Commutative property of addition, Switching/Moving: a+b = b+a, Commutative property of multiplication, Switching/Moving: a(b) = b(a), Associative property of addition, Regrouping like operations: a+(b+c) = (a+b)+c, Associative property of multiplication, Regrouping like operations: a(bc) = (ab)c, Additive identity property, Equaling itself: a + 0 = a (what + what = itself), Multiplicative identity property, Equaling itself: a (1) = a (what * what = itself), Additive inverse property, Adding the opposite equals zero: a + (-a) = 0 | -a + a = 0, Multiplicative inverse property, Multiplying the reciprocal equals one: a/b * b/a=1 | 1/b * b/1=1, Multiplicative property of zero, Anything multiplied by zero = 0, Distributive property, Distributing the wealth (multiplying all terms), Symmetric property, Flip: **If, then, Transitive property, Connection: If x+3=5 and 5=7-x then x+3=7-x | The expressions equal each other. **If, and, then, Substitution property, NO Connection: If m+3=5 and m=w then w+3=5 | The variable can be plugged in., Reflexive property, Same on both sides. **Reflection

Algebraic Properties: Definitions

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