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