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