What are the 3 rules of multiplying and the 3 rules for adding,the 1 rule for dividing and subtracting?

Many rules exist for different types of multiplication and addition. For addition with real numbers a,b, and c:

The associative rule ensures (a+b)+c=a+(b+c)

The commutative rule ensures a+b=b+a

Property of zero ensures 0+a=a

For multiplication;

The associative rule ensures (ab)c=a(bc)

The commutative rule ensures ab=ba

The distributive rule ensures a(b+c)=ab+ac

These few rules can be extended to negative numbers and fractions, which means that they will be true under division and subtraction. A common rule of division is to not divide by 0.

Note: These rules are for real numbers. For instance, matrix multiplication is not communitive.