Chapter 1 Flashcards
a - b = a + (-b)
Definition of subtraction
a -:- b = a/b = a* 1/b
Definition of division
a(b - c) = ab - ac
Distributive property of subtraction
0 * a = 0
Multiplication by 0
-1 * a = -a
Multiplication by -1
a + b is a real number
(Addition) closure
ab is a real number
(Multiplication) closure
a + b = b + a
(Addition) Communitive
ab = ba
(Multiplication) Communitive
(a + b) + c = a + (b + c)
(Addition) associative
(ab)c = a(bc)
(Multiplication) associative
a + 0 = a, 0 + a = a
0 is the additive identity
(addition) identity
a* 1 = a, 1* a = a
1 is the multiplicative identity
(Multiplication) identity
a + (-a) = 0
(Addition) inverse
a* (1/a) = 1
(Multiplication) inverse
a(b+c) = ab + ac
Distributive (Addition & Multiplication)
Natural numbers
1, 2, 3, 4…
Numbers to count
Whole numbers
0, 1, 2, 3…
Natural numbers & zero
Integers
… -2, -1, 0, 1…
Natural numbers, their opposites, and zero
Rational numbers
… -1/2, -0.36, 1, 2, 2.45, 5…
Integers and parts of a number
Plus perfect squares
Irrational numbers
Square root(5)
Pi
1.33333..
Never ending numbers
a = a
Property of equality
Reflexive
If a = b, then b = a
Properties of equality
Symmetric
If a = b and b = c, then a = c
Properties of equality
Transitive
If a= b, then you can replace a with b and vice versa
Properties of equality
Substitution
If a = b, then a + c = b + c
Property of equality
Addition
If a = b, then a - c = b - c
Property of equality
Subtraction
If a = b, then ac = bc
Property of equality
Multiplication
If a = b, a/c = b/c
Property of equality
Division
