Vogts Important
Properties of Introductory Algebra
Directions: Write the rule title and then find the
corresponding statement or example of that rule (a list, A T, of
possibilities is provided but write out the answer do NOT write the letter
only. This exercise is designed to assist in the memorization of the rules and
the names corresponding to them). E.G.
20) Transitive Property of Equality:
[Q] If a
= b and b = c then a = c.
1.) Addition property of equality (A.P.E.)
2.) Additive Inverse
3.) Associative Property for Addition
4.) Associative Property for Multiplication
5.) Commutative Property for Addition
6.) Commutative Property for Multiplication
7.) Definition of Brackets and Parentheses
8.) Definition of Division
9.) Definition of Subtraction
10.) Distributive Property
11.) Identity Property for Addition
12.) Identity Property for Multiplication
13.) Multiplication Property of Equality (M.P.E.)
14.) Multiplicative Inverse
15.) Multiplicative Property of Zero
16.) Order of Operations
17.) Reflexive Property of Equality
18.) Substitution Property of Equality
19.) Symmetric Property of Equality
20.) Transitive Property of Equality
Rule Possibilities:
A) a = a
B) a + 0 = a
C) a + (-a) = 0
D) a + b = b + a
E) If a = b then b = a
F) If a = b then a + c = b + c
G) a + (b + c) = (a + b) + c
H) a b = a + (-b)
I) a 0 = 0
J) a 1 = a
K) a b = b a
L) a (b c) = (a b) c
M) a (1/a) = 1 or a/b
(b/a) = 1 {a ≠
0, b ≠ 0}
N) a ๗ b = a 1/b
O) a (b + c) = (a b + a c)
P) If a = b then a c = b c
Q) If a = b and
b = c then a = c
R) The defined priority for simplifying any
arithmetic expression to ensure equivalence to one unique value.
S) If two values are equivalent then they can be used interchangeably in an expression to create an equivalent expression.
T) Operations grouped within them should be simplified first because these symbols define any operations within them to be in the highest priority category. They can be inserted or removed as long as doing so does not change the order of operations.
