1. **State the problem:** We are given that the area of Manitoba is about $1 \frac{1}{5}$ times the total area of the four Atlantic provinces, and the area of Yukon Territory is about $\frac{3}{4}$ the area of Manitoba. We need to express the area of Yukon Territory as a fraction of the total area of the Atlantic provinces. 2. **Convert mixed number to improper fraction:** $$1 \frac{1}{5} = \frac{6}{5}$$ 3. **Express Manitoba's area in terms of Atlantic provinces' area:** Let the total area of the Atlantic provinces be $A$. Then the area of Manitoba is: $$M = \frac{6}{5} A$$ 4. **Express Yukon Territory's area in terms of Manitoba's area:** $$Y = \frac{3}{4} M = \frac{3}{4} \times \frac{6}{5} A$$ 5. **Multiply fractions:** $$Y = \frac{3 \times 6}{4 \times 5} A = \frac{18}{20} A$$ 6. **Simplify the fraction by canceling common factors:** $$\frac{18}{20} = \frac{\cancel{18}^{9}}{\cancel{20}^{10}} = \frac{9}{10}$$ 7. **Final answer:** The area of Yukon Territory as a fraction of the total area of the Atlantic provinces is: $$\boxed{\frac{9}{10}}$$