I wasn't trying to be clever, I was just choosing random numbers.

You're right, though, and you definitely can use long multiplication to multiply any two rationals using only addition (though not sure if/how you can reduce to the lowest terms).

I got lost/distracted and started arguing something I didn't mean to initially. My initial argument that I still hold is that you can't define multiplication as simply repeated addition, and to further clarify I mean strictly that if you multiply a and b you add a to itself b-1 times.