Which Number Is The Additive Inverse Of -5?A. $-\frac{1}{5}$B. 0C. $\frac{1}{5}$D. 5

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In mathematics, the additive inverse of a number is the value that, when added to the original number, results in a sum of zero. This concept is crucial in various mathematical operations, including arithmetic and algebra. In this article, we will explore the additive inverse of -5 and determine which of the given options is the correct answer.

What is Additive Inverse?

The additive inverse of a number 'a' is denoted as '-a' and is the value that, when added to 'a', results in a sum of zero. For example, the additive inverse of 5 is -5, because 5 + (-5) = 0. Similarly, the additive inverse of -5 is the value that, when added to -5, results in a sum of zero.

Finding the Additive Inverse of -5

To find the additive inverse of -5, we need to determine the value that, when added to -5, results in a sum of zero. Let's denote this value as 'x'. We can write the equation as:

-5 + x = 0

To solve for 'x', we can add 5 to both sides of the equation:

x = 5

Therefore, the additive inverse of -5 is 5.

Analyzing the Options

Now that we have determined the additive inverse of -5, let's analyze the given options:

A. βˆ’15-\frac{1}{5}

B. 0

C. 15\frac{1}{5}

D. 5

Based on our calculation, the correct answer is option D, 5.

Why is Option D the Correct Answer?

Option D, 5, is the correct answer because it is the value that, when added to -5, results in a sum of zero. This is in line with the definition of additive inverse, which states that the additive inverse of a number 'a' is the value that, when added to 'a', results in a sum of zero.

Conclusion

In conclusion, the additive inverse of -5 is 5. This is because 5 is the value that, when added to -5, results in a sum of zero. This concept is crucial in mathematics and is used in various mathematical operations, including arithmetic and algebra.

Frequently Asked Questions

Q: What is the additive inverse of a number?

A: The additive inverse of a number 'a' is the value that, when added to 'a', results in a sum of zero.

Q: How do you find the additive inverse of a number?

A: To find the additive inverse of a number, you need to determine the value that, when added to the original number, results in a sum of zero.

Q: What is the additive inverse of -5?

A: The additive inverse of -5 is 5.

Q: Why is option D the correct answer?

A: Option D, 5, is the correct answer because it is the value that, when added to -5, results in a sum of zero.

Additional Resources

For more information on additive inverse, you can refer to the following resources:

  • Khan Academy: Additive Inverse
  • Math Is Fun: Additive Inverse
  • Wikipedia: Additive Inverse

References

In this article, we will answer some frequently asked questions about additive inverse, a fundamental concept in mathematics.

Q: What is the additive inverse of a number?

A: The additive inverse of a number 'a' is the value that, when added to 'a', results in a sum of zero. In other words, if 'a' is a number, then its additive inverse is the number that, when added to 'a', gives 0.

Q: How do you find the additive inverse of a number?

A: To find the additive inverse of a number, you need to determine the value that, when added to the original number, results in a sum of zero. For example, to find the additive inverse of 5, you need to find the number that, when added to 5, gives 0. In this case, the additive inverse of 5 is -5, because 5 + (-5) = 0.

Q: What is the additive inverse of -5?

A: The additive inverse of -5 is 5, because -5 + 5 = 0.

Q: Why is the additive inverse of a number important?

A: The additive inverse of a number is important because it helps us to understand the concept of zero and the properties of numbers. It also helps us to solve equations and inequalities, and to understand the relationships between numbers.

Q: Can you give an example of how to use the additive inverse in a real-world situation?

A: Yes, here's an example: Imagine you have a bank account with a balance of $100. If you want to know how much money you have left after withdrawing $50, you can use the additive inverse to find the answer. The additive inverse of $50 is -$50, because $50 + (-$50) = $0. So, if you withdraw $50 from your account, you will be left with $0.

Q: What is the difference between additive inverse and multiplicative inverse?

A: The additive inverse of a number is the value that, when added to the original number, results in a sum of zero. The multiplicative inverse of a number is the value that, when multiplied by the original number, results in a product of 1. For example, the additive inverse of 5 is -5, but the multiplicative inverse of 5 is 1/5, because 5 Γ— (1/5) = 1.

Q: Can you give an example of how to use the additive inverse in a mathematical equation?

A: Yes, here's an example: Solve the equation 2x + 5 = 11. To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 5 from both sides of the equation, which gives us 2x = 6. Then, we can divide both sides of the equation by 2, which gives us x = 3. But what if we want to find the value of x that makes the equation true? In this case, we can use the additive inverse to find the value of x. The additive inverse of 5 is -5, so we can rewrite the equation as 2x + (-5) = 11. Then, we can simplify the equation by combining like terms, which gives us 2x - 5 = 11. Finally, we can add 5 to both sides of the equation, which gives us 2x = 16. Then, we can divide both sides of the equation by 2, which gives us x = 8.

Q: What are some common mistakes to avoid when working with additive inverse?

A: Here are some common mistakes to avoid when working with additive inverse:

  • Not understanding the concept of zero and the properties of numbers
  • Not using the correct notation for additive inverse (e.g. using a minus sign instead of a plus sign)
  • Not checking the signs of the numbers when working with additive inverse
  • Not using the correct order of operations when working with additive inverse

Q: How can I practice working with additive inverse?

A: Here are some ways to practice working with additive inverse:

  • Use online resources, such as Khan Academy or Mathway, to practice solving equations and inequalities that involve additive inverse.
  • Work with a partner or tutor to practice solving problems that involve additive inverse.
  • Use real-world examples, such as banking or finance, to practice working with additive inverse.
  • Create your own problems that involve additive inverse and solve them on your own.

Conclusion

In conclusion, additive inverse is an important concept in mathematics that helps us to understand the properties of numbers and to solve equations and inequalities. By understanding the concept of additive inverse, we can better understand the relationships between numbers and solve problems that involve additive inverse.