To simplify the expression $1 - \frac{4}{5} + \frac{1}{2}$, let's break it down into steps.

Step 1: Convert to Common Denominator

The least common multiple of 5 and 2 is 10. Rewrite each fraction with a denominator of 10: $\frac{4}{5} = \frac{8}{10} \quad \text{and} \quad \frac{1}{2} = \frac{5}{10}$

Now, the expression becomes: $1 - \frac{8}{10} + \frac{5}{10}$

Step 2: Simplify the Expression

Convert 1 to a fraction with a denominator of 10 as well: $1 = \frac{10}{10}$

Now substitute and combine all terms: $\frac{10}{10} - \frac{8}{10} + \frac{5}{10}$

Step 3: Perform the Operations

Combine the fractions: $\frac{10 - 8 + 5}{10} = \frac{7}{10}$

Final Answer:

$1 - \frac{4}{5} + \frac{1}{2} = \frac{7}{10}$

Would you like further details or have any questions?

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Related Questions:

1. How do you add fractions with different denominators?
2. Why is finding the least common multiple helpful in fraction addition?
3. How can you simplify complex expressions involving fractions?
4. How do you convert whole numbers to fractions?
5. What are alternative methods to simplify fractions?

Tip: When adding or subtracting fractions, always ensure they have a common denominator for easier computation.