Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: Emma had just been given some coins by her parents.  On the way to school she lost exactly half of them, and then by retracing her steps she found exactly four-fifths of the coins she had lost.  What fraction of the coins that she received from her parents were still missing after Emma retraced her steps? Express your answer as a common fraction.
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