To solve the expression \(-1 + \frac{44}{75} + \frac{8}{25}\), let's first convert \(\frac{8}{25}\) to a fraction with a denominator of 75 so that we can combine the fractions.
Convert \(\frac{8}{25}\) to a fraction with a denominator of 75: \[ \frac{8}{25} = \frac{8 \times 3}{25 \times 3} = \frac{24}{75} \]
Now, substitute \(\frac{24}{75}\) back into the expression: \[ -1 + \frac{44}{75} + \frac{24}{75} \]
Combine the fractions: \[ -1 + \frac{44 + 24}{75} = -1 + \frac{68}{75} \]
Now, convert \(-1\) to a fraction with a denominator of 75: \[ -1 = \frac{-75}{75} \]
Now, combine \(\frac{-75}{75}\) and \(\frac{68}{75}\): \[ \frac{-75 + 68}{75} = \frac{-7}{75} \]
So, the final result is: \[ -1 + \frac{44}{75} + \frac{8}{25} = \frac{-7}{75} \]
