We know that Emilie uses less than 1/2 cup of sugar.
Now, 1/2 is a cup divided by two.
To find less than that we just have to divide the cup by a bigger number. For example 3, that give us 1/3 of a cup and that less than 1/2.
Other examples will be 1/4, 1/5, 1/6, 1/7, etc. As long as the denominator is bigger than two and the numerator is the same (1 in this case) we have less sugar.
1/2 a cup can be represented as:
On the other hand 1/3 of a cup is:
notice that this in fact is less than 1/2.