To determine how many backpacks Martin can make with 9 yards of fabric, we need to divide the total amount of fabric he has by the amount of fabric required for one backpack.
The calculation is as follows:
\[ \text{Number of backpacks} = \frac{\text{Total fabric}}{\text{Fabric per backpack}} = \frac{9 \text{ yards}}{\frac{3}{5} \text{ yard/backpack}} \]
To perform the division, we multiply by the reciprocal of \(\frac{3}{5}\):
\[ \frac{9}{\frac{3}{5}} = 9 \times \frac{5}{3} = \frac{9 \times 5}{3} \]
Calculating the multiplication in the numerator:
\[ 9 \times 5 = 45 \]
Now, divide by 3:
\[ \frac{45}{3} = 15 \]
Therefore, Martin can make 15 backpacks.