Question

You know that multiplication can also be expressed as repeated addition. Why is it more difficult to use repeated addition when multiplying two mixed numbers than it is to use repeated addition when you are multiplying a mixed number by a whole number?​

Answer 1

Multiplication as repeated addition is problematic because addition is referent preserving, whereas multiplication is referent transforming. Repetitions of addition therefore cannot yield the referent that is appropriate for the product in a multiplicative situation.

Answer 2

Let's start with the underlying fact. Multiplication simply is not repeated addition, and telling young pupils it is inevitably leads to problems when they subsequently learn that it is not. Multiplication of natural numbers certainly gives the same result as repeated addition, but that does not make it the same.

Explanation: