expression. We will then follow the order of operations (PEMDAS) to simplify the expression.

Q: What are some real-world applications of evaluating expressions?

A: Some real-world applications of evaluating expressions include:

In science, we use expressions to model real-world phenomena, such as the motion of objects or the growth of populations.
In finance, we use expressions to calculate interest rates or investment returns.
In engineering, we use expressions to design and optimize systems, such as bridges or buildings.

Conclusion

In conclusion, evaluating expressions is a crucial skill in mathematics that helps us simplify complex mathematical statements. By following the order of operations (PEMDAS), we can simplify expressions and arrive at a final value. In this article, we answered some frequently asked questions about evaluating expressions and provided some tips and tricks for simplifying expressions.

Additional Resources

For more information on evaluating expressions, we recommend the following resources:

Khan Academy: Evaluating Expressions
Mathway: Evaluating Expressions
Wolfram Alpha: Evaluating Expressions

Practice Problems

To practice evaluating expressions, try the following problems:

Evaluate the expression $2x^2 + 3x - 1$ for $x = 4$ .
Evaluate the expression $\frac{x + 2}{x - 1}$ for $x = 3$ .
Evaluate the expression $x^2 - 4x + 4$ for $x = 2$ .

Conclusion

In conclusion, evaluating expressions is a crucial skill in mathematics that helps us simplify complex mathematical statements. By following the order of operations (PEMDAS), we can simplify expressions and arrive at a final value. We hope this article has provided you with a better understanding of evaluating expressions and has given you the confidence to tackle more complex mathematical problems.