What is Multiplication?

Keith Devlin claims

“Multiplication simply is not repeated addition, and telling young pupils it is inevitably leads to problems when they subsequently learn that it is not.”

http://letsplaymath.net/2008/07/28/whats-wrong-with-repeated-addition/

Addition requires identical units.

The sum must always have the same units as the addends.

Multiplication requires different units.

The product does not have the same units as either the multiplier or the multiplicand.

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Multiplication: multiplier X multiplicand = product. 

The multiplier and multiplicand have different names, even though many of us have trouble remembering which is which.

• multiplier= “how many or how much”
• multiplicand= the size of the “unit” or “group”