1. **State the problem:** We need to find the volume of a rectangular prism with side lengths $\frac{3}{5}$ m, $\frac{5}{6}$ m, and $\frac{1}{4}$ m. 2. **Formula for volume of a rectangular prism:** $$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$ 3. **Substitute the given values:** $$V = \frac{3}{5} \times \frac{5}{6} \times \frac{1}{4}$$ 4. **Multiply the fractions:** Multiply numerators: $$3 \times 5 \times 1 = 15$$ Multiply denominators: $$5 \times 6 \times 4 = 120$$ So, $$V = \frac{15}{120}$$ 5. **Simplify the fraction:** Divide numerator and denominator by 15: $$\frac{15 \div 15}{120 \div 15} = \frac{1}{8}$$ 6. **Final answer:** The volume of the rectangular prism is $$\boxed{\frac{1}{8}}$$ cubic meters.