Step-by-step solution for finding the additive inverse of 1/a, illustrating the concept with algebraic steps and a definition.

You're asked to find the additive inverse of $ \frac{1}{2} $.

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✔ What is an Additive Inverse?

The additive inverse of a number $ a $ is the number that, when added to $ a $, gives zero.

In symbols:
> $ a + (-a) = 0 $

So, the additive inverse of $ a $ is $ -a $.

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🧮 Applying This to $ \frac{1}{2} $

We want to find a number $ x $ such that:

> $ \frac{1}{2} + x = 0 $

To solve for $ x $, subtract $ \frac{1}{2} $ from both sides:

> $ x = 0 - \frac{1}{2} = -\frac{1}{2} $

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✔ Final Answer:

> The additive inverse of $ \frac{1}{2} $ is $ -\frac{1}{2} $.

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🔍 Why This Makes Sense

Think of it on a number line:
- $ \frac{1}{2} $ is halfway between 0 and 1.
- Its additive inverse, $ -\frac{1}{2} $, is the same distance from 0 but in the opposite direction (to the left).
- When you add them: $ \frac{1}{2} + (-\frac{1}{2}) = 0 $ — they cancel each other out.

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✔ So, as shown in your image, the solution is correct:

> $ \boxed{-\frac{1}{2}} $

This matches the general rule: the additive inverse of any number $ a $ is simply $ -a $.