Inverse property of addition

Definition

The inverse property of addition states that for every real number $a$, there exists a number $-a$ such that $a + (-a) = 0$. This property is essential in solving equations and simplifying expressions.

5 Must Know Facts For Your Next Test

1. The additive inverse of any number $a$ is $-a$.
2. The sum of a number and its additive inverse is always zero: $a + (-a) = 0$.
3. This property helps in isolating variables when solving equations.
4. The additive inverse of zero is itself: $0 + 0 = 0$.
5. Understanding this property aids in mastering the concept of opposites in algebra.

Review Questions

• What is the additive inverse of 7?
• Simplify the expression: $5 + (-5)$.
• Why is the inverse property of addition important for solving equations?

Related terms

Additive Identity: The number 0, which when added to any real number does not change its value. For any real number $a$, $a+0=a$.

Multiplicative Inverse: For any non-zero real number $b$, there exists a number $\frac{1}{b}$ such that $b \cdot \frac{1}{b} = 1$.

Commutative Property of Addition: States that the order in which two numbers are added does not change their sum. For any real numbers $a$ and $b$, $a + b = b + a$.