Any fragmentation perceived from a spiritual perspective suggests that integration has not yet taken place or has broken down. We have only partial information available to us.
Psychological / emotional perspective: When we recognize that we can see only a fraction or fragment of a dream object we need to take further action to gain control of emotions and feelings associated with whatever is represented.
The shape of the fragment might be relevant.
Material aspects: It may be unusual to be aware of fractions in dreams except in the sense of ‘things half-done’ however, when allowing dreams to help us work through our problems fractions and fragments become much more relevant.
A dream in three parts may give us the information we need.