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-\frac{5}{50}-\frac{8}{50}
Least common multiple of 10 and 25 is 50. Convert -\frac{1}{10} and \frac{4}{25} to fractions with denominator 50.
\frac{-5-8}{50}
Since -\frac{5}{50} and \frac{8}{50} have the same denominator, subtract them by subtracting their numerators.
-\frac{13}{50}
Subtract 8 from -5 to get -13.