1. **State the problem:** We need to find how many pieces of length $\frac{3}{5}$ metres can be cut from a wire that is $\frac{9}{5}$ metres long. 2. **Formula used:** To find the number of pieces, divide the total length of the wire by the length of each piece: $$\text{Number of pieces} = \frac{\text{Total length}}{\text{Length of each piece}}$$ 3. **Apply the formula:** $$\frac{9}{5} \div \frac{3}{5}$$ 4. **Division of fractions rule:** Dividing by a fraction is the same as multiplying by its reciprocal: $$\frac{9}{5} \times \frac{5}{3}$$ 5. **Multiply numerators and denominators:** $$\frac{9 \times 5}{5 \times 3} = \frac{45}{15}$$ 6. **Simplify the fraction:** $$\frac{45}{15} = 3$$ 7. **Interpretation:** You can cut exactly 3 pieces of length $\frac{3}{5}$ metres from the wire of length $\frac{9}{5}$ metres.