35/24:15/32-3

To solve the expression \( \frac{35}{24} : \frac{15}{32} - 3 \), let's break it down step by step.

1. First, simplify the division \( \frac{35}{24} : \frac{15}{32} \). Dividing by a fraction is the same as multiplying by its reciprocal:

   \[ \frac{35}{24} \div \frac{15}{32} = \frac{35}{24} \times \frac{32}{15} \]

2. Now, multiply the fractions:

   \[ = \frac{35 \times 32}{24 \times 15} \]

3. Calculate the numerator and denominator:

   \[ 35 \times 32 = 1120 \] \[ 24 \times 15 = 360 \]

   Therefore, we have:

   \[ \frac{1120}{360} \]

4. Simplify \( \frac{1120}{360} \) by finding the greatest common divisor (GCD). Both numbers can be divided by 40:

   \[ \frac{1120 \div 40}{360 \div 40} = \frac{28}{9} \]

5. Now we subtract 3 from \( \frac{28}{9} \). To do this, convert 3 into a fraction with a denominator of 9:

   \[ 3 = \frac{27}{9} \]

6. Now, perform the subtraction:

   \[ \frac{28}{9} - \frac{27}{9} = \frac{28 - 27}{9} = \frac{1}{9} \]

So, the final result of the expression \( \frac{35}{24} : \frac{15}{32} - 3 \) is:

\[ \frac{1}{9} \]