Math 1521 Chapters 1 and 2

Natural numbers

Counting numbers

1, 2, 3, …

Terminating decimals

Whole numbers

Counting numbers and 0

0, 1, 2, 3, …

Terminating decimals

Integers

Natural numbers, their negatives, and 0

-3, -2, -1, 0, 1, 2, 3, …

Terminating decimals

Rational numbers

Numbers that can be written in the form a/b, where and and b are integers and b does not equal 0

-3, -3/4, -0.222…, 0, 5/6, 2, 4.3111

Terminating or repeating decimals

Irrational numbers

Numbers that cannot be written in the form a/b, where a and b are integers and b does not equal 0

Square roots, pi, 1.414213…, 1.732050…

Non-terminating, non-repeating decimals

Real numbers

Rational and irrational numbers

All of the above

All types of decimals

Commutative Law of Addition

a + b = b + a

ex. 2 + 3 = 3 + 2

Associative Law of Addition

a + (b + c) = (a + b) + c

ex. 4 + (2 + 3) = (4 + 2) + 3

Identity Law of Addition

a + 0 = a

ex. 6 + 0 = a

Inverse Law of Addition

a + (-a) = 0

ex. 5 + (-5) = 0

Commutative Law of Multiplication

ab = ba

ex. 3(2) = (2)3

Associative Law of Multiplication

a(bc) = (ab)c

ex. 4(3×2) = (4×3)2

Identity Law of Multiplication

a×1 = 1×a

4×1 = 1×4

Inverse Law of Multiplication

a(1/a)=1 (a does not equal zero)

ex. 3(1/3)=1

Distributive Law of Multiplication with respect to Addition

a(b + c) = ab + ac

ex. 3 (4 + 5) = 3(4) + 3(5)