Properties of Real NumbersAlgebra AUnit 1, Lesson 4

Natural Numbers

1,2,3,4,…Also called the “Counting Numbers”

Whole Numbers

The whole numbers are the counting numbers with the addition of the number zero.

IntegersThe integers is the set of whole numbers

and their opposites.additive inverses.

Rational Numbers

Any number that you can write as a fraction.

Irrational Numbers

Any number that you cannot write as a fraction.

7

Real Numbers

The combination of all rational and irrational numbers.

Properties

Identity Properties Addition: if you add zero to a number,

you get back the original number.

Multiplication: if you multiply a number by one, you get back the original number.

8 0 8

6 1 6

Multiplication Property of 0 Any number multiplied by 0 equals 0!

9 0 0

8,823, 427 0 0

1,000,000 0 0

Commutative Property Changing the order in which you add or

multiply does not change the sum or product.

a b b a

5 3 3 5

ab ba

12 2 2 12

Associative Property Changing the way the numbers are grouped

does not change the sum or product.

(a b) c a (b c)

(31) 6 3 (1 6)

(ab) c a(bc)

(6 3) 1 6 (31)