Why Was 5 x 3 = 5 + 5 + 5 Marked Wrong
Brett Berry
4.6K748

Not only is this wrong but harmful teaching of math. It is also false.

The following equivalence
5 x 3 = 3 + 3 + 3 + 3 + 3
is only true for Whole Numbers “when thinking of multiplication as repeated addition” but in abstract multiplication as a concept is much broader.

Multiplication of real numbers can not be “demonstrated” so easily in such groups.

5.0 x 3.0 = ????

Or can the that “concept” be applied to geometry which has an arbitrary orientation in multiplication.

5m x 3m = ??????

And most importantly multiplication as a function contradicts this logic.
Let X and Y be two sets. Let f:XY and g:XY be two functions. f=g iff f(x)=g(x) for all xX.

let f(x)=3 x x
let g(x)=x x 3

since f(x)=g(x) for all xX

f = g

then let x = 5
3 x 5 = 5 x 3:

therefore 3 x 5 = 5 x 3 = 5 + 5 + 5 = 15

this implies that 3 x 5 = 5+ 5 + 5 = 15 and it is EQUIVALENT as a function.

IN ABSTRACT MATH 3 x 5 represents many different things and it is important for the child to see MANY interpretations of this ABSTRACT concept .

Math Teacher please teach MATH as a Science and not as a Political Science.

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