Math 6H (Periods 6 & 7)

Properties of Addition & Multiplication 1-2

1, 2, 3, 4,5 .... are counting numbers or natural numbers.
If we add 0... we have 0,1,2,3,4,... and we have the set of whole numbers

Some important properties are found using whole numbers:

Commutative Property of Addition (C+)
for any whole numbers a and b
a + b = b + a

Commutative Property of Multiplication (Cx)
for any whole numbers a and b
ab = ba

You HEAR the differences.. remember we made the big C into an ear... or at least we attempted to!!

However look at the following
(6 +5) + 7 = 11 + 7 = 18
but so does
6 + (5 + 7) = 6 + 12 = 18

Associative Property of Addition ( A+)
For any whole numbers a, b, and c
(a + b) + c = a + ( b + c)

Associative Property of Multiplication ( Ax)
For any whole numbers a, b, and c
(ab)c = a(bc)

You SEE the difference with the hugs ( ).. hugs are really important in life.. and in math!!

Addition Property of Zero from the book
also known as the Identity Property of Addition ( Id+)
for any whole number a
a + 0 = a and 0 + a = a

Multiplication Property of One
also know as the Identity Property of Multiplication (Idx)
For any whole number a
a(1) = a and 1(a) = a

Multiplication Property of Zero
for any whole number a
0(a) = 0 and 0(a) = 0

So how do we justify?

16 + 19 + 34 ---> given
16 + 34 + 19 ---> C+
(16 + 34) + 19---> A+
50 + 19---> simplify
69---> simplify


2 (14)(15)---> given
2 (15) (14) ---> Cx
[2(15)] (14) ---> Ax
30 (14)---> simplify
420---> simplify

how about the following. What would make it easier to simplify???
8⋅ 14⋅ 25 ⋅5 ---> given
14 ⋅ 8 ⋅ 5⋅ 25 ---> Cx
14 ⋅ (8 ⋅ 5)⋅ 25 ---> Ax
14 ⋅ 40⋅ 25--->simplify
14 ⋅ (40⋅ 25) ---> Ax
14 ⋅ 1000 ---> simplify
14000 ---> simplify

Make sure you justify each step of tonight's homework!!