Real # System

Rational

Can be written as a fraction, a/b where a and b are not 0 Integers, fractions, decimals that terminate, decimals that repeat

Natural Numbers

Counting Numbers 1, 2, 3...

Counter Example

If a statement is true, you must provide properties that make it true. If a statement is false, you must provide a counter example.

Addition Property of Equality

If a=b, then a +c=b + c 2x-6=10 2x-6+6=10+6

Subtraction Property of Equality

If a=b, then a -c=b - c 2x+6=10 2x+6-6=10-6

Division Property of Equality

If a=b, then a/c= b/c

Multiplication Property of Equality

If a=b, then ac=bc x/2=10 x/2 * 2= 10 * 2

Multiplicative Property of Zero

Let a be any real number a*0=0 43 * 0= 0

Whole Numbers

Natural numbers and zero 0, 1, 2, 3...

Irrational

Numbers that cannot be represented as a quotient of two integers Pi, number with a decimal that does not repeat

Additive Identity

The additive identity is the number 0.

Integers

Whole numbers and their opposites ...-3, -2, -1, 0, 1, 2, 3...

Multiplicative Identity Property

a * 1= a 130 * 1= 130

Additive Inverse Property

a + (-a)= 0 12 + (-12)= 0

Associative Property of Addition

a + (b + c) = (a+b) + c *Let a, b, and c represent real numbers 1 + (2+3)= (1 +2) + 3

Additive Identity Property

a + 0 = a * Let a represent a real number 12+0=12 -56+0= -56

Commutative Property of Addition

a + b= b + a *Let a and b represent real numbers 2+3=3+2

Not a real number

a number divided by 0, the square root of a negative number

Distributive Property

a(b+c)= ab + ac

Associate Property of Multiplication

a* (b*c)= (a*b) *c *Let a, b and c represent real numbers 2*(3 * 4)= (2 * 3) * 4

Commutative Property of Multiplication

ab=ba *Let a and b represent real numbers 2 * 3 =3 * 2

Additive Inverse

the additive inverse is the opposite of the number

Multiplicative Inverse

the reciprocal of a number a* 1/a= 1