Algebra II, Lesson 2

The ___ Identify Element defines 0 as such that a+0 = 0+a for all real numbers.

Additive

The ___ Property of Addition states that for any a, b, and c, a+(b+c) = (a+b) +c.

Associative

The ___ Property of Multiplication states that for any numbers a, b, and c, a*(b*c) = (a*b)*c.

Associative

The ___ Property of Addition states that for any numbers a and b, a+b =b+a.

Commutative

The ___ Property of Multiplication states that for any numbers a and b, a*b = b*a.

Commutative

The ___ Property of Multiplication states that for any numbers a, b, and c, a* (b+c) = (a*b) + (a*c).

Distributive

The Additive ___ Property states that for every number a, there is a number -a, such that a+ (-a) = (-a) +a = 0

Inverse

The ___ Identity Property defines 1 as the multiplicative identity element because for every number a, a*1 = 1*a = a

Multiplicative

The ___ Inverse Property states that for every number a except 0, there is a number a^-1 = 1/a such that a * (a^-1) = (a^-1) * a = 1

Multiplicative

The ___ Property of Equality states that for any number a, a=a

Reflexive

The ___ Property of Equality states that for any numbers a and b, a=b, then b=a

Symmetric

Of the three properties, reflexive, symmetric, and transitive that define the relation "is equal to," which one could also apply to "is less than" and "is greater than?"

Transitive

The ___ Property of Equality states that for any numbers a, b, and c, if a=b and b=c, then a=c

Transitive

The ___ Property states that for any numbers a and b, either a < b, a=b, or a>b.

Trichotomy