   SEARCH HOME Math Central Quandaries & Queries  Question from Janet, a parent: IN A MULTIPLICATION SENTENCE BASED ON A DRAWING..IS THERE ANY ORDER FOR THE MULTIPLICAND ANG MULTIPLIER FOR THE ANSWER TO RIGHT? 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
3x2 means 2+2+2. In advanced math we think of it as counting pairs, one element taken from a set of 2 objects and one from a set of 3; so the set
{a,b} x {C,D,E} has elements {(a,C),(a,D),(a,E),(b,C),(b,D),(b,E)}. These two definitions always give the same answer!

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 counting-pairs definition both are right.

If the picture is

* * *
* * *
then - unless there is a convention otherwise, to the effect that rows will be considered to be inner groups, in the course - both are right.

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