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

\[ \boxed{\frac{1}{35}}. \]