16/25 : 28/45 - 1

To solve the expression \( \frac{16}{25} : \frac{28}{45} - 1 \), we first need to perform the division and then subtract 1. 1. **Division of Fractions**: When dividing by a fraction, we multiply by its reciprocal. Thus, \[ \frac{16}{25} : \frac{28}{45} = \frac{16}{25} \times \frac{45}{28} \] Now we can simplify the multiplication: \[ = \frac{16 \times 45}{25 \times 28} \] **Calculating the numerator:** \[ 16 \times 45 = 720 \] **Calculating the denominator:** \[ 25 \times 28 = 700 \] Thus, we have: \[ \frac{16}{25} : \frac{28}{45} = \frac{720}{700} \] Now simplify \( \frac{720}{700} \): \[ = \frac{72}{70} = \frac{36}{35} \quad (\text{by dividing numerator and denominator by 20}) \] 2. **Subtracting 1**: Now we need to subtract 1 from \( \frac{36}{35} \): \[ \frac{36}{35} - 1 = \frac{36}{35} - \frac{35}{35} = \frac{36 - 35}{35} = \frac{1}{35} \] Thus, the result of \( \frac{16}{25} : \frac{28}{45} - 1 \) is \[ \boxed{\frac{1}{35}}. \]