Notice that the temperature rose 3 3/4 degrees every 1 2/3 hours and we are asked to calculate a RATE which involves a quotient.
Therefore we need to start by converting both mixed numbers into fractions, so as to be able to divide one by the other.
3 3/4 = 3 + 3/4 = 12/4 + 3/4 = 15/4
and
1 2/3 = 1 + 2/3 = 3/3 + 2/3 = 5/3
Now we can calculate the rate (degrees per hour, or degrees / hour) by dividing 15/4 by 5/3:
15/4 divided by 5/3 = 15/4 * 3/5
where we used the converting of a division of fractions as the multiplication of the first one times the reciprocal of the second one.
15/4 * 3/5 = 45 / 20 = 9 / 4 = 2.25 degrees per hour.