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The traditional Old Kingdom duplation multiplication operationally proved the arithmetic accuracy of unit fraction answers, and was not the primary Middle Kingtdom multiplication operation.
This method may be called mediation and duplation, where mediation means halving one number and duplation means doubling the other number.
He professes himself amazed at Gullberg's revelation of an alternative pencil-and-paper method of multiplication from the one we all learned at school, namely the Egyptian method of duplation, and loves the "Russian peasant" multiplication method involving "successive duplation and mediation".