Can all mathematical operations be represented by summation? I'm not good at Math, but I think all operators can be represented by summation in some way right?
Example:
A - B = A + (-B)
A * B = A + A + A (B times)

But how about /, %, ^,...?
Can it be?
How about multiplying 2 negative numbers?
Example:
-2 * -2

How can I convert it to summation
 A: Here are Wikipedia articles on tetration and hyperoperations. This pretty much shows how far you can get if ALL you do is add.

*

*Repeated addition is multiplication

*Repeated multiplication is exponentiation, so in some sense you're raising to powers with just tons of addition

*Repeated exponentiation is something called "tetration" which grows way way faster than exponentiation! Again, in the end this basically just comes back to tons and tons of additions.

*And so on... people study some more levels called pentation and even beyond.

You can get further if you're willing to allow "answers to questions stated with only addition". For example:

*

*Subtraction: $a - b$ is defined as "the number that will give me $a$ if I add $b$ to it". This also gives us negative numbers.

*Division: If $n$ is a positive integer, then $\frac p q$ is defined as "the number that will give me $p$ if I add it to itself $q$ times".

*Integer division: For $a,b$ positive integers, $a // b$ is defined as the biggest integer such that I can add it to itself $b$ times and get a result $\le a$.

*$\%$ aka modulus: For $a,b$ positive integers, $a \% b$ is defined as $a - b \cdot (a//b)$.

You can keep going like this and define lots more operators. Fun fact: when serious business math people set out to carefully prove all the math statements they use, these definitions of subtraction and division are actually exactly how arithmetic normally gets defined. So your weird question is actually a real topic that stresses out a bunch of new math majors every year :)
