2.2 Addition and Subtraction of Whole Numbers Remember to Silence Your Cell Phone and Put It In Your Bag!

Interpretations for Addition Set model Joining 2 sets Number line model Joining 2 lengths

Definition of Addition of Whole Numbers If A and B are two disjoint sets and n(A) = a and n(B) = b, then a + b = n(A  B). Addends Sum

Properties of Addition Let a, b, c  W Closure Property a + b is a unique whole number Identity Property There exists a unique whole number, 0, such that a + 0 = a and 0 + a = a.

Properties of Addition (cont.) Commutative Property a + b = b + a Associative property (a + b) + c = a + (b + c)

Ordering Whole Numbers (formalized) Let a, b  W a is less than b, denoted by a 0 such that a + k = b. b > a iff a < b.

Interpretations for Subtraction Take-away Separating a set Comparison Number line Missing addend

Definition of Subtraction For a, b  W, a – b = c iff c is a unique whole number such that c + b = a. Minuend Subtrahend Difference Note – Subtraction is the inverse operation of addition