Multiplication and Addition
Name: John W.
I once asked my Calculus teacher if multiplication was just an
advanced form of addition and he didn't seem to understand my
meaning. What I mean couldn't you say multiplication is a simplification
of addition? You either say two times three or add 3 twice or add 2 three times.
Yes, multiplication is defined as sequential addition, and division is
defined as sequential subtraction.
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
Perhaps a better way to word it is: Multiplication is a short-hand way to
do multiple additions. If you want to add 8 to something, but you want to
add it seven times, it is quicker to add 8x7 to that something. This
becomes less easy to see when decimals, fractions, and algebra are
considered. However, it is still there.
I complement you on realizing an attribute of multiplication missed by many
students. It indicates a desire to understand rather than to simply repeat.
You are quite correct n*m is just (m+m+m+...m) n-times or \
(n+n+...+n) m-times. However, you have to be careful when the definition of
multiplication is generalized to decimals and fractions.
For example, what does 3*(2.71) mean?
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Update: June 2012