Adding (or subtracting) the same number or the same algebraic expression on both sides of the (1) equation at the same time, the result is still an equation. Expressed in letters as:

If a=b, c is a number or an algebraic expression. Then: (1) A+C = B+C (2) A-C = B-C.

(2) The result obtained by multiplying or dividing both sides of an equation by the same non-zero number is still an equation.

(3) If a=b, then b=a (symmetry of the equation).

(4) If a = b and b = c, then a=c (transitivity of the equation).

If a=b and c is a number or an algebraic expression (not 0), then there is

a×c = b×c

a \c = b \c