1. **State the problem:** Calculate the sum and difference of the fractions $\frac{14}{27} + \frac{5}{27} - \frac{16}{27}$ and simplify the result. 2. **Formula and rules:** When adding or subtracting fractions with the same denominator, add or subtract the numerators and keep the denominator the same: $$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$$ $$\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$$ 3. **Calculate the numerator:** $$14 + 5 - 16 = 19 - 16 = 3$$ 4. **Write the combined fraction:** $$\frac{14}{27} + \frac{5}{27} - \frac{16}{27} = \frac{3}{27}$$ 5. **Simplify the fraction:** Both numerator and denominator are divisible by 3. $$\frac{\cancel{3}^1}{\cancel{27}^9} = \frac{1}{9}$$ 6. **Final answer:** $$\boxed{\frac{1}{9}}$$