（7 3/5-2 4/15）· 9/32

To solve the expression \( (7 \frac{3}{5} - 2 \frac{4}{15}) \cdot \frac{9}{32} \), we will follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Subtract the two fractions.
3. Multiply the result by \( \frac{9}{32} \).

Step 1: Convert to Improper Fractions

For \( 7 \frac{3}{5} \): \[ 7 \frac{3}{5} = 7 \cdot 5 + 3 = 35 + 3 = \frac{38}{5} \]

For \( 2 \frac{4}{15} \): \[ 2 \frac{4}{15} = 2 \cdot 15 + 4 = 30 + 4 = \frac{34}{15} \]

Step 2: Subtract the Two Fractions

We need to find a common denominator to subtract \( \frac{38}{5} \) and \( \frac{34}{15} \). The least common multiple of 5 and 15 is 15.

Rewrite \( \frac{38}{5} \) with a denominator of 15: \[ \frac{38}{5} = \frac{38 \cdot 3}{5 \cdot 3} = \frac{114}{15} \]

Now, subtract: \[ \frac{114}{15} - \frac{34}{15} = \frac{114 - 34}{15} = \frac{80}{15} \]

Step 3: Simplify the Result

Now, simplify \( \frac{80}{15} \): \[ \frac{80}{15} = \frac{16}{3} \]

Step 4: Multiply by \( \frac{9}{32} \)

Now, multiply \( \frac{16}{3} \) by \( \frac{9}{32} \): \[ \frac{16}{3} \cdot \frac{9}{32} = \frac{16 \cdot 9}{3 \cdot 32} = \frac{144}{96} \]

Step 5: Simplify the Final Fraction

Now simplify \( \frac{144}{96} \): \[ \frac{144 \div 48}{96 \div 48} = \frac{3}{2} \]

Final Answer

The result is: \[ \frac{3}{2} \] or \( 1 \frac{1}{2} \) as a mixed number.