Unit 1 Section 4 Prop of Add & Mult.notebook
September 10, 2015
Bellringer
Name the subset(s) of the real numbers to which each
number belongs.
1.) 2
3
2.) √6
3.) ­7
4.) Order the numbers from least to greatest.
­13
6
,
,
­2.1
­26
13
,
­9
4
, ­√2
Between which two integers does each lie?
5) √35
6) -√95
7) √150
Sep 8­11:02 AM
Bellringer
1.) (4)(10) ÷ 5(2)3
2.) 8{(15÷3)[5(4)÷5(2)]}
(
(
2
3.) 15÷3(5)
2-(-8)
Sep 11­9:11 AM
Unit 1 Section 4 Prop of Add & Mult.notebook
September 10, 2015
Sep 12­7:08 AM
Properties of Addition and Multiplication
Sep 8­9:45 AM
Unit 1 Section 4 Prop of Add & Mult.notebook
September 10, 2015
Homework Packet Page 12
Commutative Property of Addition: For all real numbers a
and b:
a+b=b+a
Commutative Property of Multiplication: For all real
numbers a and b:
ab = ba
Sep 8­9:56 AM
Associative Property of Addition: For all real numbers
a, b and c:
(a + b) + c = a + (b + c)
Associative Property of Multiplication: For all real numbers
a, b, and c:
(ab)c= a(bc)
Sep 8­9:58 AM
Unit 1 Section 4 Prop of Add & Mult.notebook
September 10, 2015
Identity Property of Addition: For every real number a:
and
a+0=a
0+a=a
Identity Property of Multiplication: For every real number a:
a(1) = a
and
1(a) = a
Sep 8­9:50 AM
Zero Property of Multiplication: For every real number a:
a
. 0=0
Multiplication Property of -1: For every real number a:
-1
. a = -a
Jul 23­9:22 AM
Unit 1 Section 4 Prop of Add & Mult.notebook
September 10, 2015
Inverse property of Addition: For every real number a,
there is exactly one real number -a, such that:
a + (-a) = 0
and
-a + a = 0
Inverse property of Multiplication- For every non-zero real
1
number a, there is exactly one real number ___ such that:
a
1
)=1
a ( ___
a
and
1
___
a
(a) = 1
What does non­zero mean?
Sep 8­9:52 AM
Distributive Property: For all real numbers a, b, and c:
a(b + c)= ab + ac
and
(b + c)a = ba + ca
a(b - c)= ab - ac
and
(b - c)a = ba - ca
Sep 8­9:59 AM
Unit 1 Section 4 Prop of Add & Mult.notebook
September 10, 2015
Which property of real numbers justifies
each statement.
1.) -3(a + 2) = -3(a) + (-3)(2)
2.) (5 + y)(-2) = 5(-2)+y(-2)
3.) 8 - 7xy = 8 - 7yx
4.) 5 + (9 + 3) = (5 + 9) + 3
5.) -1 + 1 = 0
6.)
7.) 0(1) = 0
8.) 5 + 0 = 5
9.) 3(1) = 3
10.) 23(-1) = -23
Sep 8­10:01 AM
An Algebra student was given the expression 8 + (4 + 1) to simplify. Which choice below shows an equivalent expression and the correct property?
A.) (8 + 4) + 1; Identity Property of Addition
B.) (8 + 4) + 1; Commutative Property of Addition
C.) (8 + 4) + (­1); Inverse Property of Addition
D.) (8 + 4) + 1; Associative Property of Addition
Sep 14­8:41 AM
Unit 1 Section 4 Prop of Add & Mult.notebook
September 10, 2015
Homework: Homework packet page 13 and 14 and 15
Aug 29­10:21 AM
Sep 3­1:09 PM