Which Expression Is Equivalent To $6 - (-8)$?A. $-6 + 8$B. $ − 6 + ( − 8 ) -6 + (-8) − 6 + ( − 8 ) [/tex]C. $6 + (-8)$D. $6 + 8$

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Introduction

In mathematics, equivalent expressions are those that have the same value or result when evaluated. They may look different, but they represent the same mathematical concept. In this article, we will explore the concept of equivalent expressions, focusing on the given expression $6 - (-8)$ and its possible equivalent forms.

What are Equivalent Expressions?

Equivalent expressions are mathematical expressions that have the same value or result when evaluated. They may differ in their appearance, but they represent the same mathematical concept. For example, the expressions $2 \times 3$ and $3 \times 2$ are equivalent because they both represent the same value, which is $6$.

Understanding the Given Expression

The given expression is $6 - (-8)$. To evaluate this expression, we need to follow the order of operations (PEMDAS), which states that we should perform operations inside parentheses first, then exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).

Evaluating the Given Expression

To evaluate the given expression, we need to follow the order of operations. The expression inside the parentheses is $-8$, which is a negative number. When we subtract a negative number, we are essentially adding its positive counterpart. Therefore, $6 - (-8)$ is equivalent to $6 + 8$.

Analyzing the Options

Now that we have evaluated the given expression, let's analyze the options provided:

A. $-6 + 8$ B. $-6 + (-8)$ C. $6 + (-8)$ D. $6 + 8$

Option A: $-6 + 8$

This option is incorrect because it does not represent the equivalent expression of $6 - (-8)$. When we subtract a negative number, we are essentially adding its positive counterpart. Therefore, $-6 + 8$ is not equivalent to $6 - (-8)$.

Option B: $-6 + (-8)$

This option is also incorrect because it does not represent the equivalent expression of $6 - (-8)$. When we subtract a negative number, we are essentially adding its positive counterpart. Therefore, $-6 + (-8)$ is not equivalent to $6 - (-8)$.

Option C: $6 + (-8)$

This option is incorrect because it does not represent the equivalent expression of $6 - (-8)$. When we subtract a negative number, we are essentially adding its positive counterpart. Therefore, $6 + (-8)$ is not equivalent to $6 - (-8)$.

Option D: $6 + 8$

This option is correct because it represents the equivalent expression of $6 - (-8)$. When we subtract a negative number, we are essentially adding its positive counterpart. Therefore, $6 + 8$ is equivalent to $6 - (-8)$.

Conclusion

In conclusion, the equivalent expression of $6 - (-8)$ is $6 + 8$. This is because when we subtract a negative number, we are essentially adding its positive counterpart. Therefore, option D is the correct answer.

Frequently Asked Questions

  • Q: What is the concept of equivalent expressions in mathematics? A: Equivalent expressions are those that have the same value or result when evaluated. They may look different, but they represent the same mathematical concept.
  • Q: How do we evaluate the expression $6 - (-8)$? A: To evaluate the expression $6 - (-8)$, we need to follow the order of operations (PEMDAS). The expression inside the parentheses is $-8$, which is a negative number. When we subtract a negative number, we are essentially adding its positive counterpart. Therefore, $6 - (-8)$ is equivalent to $6 + 8$.
  • Q: What is the correct equivalent expression of $6 - (-8)$? A: The correct equivalent expression of $6 - (-8)$ is $6 + 8$.

Final Thoughts

In conclusion, the concept of equivalent expressions is an important one in mathematics. It allows us to simplify complex expressions and make them easier to evaluate. By understanding the concept of equivalent expressions, we can better solve mathematical problems and make informed decisions.

Introduction

In our previous article, we explored the concept of equivalent expressions in mathematics, focusing on the given expression $6 - (-8)$ and its possible equivalent forms. In this article, we will answer some frequently asked questions related to equivalent expressions.

Q&A

Q: What is the concept of equivalent expressions in mathematics?

A: Equivalent expressions are those that have the same value or result when evaluated. They may look different, but they represent the same mathematical concept.

Q: How do we evaluate the expression $6 - (-8)$?

A: To evaluate the expression $6 - (-8)$, we need to follow the order of operations (PEMDAS). The expression inside the parentheses is $-8$, which is a negative number. When we subtract a negative number, we are essentially adding its positive counterpart. Therefore, $6 - (-8)$ is equivalent to $6 + 8$.

Q: What is the correct equivalent expression of $6 - (-8)$?

A: The correct equivalent expression of $6 - (-8)$ is $6 + 8$.

Q: Can you give an example of equivalent expressions?

A: Yes, here are a few examples:

  • 2 \times 3$ and $3 \times 2$ are equivalent because they both represent the same value, which is $6$.

  • 4 + 5$ and $5 + 4$ are equivalent because they both represent the same value, which is $9$.

  • -3 + 7$ and $7 - (-3)$ are equivalent because they both represent the same value, which is $10$.

Q: How do we simplify equivalent expressions?

A: To simplify equivalent expressions, we need to follow the order of operations (PEMDAS). We should perform operations inside parentheses first, then exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).

Q: Can you give an example of simplifying equivalent expressions?

A: Yes, here is an example:

  • The expression $3 \times (2 + 4)$ can be simplified as follows:
    1. Evaluate the expression inside the parentheses: $2 + 4 = 6$
    2. Multiply $3$ by the result: $3 \times 6 = 18$ Therefore, the simplified expression is $18$.

Q: What is the importance of equivalent expressions in mathematics?

A: Equivalent expressions are important in mathematics because they allow us to simplify complex expressions and make them easier to evaluate. By understanding the concept of equivalent expressions, we can better solve mathematical problems and make informed decisions.

Q: Can you give an example of using equivalent expressions in real-life situations?

A: Yes, here is an example:

  • Suppose we want to calculate the total cost of buying $2$ items at $$5$ each. We can use the equivalent expression $2 \times 5$ to represent the total cost, which is equivalent to $10$.

Conclusion

In conclusion, equivalent expressions are an important concept in mathematics that allows us to simplify complex expressions and make them easier to evaluate. By understanding the concept of equivalent expressions, we can better solve mathematical problems and make informed decisions. We hope that this article has helped to clarify any questions you may have had about equivalent expressions.

Final Thoughts

Equivalent expressions are a fundamental concept in mathematics that can be applied to a wide range of situations. By understanding the concept of equivalent expressions, we can better solve mathematical problems and make informed decisions. We hope that this article has been helpful in clarifying any questions you may have had about equivalent expressions.

Additional Resources

  • For more information on equivalent expressions, please refer to the following resources:
    • Khan Academy: Equivalent Expressions
    • Mathway: Equivalent Expressions
    • Wolfram Alpha: Equivalent Expressions

Related Articles

  • Understanding the Concept of Equivalent Expressions in Mathematics
  • Simplifying Equivalent Expressions: A Step-by-Step Guide
  • Using Equivalent Expressions in Real-Life Situations

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