45/7:15/56•3/8

To solve the expression \( \frac{45}{7} : \frac{15}{56} \cdot \frac{3}{8} \), we first rewrite the division as multiplication by the reciprocal.

1. Rewrite the division: \[ \frac{45}{7} \div \frac{15}{56} = \frac{45}{7} \cdot \frac{56}{15} \]

2. Now, we need to multiply this by \( \frac{3}{8} \): \[ \left( \frac{45}{7} \cdot \frac{56}{15} \right) \cdot \frac{3}{8} \]

3. Combine the fractions: \[ = \frac{45 \cdot 56 \cdot 3}{7 \cdot 15 \cdot 8} \]

4. Now calculate the numerator and the denominator separately:

   • Numerator: \[ 45 \cdot 56 \cdot 3 = 7560 \]
   • Denominator: \[ 7 \cdot 15 \cdot 8 = 840 \]

5. Now our expression is: \[ \frac{7560}{840} \]

6. To simplify \( \frac{7560}{840} \), we can divide both the numerator and the denominator by 840: \[ = 9 \]

Thus, the final result of the expression \( \frac{45}{7} : \frac{15}{56} \cdot \frac{3}{8} \) is \( 9 \).