a + 0 = a and 0 + a = a

example: 5 + 0 = 5

a * 1 = a or 1 * a = a

example: 25 * 1 = 25

a * 0 = 0 or 0 * a = 0

example: 150 * 0 = 0

a/b * b/a = 1

example: 8/3 * 3/8 = 24/24 = 1

if a =b, then b = a

example: if 5 + 3 = 6 + 2, then 6 + 2 = 5 + 3

if a = b, then a can be replaced by b in any expression

example: given the expression 2x - 5,

if x = 4, then 2 * 4 - 5

if a = b and b = c, then a = c

example: if 5 + 1 = 6 and 6 = 4 + 2,

then 5 + 1 = 4 + 2

a(b + c) = ab + ac

example: 5(x + y) = 5x + 5y

a + b = b + a

example: 3 + x = x + 3

a * b = b * a

example: 5 * 3 = 3 * 5

a + (b + c) = (a + b) + c

example: 6 + (4 + 2) = (6 + 4) + 2

a * (b * c) = (a * b) * c

example: 10 * (2 * 8) = (10 * 2) * 8

a + (-a) = 0

example: 9 + (-9) = 0