Basic Properties of Real Numbers
Rules that real numbers follow
Commutative
Commutative
•Addition
•a+b+c=c+a+b
•45+98+15=15+98+45
Commutative
•Multiplication
•a x b x c = c x a x b• 25 x 21 x 4 = 4 x 25 x 21
Commutative
•Caution!
•Works with + & x
•Not with - & /
Associative
Associative
•Addition
• (a + b) + c = a + (b + c)
• (8 + 7) + 3 = 8 + (7 + 3)
Associative
•Multiplication
• (a x b) x c = a x (b x c)
• (6 x 4) x 5 = 6 x (4 x 5)
Distributive
Distributive
•Addition
•a(b + c) = ab + ac
•4(2x + 5) = 8x + 20
Distributive
•Subtraction
•a(b + c) = ab + ac
•4(4x - 2) = 16x - 8
Identity
Identity
•Addition
•a + 0 = a
•5 + 0 = 5
Identity
•Multiplication
•a x 1 = a
•9 x 1 = 9
Zero Property
Zero Property
•Multiplication
•a x 0 = 0
•8 x 0 = 0
Inverse
Inverse
•Addition
•a + -a = 0
•7 + - 7 = 0
Inverse
•Multiplication
•a x 1/a = 1
•3 x 1/3 = 1
Equality
Equality
•Addition
• If a=b, then
• a+c=b+c
Equality
•Subtraction
• If a=b, then
• a-c=b-c
Equality
•Multiplication
• If a=b, then
• ac=bc
Equality
•Division
• If a=b, then
• a/c=b/c
Review
•Associative?
•Commutative?
•Distributive?
Review
• Inverse?
•Zero?
•Equality?