1. **State the problem:** We need to find the area of a rectangular tile with width $\frac{2}{5}$ m and length $\frac{7}{8}$ m. 2. **Formula for area of a rectangle:** $$\text{Area} = \text{width} \times \text{length}$$ 3. **Substitute the given values:** $$\text{Area} = \frac{2}{5} \times \frac{7}{8}$$ 4. **Multiply the fractions:** $$\frac{2 \times 7}{5 \times 8} = \frac{14}{40}$$ 5. **Simplify the fraction:** Both numerator and denominator can be divided by 2: $$\frac{14 \div 2}{40 \div 2} = \frac{7}{20}$$ 6. **Final answer:** The area of each tile is $\frac{7}{20}$ m$^2$. This means each tile covers $\frac{7}{20}$ square meters of floor space.