1. Evaluate: a) $\frac{1}{4} + \left(-\frac{3}{4}\right)$ Start by adding the fractions: $$\frac{1}{4} + \left(-\frac{3}{4}\right) = \frac{1 - 3}{4} = \frac{-2}{4}$$ Simplify the fraction by dividing numerator and denominator by 2: $$\frac{\cancel{-2}}{\cancel{4}} = \frac{-1}{2}$$ Answer: $-\frac{1}{2}$ b) $-\frac{3}{4} - \frac{1}{-4}$ Rewrite subtraction as addition of negative: $$-\frac{3}{4} + \left(-\frac{1}{-4}\right) = -\frac{3}{4} + \frac{1}{4}$$ Add the fractions: $$\frac{-3 + 1}{4} = \frac{-2}{4} = -\frac{1}{2}$$ Answer: $-\frac{1}{2}$ c) $-\frac{1}{4} - 1 \frac{1}{3}$ Convert mixed number to improper fraction: $$1 \frac{1}{3} = \frac{4}{3}$$ Rewrite subtraction: $$-\frac{1}{4} - \frac{4}{3} = -\frac{1}{4} + \left(-\frac{4}{3}\right)$$ Find common denominator 12: $$-\frac{3}{12} - \frac{16}{12} = -\frac{19}{12}$$ Answer: $-\frac{19}{12}$ d) $\frac{2}{-3} - 1 \frac{5}{6}$ Convert mixed number: $$1 \frac{5}{6} = \frac{11}{6}$$ Rewrite subtraction: $$-\frac{2}{3} - \frac{11}{6}$$ Common denominator 6: $$-\frac{4}{6} - \frac{11}{6} = -\frac{15}{6} = -\frac{5}{2}$$ Answer: $-\frac{5}{2}$ e) $-\frac{3}{5} + -\frac{3}{4} - \frac{7}{10}$ Rewrite as sum: $$-\frac{3}{5} - \frac{3}{4} - \frac{7}{10}$$ Common denominator 20: $$-\frac{12}{20} - \frac{15}{20} - \frac{14}{20} = -\frac{41}{20}$$ Answer: $-\frac{41}{20}$ This completes the first question.