1. The problem is to calculate $160 \frac{1}{9} - 125 \frac{16}{27}$. 2. Convert mixed numbers to improper fractions: $$160 \frac{1}{9} = \frac{160 \times 9 + 1}{9} = \frac{1440 + 1}{9} = \frac{1441}{9}$$ $$125 \frac{16}{27} = \frac{125 \times 27 + 16}{27} = \frac{3375 + 16}{27} = \frac{3391}{27}$$ 3. Find a common denominator for $\frac{1441}{9}$ and $\frac{3391}{27}$. Since $27 = 3 \times 9$, the least common denominator is $27$. 4. Convert $\frac{1441}{9}$ to denominator $27$: $$\frac{1441}{9} = \frac{1441 \times 3}{9 \times 3} = \frac{4323}{27}$$ 5. Now subtract: $$\frac{4323}{27} - \frac{3391}{27} = \frac{4323 - 3391}{27} = \frac{932}{27}$$ 6. Convert $\frac{932}{27}$ back to a mixed number: Divide $932$ by $27$: $$27 \times 34 = 918$$ Remainder: $932 - 918 = 14$ So, $$\frac{932}{27} = 34 \frac{14}{27}$$ 7. Therefore, the answer is $34 \frac{14}{27}$. This corresponds to option D). Final answer: $34 \frac{14}{27}$