To evaluate the expression \(-0.8 + 0.75 - (-\frac{3}{4}) + \frac{4}{5}\), we will convert all the numbers to fractions, perform the calculations, and simplify.
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Convert all decimal numbers to fractions: \[ -0.8 = -\frac{8}{10} = -\frac{4}{5} \] \[ 0.75 = \frac{75}{100} = \frac{3}{4} \]
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Now rewrite the expression using fractions: \[ -\frac{4}{5} + \frac{3}{4} - \left(-\frac{3}{4}\right) + \frac{4}{5} \]
The term \(-(-\frac{3}{4})\) simplifies to \(+\frac{3}{4}\), so the expression now is: \[ -\frac{4}{5} + \frac{3}{4} + \frac{3}{4} + \frac{4}{5} \]
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Combine like terms:
- The \(-\frac{4}{5}\) and \(+\frac{4}{5}\) cancel each other out: \[ -\frac{4}{5} + \frac{4}{5} = 0 \]
- Thus, we are left with: \[ \frac{3}{4} + \frac{3}{4} = \frac{6}{4} \]
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Simplify \(\frac{6}{4}\) to its simplest form: \[ \frac{6}{4} = \frac{3}{2} \]
Therefore, the final answer is: \[ \boxed{\frac{3}{2}} \]
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