To find out how many backpacks Martin can make with 9 yards of fabric when each backpack requires \( \frac{3}{5} \) yard of fabric, you can divide the total amount of fabric by the amount needed for one backpack.
\[ \text{Number of backpacks} = \frac{\text{Total fabric}}{\text{Fabric per backpack}} = \frac{9 \text{ yards}}{\frac{3}{5} \text{ yard/backpack}} \]
To divide by a fraction, you can multiply by its reciprocal:
\[ \frac{9}{\frac{3}{5}} = 9 \times \frac{5}{3} = \frac{9 \times 5}{3} = \frac{45}{3} = 15 \]
So, Martin can make 15 backpacks with 9 yards of fabric.
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