To find out how many backpacks Martin can make with 9 yards of fabric, we can divide the total amount of fabric he has by the amount of fabric needed for one backpack.
The formula is:
\[ \text{Number of backpacks} = \frac{\text{Total fabric}}{\text{Fabric per backpack}} = \frac{9 \text{ yards}}{\frac{3}{5} \text{ yards per backpack}} \]
Dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite the equation as:
\[ \frac{9}{\frac{3}{5}} = 9 \times \frac{5}{3} = \frac{9 \times 5}{3} = \frac{45}{3} = 15 \]
Therefore, Martin can make 15 backpacks.