Why mixed numbers need a common denominator
A mixed number is a whole part plus a fraction. To add two mixed numbers, first turn them into improper fractions, then rewrite both fractions with the same denominator.
That denominator is usually the least common denominator, which keeps the strip model compact and makes the final simplification easier to read.
The summary cells, substitution board, and strip model are all showing the same idea in three forms: number sentence, symbolic form, and partitioned units.