Select The Correct Answer.Simplify: $6 \div 3 + 3^2 \cdot 4 - 2$A. 42 B. 98 C. 22 D. 36

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will focus on simplifying a specific algebraic expression: $6 \div 3 + 3^2 \cdot 4 - 2$. We will break down the expression step by step, using the order of operations (PEMDAS) to ensure that we arrive at the correct answer.

Understanding the Order of Operations

Before we dive into simplifying the expression, it's essential to understand the order of operations, also known as PEMDAS. PEMDAS stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Simplifying the Expression

Now that we understand the order of operations, let's simplify the expression step by step:

6÷3+32⋅4−26 \div 3 + 3^2 \cdot 4 - 2

Step 1: Evaluate Exponents

The first step is to evaluate any exponential expressions. In this case, we have 323^2, which means 3 squared.

32=3×3=93^2 = 3 \times 3 = 9

So, the expression becomes:

6÷3+9⋅4−26 \div 3 + 9 \cdot 4 - 2

Step 2: Evaluate Multiplication and Division

Next, we need to evaluate any multiplication and division operations from left to right. In this case, we have 6÷36 \div 3 and 9⋅49 \cdot 4.

6÷3=26 \div 3 = 2

9⋅4=369 \cdot 4 = 36

So, the expression becomes:

2+36−22 + 36 - 2

Step 3: Evaluate Addition and Subtraction

Finally, we need to evaluate any addition and subtraction operations from left to right. In this case, we have 2+36−22 + 36 - 2.

2+36=382 + 36 = 38

38−2=3638 - 2 = 36

Conclusion

And there you have it! The simplified expression is:

3636

Answer

So, the correct answer is:

D. 36

Discussion

Now that we have simplified the expression, let's discuss the importance of following the order of operations. If we had not followed the order of operations, we may have arrived at a different answer. For example, if we had evaluated the multiplication and division operations first, we may have gotten:

6÷3=26 \div 3 = 2

32⋅4=363^2 \cdot 4 = 36

2+36=382 + 36 = 38

38−2=3638 - 2 = 36

But, as we can see, this would have led to the same answer: 36. However, if we had not followed the order of operations, we may have arrived at a different answer, which would have been incorrect.

Tips and Tricks

Here are some tips and tricks to help you simplify algebraic expressions:

  • Always follow the order of operations (PEMDAS).
  • Evaluate any exponential expressions first.
  • Evaluate any multiplication and division operations from left to right.
  • Evaluate any addition and subtraction operations from left to right.
  • Use parentheses to group expressions and make them easier to evaluate.

Introduction

In our previous article, we discussed how to simplify algebraic expressions using the order of operations (PEMDAS). We walked through a step-by-step example of how to simplify the expression $6 \div 3 + 3^2 \cdot 4 - 2$. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q&A

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 simplifying algebraic expressions. The acronym PEMDAS stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

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

A: Following the order of operations is crucial when simplifying algebraic expressions because it ensures that we arrive at the correct answer. If we don't follow the order of operations, we may arrive at a different answer, which can lead to errors in calculations.

Q: What happens if I have multiple operations with the same precedence (e.g., multiplication and division)?

A: If you have multiple operations with the same precedence (e.g., multiplication and division), you need to evaluate them from left to right. For example, if you have the expression $2 \cdot 3 + 4 \div 2$, you would evaluate the multiplication first (2 \cdot 3 = 6) and then the division (4 \div 2 = 2). Finally, you would add the two results together (6 + 2 = 8).

Q: Can I use parentheses to group expressions and make them easier to evaluate?

A: Yes, you can use parentheses to group expressions and make them easier to evaluate. For example, if you have the expression $2 + 3 \cdot 4$, you can use parentheses to group the multiplication and division operations: $(2 + 3) \cdot 4$. This makes it easier to evaluate the expression.

Q: What if I have a negative exponent (e.g., 2^(-3))?

A: If you have a negative exponent (e.g., 2^(-3)), you can rewrite it as a fraction. For example, 2^(-3) is equal to 1/2^3. You can then simplify the fraction by evaluating the exponent: 1/8.

Q: Can I simplify expressions with variables (e.g., 2x + 3)?

A: Yes, you can simplify expressions with variables (e.g., 2x + 3). However, you need to follow the order of operations and evaluate any exponential expressions first. For example, if you have the expression 2x^2 + 3, you would evaluate the exponent first (2x^2) and then add 3.

Q: What if I have a fraction with a variable in the denominator (e.g., 1/x + 2)?

A: If you have a fraction with a variable in the denominator (e.g., 1/x + 2), you need to be careful when simplifying the expression. You can't simply add the two fractions together because they have different denominators. Instead, you need to find a common denominator and then add the fractions.

Conclusion

Simplifying algebraic expressions can be a challenging task, but by following the order of operations and using parentheses to group expressions, you can make it easier. Remember to evaluate any exponential expressions first, and then evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right. By following these tips and tricks, you will be able to simplify algebraic expressions with ease and arrive at the correct answer every time.