1. We are asked to simplify the fractions: a) $\frac{15}{35}$, b) $\frac{20}{36}$, c) $\frac{4}{48}$, d) $\frac{75}{90}$, e) $\frac{64}{256}$, f) $\frac{112}{144}$. Simplifying fractions means dividing numerator and denominator by their greatest common divisor (GCD). 2. a) Simplify $\frac{15}{35}$: - GCD of 15 and 35 is 5. - Divide numerator and denominator by 5: $$\frac{\cancel{15}^3}{\cancel{35}^7} = \frac{3}{7}$$ 3. b) Simplify $\frac{20}{36}$: - GCD of 20 and 36 is 4. - Divide numerator and denominator by 4: $$\frac{\cancel{20}^5}{\cancel{36}^9} = \frac{5}{9}$$ 4. c) Simplify $\frac{4}{48}$: - GCD of 4 and 48 is 4. - Divide numerator and denominator by 4: $$\frac{\cancel{4}^1}{\cancel{48}^{12}} = \frac{1}{12}$$ 5. d) Simplify $\frac{75}{90}$: - GCD of 75 and 90 is 15. - Divide numerator and denominator by 15: $$\frac{\cancel{75}^5}{\cancel{90}^6} = \frac{5}{6}$$ 6. e) Simplify $\frac{64}{256}$: - GCD of 64 and 256 is 64. - Divide numerator and denominator by 64: $$\frac{\cancel{64}^1}{\cancel{256}^4} = \frac{1}{4}$$ 7. f) Simplify $\frac{112}{144}$: - GCD of 112 and 144 is 16. - Divide numerator and denominator by 16: $$\frac{\cancel{112}^7}{\cancel{144}^9} = \frac{7}{9}$$ Final answers: a) $\frac{3}{7}$ b) $\frac{5}{9}$ c) $\frac{1}{12}$ d) $\frac{5}{6}$ e) $\frac{1}{4}$ f) $\frac{7}{9}$