Chapter 1 Vocabulary Flashcards
Natural numbers
numbers used for counting
Whole numbers
natural numbers and 0
Integers
natural numbers, their opposites, and 0
Rational numbers
fractions and decimals
Irrational numbers
square roots and decimals that don’t terminate or repeat
Properties of Real Numbers:
Closure, Commutative, Associative, Identity, Inverse, Distributive
Closure
a+b, ab
Commutative
a+b=b+a, ab=ba
Associative
(a+b)+c=a+(b+c), (ab)c=a(bc)
Identity
a+0=a, 0+a=a, a x 1=a, 1 x a=a
Inverse
a+(-a)=0, a x 1/a = 1, a does not equal 0
Distributive
a(b+c) = ab+ac
Properties for Simplifying Algebraic Expressions
Definition of Subtraction, Definition of Division, Distributive Property for Subtraction, Multiplication by 0, Multiplication by -1, Opposite of a Sum, Opposite of a Difference, Opposite of a Product, Opposite of an Opposite
Definition of Subtraction
a-b=a+ (-b)
Definition of Division
a/b=a/b=a x 1/b, b does not equal zero
Distributive Property for Subtraction
a(b-c)=ab-ac
Multiplication by 0
0 x a =0
Multiplication by -1
-1 x a = -a
Properties of Equality
Reflexive Property, Symmetric Property, Transitive Property, Addition Property, Subtraction property, Multiplication Property, Division Property, Substitution Property
Reflexive Property
a=a
Symmetric Property
If a=b, then b=a
Transitive
If a=b, and b=c, then a=c
Addition
If a=b, then a+c=b+c
Subtraction
If a=b, then a-c=b-c
Multiplication
If a=b, then ac=bc
Division
If a=b and c doesn’t equal 0, then a/c=b/c
Substitution
If a=b, the b may be substituted for a in any expression to obtain an equivalent expression
