To divide rational numbers, we multiply the first number by the reciprocal of the second number.

So, 125/64 ÷ -45/48 can be written as 125/64 × -48/45.

Now, let’s simplify the expression:

125/64 × -48/45 = (125 × -48) / (64 × 45) = -6000 / 2880

To simplify further, we can divide both the numerator and denominator by their greatest common divisor, which is 240:

-6000 / 2880 = (-6000 ÷ 240) / (2880 ÷ 240) = -25 / 12

Therefore, 125/64 ÷ -45/48 simplifies to -25/12.