



 
Not normally... indeed, many mathematicians would say "never" (while others, particularly elementary school math teaching experts, would say "sometimes".) It depends on whether you consider multiplication to be a primitive function, commutative by definition, or whether it "is" repeated addition and "just happens" to be commutative  a distinction that perhaps we need not worry about too much! The "elementary teacher" view is that (eg) 2x3 means 3+3 while If the picture suggests an inner grouping, like [* * *] [* * *] then with the repeated addition definition this would be 2x3 and not 3x2. If we use the countingpairs definition both are right. If the picture is * * * Good Hunting!  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 