In a certain recipe that produces enough for 8 servings, 1/2 cup of sugar is required. if you were asked to expand this recipe so that it could serve 26 people, how much sugar would be required?

We have to apply the rule of three

8 servings1/2 cup of sugar
26 servings  x

x=(26 servings*(1/2) cup of sugar) / 26 servings=1.625 cup of sugar.

For making a serving for 8 people, the amount of sugar required = 1/2 cup
Then
The amount of sugar required for
making a serving for 26 people = [ (1/2)/8] * 26
                                                   =(1/16) * 26 cups
                                                   = 13/8 cups
                                                   = 1 5/8 cups
                                                   = 1.625 cups.
So for making a receipe for 26 people the amount of sugar required is 1 5/8 cups or 1.625 cups. I hope the procedure is clear enough for you to understand. In future you can always use this method for solving similar problems without requiring any help from outside.