When adding two numbers, the order does not matter. EXAMPLES: = a + b = b + a

When multiplying two numbers, the order does not matter. EXAMPLES: 5 6 = 6 5 a b = b a

When adding three numbers, the order does not matter. Always involves parenthesis EXAMPLES: (3 + 2) + 4 = 3 + (2 + 4) (a + b) + c = a + (b + c)

When multiplying three numbers, the order does not matter. Always involves parenthesis EXAMPLES: (3 2) 4=3 (2 4) (a b) c=a (b c)

Any number plus zero equals itself EXAMPLES: = d = d

Any number times one equals itself EXAMPLES: 8 1 = 8 1 m = m

Any number added to its inverse equals zero. EXAMPLES: 8 + (-8) = 0 -a + a = 0

Any number multiplied by its inverse (reciprocal) equals one. EXAMPLES: and

Any number times zero equals zero EXAMPLES: 4 0 = 0 0 h = 0

Multiplying the number outside of the parentheses (distributing) to each number inside the parentheses EXAMPLES: 2(3 + 4) = 2(3) + 2(4) = = 14 2(d – 6) = 2d – 2(6) = 2d - 12

The distance from zero on a number line The absolute value of any number is positive