The Goal

Which is the smaller fraction:

The Mistake

The smaller fraction is:

Need a hint? Look carefully at the red part of the algebra:

The Correction

The smaller fraction is:

An Explanation

When the numerators of two fractions are equal (they are both 1 in this mistake), the fraction with the larger denominator (namely, 28) is the smaller fraction.
Why?
If you think of fractions in terms of pieces of pizza, then you'll have a smaller piece if the pizza is divided into 28 pieces than if the pizza is divided into 12 pieces. 1/28 of a pizza is smaller than 1/12 of a pizza. The fraction 1/28 is smaller than 1/12.