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ADDITIVE INVERSES

Additive Inverses

The Additive Inverse of a number is the opposite of the number.

A number and its opposite add up to give zero.
They are called additive inverses of each other.

Examples of Additive Inverses

The additive inverse of 7 is - 7.
7 + (- 7) = 0
The additive inverse of - 2 is 2.
- 2 + 2 = 0



Video Examples: Additive Inverses
 

Solved Example on Additive Inverses

Ques: 
Which of the following is the additive inverse of the sum of 5 and 8?

Choices:

A. - 13
B. - 5
C. - 8
D. - 3

Correct Answer: A

Solution:

Step 1: The sum of 5 and 8 is 13.
Step 2: The additive inverse of 13 is - 13.

 

Quick Summary

  • The additive inverse is the opposite of a number.
  • A number and its additive inverse sum to zero.
  • Additive inverses are used to solve equations.
\[ a + (-a) = 0 \]

⚠️ Common Mistakes

  • Confusing additive inverse with multiplicative inverse (reciprocal).
  • Incorrectly applying the negative sign.

🌍 Real-World Uses

  • Balancing a checkbook: If you deposit $50 ( +50) and then withdraw $50 ( -50), the net change is $0, demonstrating additive inverses.
  • Temperature scales: A temperature of 5 degrees Celsius (+5) followed by a decrease of 5 degrees Celsius (-5) results in a temperature of 0 degrees Celsius.
  • Sea Level: A submarine diving 100 feet below sea level (-100) and then rising 100 feet (+100) returns to sea level (0).

📋 Standards Alignment

  • CCSS.MATH.7.NS.A.1
  • CCSS.MATH.8.EE.C.7

🔗 Related Links

🍎 Teacher Insights

Use real-world examples like temperature changes or debts and credits to illustrate additive inverses. Emphasize the relationship between a number and its opposite on the number line.

🎓 Prerequisites

  • Integers
  • Addition
  • Subtraction

Check Your Knowledge

Q1: What is the additive inverse of 15?

Q2: What is the additive inverse of -9?

Q3: What is the additive inverse of the sum of 5 and 8?

Frequently Asked Questions

Q: What is the additive inverse of 0?
A: The additive inverse of 0 is 0, because 0 + 0 = 0.

Q: Is the additive inverse always a negative number?
A: No, the additive inverse of a negative number is a positive number.

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