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?