e.g. $12$ can be expressed as a product of its factors: $2 \times 6, 3 \times 4$. The composites can be decomposed further.
$12$ can also be expressed as a sum of its
somethings: $1+11, 2+10, 3+9, ...$. The non-$1$'s can be decomposed further.
It seems to me that if primes are the atoms of multiplication, then $1$ is the atom of addition. (BTW and maybe the Fundamental Theorem of Arithmetic should be called the Fundamental Theorem of Multiplication)