Math 6 Honors ( Periods 1, 2, & 3)

Properties of Addition & Multiplication 1-2

The following was handed out in class.. if you were absent make sure to get your copy and GLUE it into your Spiral Notebook.
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!!