Remember sacrifice is the act of loosing something existing.
Here the old partners are sacrificing a part of their profit due to the admission of a new partner, or the old share or Ratio is changing to a new share or New Ratio.
Hence we have to remember Old share is greater than the new share, when the number of partners are more due to the admission.
Therefore, Sacrificing Ratio = Old Ratio - New Ratio or the Trick is to remember SR = OR-NR