Download What is a property?

The Properties of
Addition &
Multiplication
As shown in different types of algebraic
equations. Yes yes.
Notes for November 14th
11/14/2012 Do Now
1. (-10) + (-8) =
 2. (-3) + 12 =
 3. -5 – 2 =
 4.
7 – (-6) =
2  5
 5.
   
3
 6

6. -1.5 – 0.2 =
 7. The temperature at 6:00 a.m. was -5 ºF.
At 2:00 p.m. the temperature had increased
14 ºF. What was the temperature at 2:00
p.m.?
 8. -8 x 9 =

11/14/2012 Do Now
1. (-10) + (-8) = -18
 2. (-3) + 12 = 9
 3. -5 – 2 = -7
 4.
7 – (-6) = 13
2  5
1
 5.
    
3
 6
6

6. -1.5 – 0.2 = -1.7
 7. The temperature at 6:00 a.m. was -5 ºF.
At 2:00 p.m. the temperature had increased
14 ºF. What was the temperature at 2:00
p.m.? 9
 -8 x 9 = -72

Announcements
Make sure name is on homework; turn it in
 Tonight's HOMEWORK ACE 1, 2, 7 and 8-25
page 69 and 70 of Accentuate the Negative
 There is an assessment on Tuesday 11/20/12
Things you will need to know

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Adding integers, fractions and decimals
Subtracting integers, fractions and decimals
Multiplying integers, fractions and decimals
Dividing integers, fractions and decimals
Order of Operations
Answering real world math problems like last nights
homework
Concept of a ledger (withdrawals, deposits, balance, etc.)
ARE YOU READY!
•Commutative Property
•Identity Property
•Associative Property
•Inverse Property
What is a property?

What do we mean by property?

Something that a person owns
Ex. This is Chuck’s
cow. It is his property.
What is a property?

The other definition of property


A distinctive attribute or quality of
something
Ex. What are the properties of water?
The Properties of Addition
 An
addition property is
“A distinctive quality unique to problems involving addition.”
Commutative Property

Commutative Property


The order in which two numbers are added
does not change the sum
Ex. 5 + 6 = 6 + 5
Commutative Property

How will I remember?
Commute = move from one place to another
(like when you commute to school every
morning)
 With addition, numbers can commute (move
around), and we still get the same answer.

Associative Property

Associative Property




The way three numbers are grouped when
adding does not change the sum
The parentheses are used to show groups
In the order of operations, the numbers in
parentheses are done first (PEMDAS)
Ex. (4 + 3) + 9 = 4 + (3 + 9)
Associative Property

How will I remember?
Associate = to hang out
with someone
(like when you associate
with your homies)
 With addition, numbers
can associate (be
grouped with other
numbers), and we still
get the same answer.

Identity Property

Identity Property

The sum of a number and zero (0) is the
number.
Ex. 14 + 0 = 14

How will I remember?


0 has no identity (poor guy). So there is no way that
this nothing can change a number. He is worthless.
Inverse Property

Inverse Property



The sum of a number and its opposite is zero
(0).
Ex. 24 + -24 = 0
How will I remember?
What’s the opposite of…
Let’s Practice
Which property is represented in the
equation below?
8
+ (-8) = 0
Which property is represented in the
equation below?
8
+ (-8) = 0
Inverse
Property
Which property is represented in the
equation below?
(12
+ 4) +13 = 12 + (4 +13)
Which property is represented in the
equation below?
(12
+ 4) +13 = 12 + (4 +13)
Associative
Property
Which property is represented in the
equation below?
1234
+ 4321 = 4321 + 1234
Which property is represented in the
equation below?
1234
+ 4321 = 4321 + 1234
Commutative
Property
Which property is represented in the
equation below?
98765
+ 0 = 98765
Which property is represented in the
equation below?
98765
+ 0 = 98765
Identity
Property
This addition
stuff is
boring. Can’t
we do
multiplication
now?
Yes yes young
grasshopper. We
can embark on the
wonderful journey
of multiplication
properties!!!
•Distributive Property
•Commutative Property
•Identity Property
•Associative Property
•Inverse Property
Commutative Property

Commutative Property


The order in which two numbers are multiplied
does not change the product
Ex. 5 x 6 = 6 x 5
Commutative Property

How will I remember?
Commute = move from one place to another
(like when you commute to work)
 With addition, numbers can commute (move
around), and we still get the same answer.

Associative Property

Associative Property



The way three numbers are grouped when
multiplying does not change the product
Ex. (4 x 3) x 9 = 4 x (3 x 9)
Ex. (ab)c = a(bc)
Associative Property

How will I remember?
Associate = to hang out
with someone
(like when you associate
with your homies)
 With mutliplication,
numbers can associate
(be grouped with other
numbers), and we still
get the same product.

Identity Property

Identity Property

The product of a number and 1 is the number.
15 1  15

Ex.

How will I remember?

1
I am
worthles
s
Just like 0 in addition, 1 really serves no purpose in
multiplication. It is worthless and has no effect on
the number. It is the 0 of multiplication.
Inverse Property

Inverse Property

The product of a number and its reciprocal is
1.
1
15   1
15

Ex.

How will I remember?


When you are inverted, you are flipped over.
Let’s Practice
Which property is represented in the
equation below?

31(5) = 5(31)
Which property is represented in the
equation below?

31(5) = 5(31)
Commutative
Property
Which property is represented in the
equation below?
1
 39 
1
39
Which property is represented in the
equation below?
1
 39 
1
39
Inverse
Property
Which property is represented in the
equation below?
56342
x 1 = 56342
Which property is represented in the
equation below?
56342
x 1 = 56342
Identity
Property
Which property is represented in the
equation below?
(983
x 3)17 = 983(3 x 17)
Which property is represented in the
equation below?
(983
x 3)17 = 983(3 x 17)
Associative
Property
Distributive Property

Distributive Property


A number outside parenthesis must be
multiplied by everything inside
Ex.
Distributive Property

Distributive Property

A number outside parenthesis must be
multiplied by everything inside
Ex.

How will I remember?



Distribute means “to share.”
The outside number must be distributed (shared)
with every other number.
Distributive Property
Think of it like this…
Ex. 3(5 + 2) = ???

** 3 is the candy.
We must share the candy
with everyone.
That is, we must share 3
with 5 & 2.
3
3
Distributive Property
Think of it like this…
Ex. 6(2 + 7) = ???

There is too much of a
spotlight on 6. The
spotlight must be
shared with 2 and 7
6 (2 + 7)
6(2) + 6(7)
12 + 42
54
Distributive Property
Think of it like this…
Ex. -10(3 + 9) = ???

Uh oh! Don’t lose the
negative sign as you
distribute the
spotlighted number!!
-10(3 + 9)
-10(3) + -10(9)
-30 + -90
-120
Distributive Property
Think of it like this…
Ex. -5(4 – 7) = ???

Make sure you know
where your negative
signs are in this
problem!!!!!
-5 (4 – 7)
-5(4) - -5(7)
-20 – (-35)
15
Here is the same distributive property written …
symbolically:
a
×
(b + c) = a
×
b+ a
×
and pictorially (rectangular array area model):
b
a
a
c
×
b
a
×
c
c
An example: 6 x 13
using your mental math skills . . .
symbolically:
6
×
(10 + 3) = 6
×
10 + 6
and pictorially (rectangular array area model):
10
6
6×
10
3
6
×
3
×
3
And now it’s time for …
No!! It can’t be!!
Say it ain’t so!!
Yes class. It’s time
for variables!!!
Mwahahaha!!!
Distributive Property
Think of it like this…
Ex. 3(x + 4) = ???

There is too much of a
spotlight on 3. The
spotlight must be
shared with x and 4
3 (x + 4)
3(x) + 3(4)
3x + 12
Distributive Property
Think of it like this…
Ex. -11(x + 5) = ???

Uh oh! Don’t lose the
negative sign as you
distribute the
spotlighted number!!
-11 (x + 5)
-11(x) + -11(5)
-11x + -55
Distributive Property
Think of it like this…
Ex. -5(2x – y) = ???

Make sure you know
where your negative
signs are in this
problem!!!!!
-5 (2x – y)
-5(2x) - -5(y)
-10x – (-5y)
Let’s Practice
Distributive Property
1. 4(6 + 5)
2. 6(3 + 8)
3. 15(12 + t)
4. -6(x + 12)
5. -12(3 + r)
6. -15(4 + t)
7. -9(6 + p)
8. -5(7 + t)