Select The Correct Answer.Simplify: $3 \cdot 3^2 + 8 \div 2 - (4 + 3)$A. 24 B. 30 C. 23 D. 32

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Introduction

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Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying a specific algebraic expression: $3 \cdot 3^2 + 8 \div 2 - (4 + 3)$. We will break down the expression into smaller parts, apply the order of operations, and arrive at the correct answer.

Understanding the Order of Operations

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Before we dive into the expression, it's essential to understand the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). This rule dictates the order in which we perform operations in an expression.

PEMDAS: A Quick Recap

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next (e.g., 2^3).
• 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.

Breaking Down the Expression

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Now that we understand the order of operations, let's break down the given expression:

$$3 \cdot 3^2 + 8 \div 2 - (4 + 3)$$

Step 1: Evaluate Exponents

The first step is to evaluate the exponential expression: $3^2$. This means we need to raise 3 to the power of 2.

$$3^2 = 3 \cdot 3 = 9$$

So, the expression becomes:

$$3 \cdot 9 + 8 \div 2 - (4 + 3)$$

Step 2: Evaluate Multiplication

Next, we need to evaluate the multiplication operation: $3 \cdot 9$. This means we need to multiply 3 by 9.

$$3 \cdot 9 = 27$$

So, the expression becomes:

$$27 + 8 \div 2 - (4 + 3)$$

Step 3: Evaluate Division

Now, we need to evaluate the division operation: $8 \div 2$. This means we need to divide 8 by 2.

$$8 \div 2 = 4$$

So, the expression becomes:

$$27 + 4 - (4 + 3)$$

Step 4: Evaluate Parentheses

The next step is to evaluate the expression inside the parentheses: $(4 + 3)$. This means we need to add 4 and 3.

$$(4 + 3) = 7$$

So, the expression becomes:

$$27 + 4 - 7$$

Step 5: Evaluate Addition and Subtraction

Finally, we need to evaluate the addition and subtraction operations from left to right. First, we add 27 and 4:

$$27 + 4 = 31$$

Then, we subtract 7 from 31:

$$31 - 7 = 24$$

Conclusion

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In conclusion, the correct answer to the given algebraic expression is:

$$3 \cdot 3^2 + 8 \div 2 - (4 + 3) = 24$$

This expression can be simplified by following the order of operations: evaluating exponents, multiplication, division, and finally, addition and subtraction.

Final Answer

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The final answer is: A. 24

=====================================================

Introduction

---

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying a specific algebraic expression: $3 \cdot 3^2 + 8 \div 2 - (4 + 3)$. We will break down the expression into smaller parts, apply the order of operations, and arrive at the correct answer.

Understanding the Order of Operations

---

Before we dive into the expression, it's essential to understand the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). This rule dictates the order in which we perform operations in an expression.

PEMDAS: A Quick Recap

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next (e.g., 2^3).
• 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.

Breaking Down the Expression

---

Now that we understand the order of operations, let's break down the given expression:

$$3 \cdot 3^2 + 8 \div 2 - (4 + 3)$$

Step 1: Evaluate Exponents

The first step is to evaluate the exponential expression: $3^2$. This means we need to raise 3 to the power of 2.

$$3^2 = 3 \cdot 3 = 9$$

So, the expression becomes:

$$3 \cdot 9 + 8 \div 2 - (4 + 3)$$

Step 2: Evaluate Multiplication

Next, we need to evaluate the multiplication operation: $3 \cdot 9$. This means we need to multiply 3 by 9.

$$3 \cdot 9 = 27$$

So, the expression becomes:

$$27 + 8 \div 2 - (4 + 3)$$

Step 3: Evaluate Division

Now, we need to evaluate the division operation: $8 \div 2$. This means we need to divide 8 by 2.

$$8 \div 2 = 4$$

So, the expression becomes:

$$27 + 4 - (4 + 3)$$

Step 4: Evaluate Parentheses

The next step is to evaluate the expression inside the parentheses: $(4 + 3)$. This means we need to add 4 and 3.

$$(4 + 3) = 7$$

So, the expression becomes:

$$27 + 4 - 7$$

Step 5: Evaluate Addition and Subtraction

Finally, we need to evaluate the addition and subtraction operations from left to right. First, we add 27 and 4:

$$27 + 4 = 31$$

Then, we subtract 7 from 31:

$$31 - 7 = 24$$

Conclusion

---

In conclusion, the correct answer to the given algebraic expression is:

$$3 \cdot 3^2 + 8 \div 2 - (4 + 3) = 24$$

This expression can be simplified by following the order of operations: evaluating exponents, multiplication, division, and finally, addition and subtraction.

Final Answer

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The final answer is: A. 24

Q&A: Simplifying Algebraic Expressions

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Q: What is the order of operations in mathematics?

A: The order of operations is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

Q: How do I evaluate exponents in an algebraic expression?

A: To evaluate exponents, you need to raise the base number to the power of the exponent. For example, $3^2 = 3 \cdot 3 = 9$.

Q: What is the difference between multiplication and division in the order of operations?

A: Multiplication and division are evaluated from left to right. This means that if you have an expression like $3 \cdot 4 + 2 \div 2$, you need to evaluate the multiplication first, then the division.

Q: How do I evaluate parentheses in an algebraic expression?

A: To evaluate parentheses, you need to evaluate the expression inside the parentheses first. For example, $(4 + 3) = 7$.

Q: What is the final step in simplifying an algebraic expression?

A: The final step is to evaluate any addition and subtraction operations from left to right.

Q: Can you give an example of an algebraic expression that requires simplification?

A: Here's an example: $3 \cdot 3^2 + 8 \div 2 - (4 + 3)$. This expression can be simplified by following the order of operations.

Q: What is the correct answer to the given algebraic expression?

A: The correct answer is: $3 \cdot 3^2 + 8 \div 2 - (4 + 3) = 24$.

Final Thoughts

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Simplifying algebraic expressions is an essential skill for students and professionals alike. By following the order of operations and breaking down the expression into smaller parts, you can arrive at the correct answer. Remember to evaluate exponents, multiplication, division, and finally, addition and subtraction. With practice and patience, you'll become a pro at simplifying algebraic expressions in no time!