Transcript Evaluating_and_Prope..

Algebra 2
1.3
Pinkston
Review:
Prove that .135 is a rational number.
1000n  135.135
n
.135
999n  135
135 5
n

999 37
Algebraic evaluation
• Algebraic expressions consist of
variables, constants, and mathematical
symbols.
• We substitute numbers for the
variables when we evaluate.
Example 1: Evaluate 2 y  x
for x = 3 and y = 5.
2(5)  3  10  3  13
Example 2: Evaluate (  x )
for x = -7.
    7   7
Example 3: Evaluate x  2 y
for x = 15 and y = -10.
15  2 10  15  2(10)  35
Try This, p. 15
5x  y
for x = 10 and y = 5
5(10)  5  45
( y ) for y = -8
    8     8
x  2 y for x = -16 and y = -4.
16  2 4  16  2(4)  16  8  8
Properties
of Numbers
In
Algebra County
Commutative
Property
We
commute
when we
go back
and forth
from work
to home.
Algebra terms commute
when they trade places
xy
y x
This is a statement of the
commutative property
for addition:
x y  y x
It also works for
multiplication:
xy  yx
To associate with someone
means that we like to
be with them.
The tiger and the panther
are associating with each
other.
They are leaving the
lion out.
In algebra:
( x  y)  z
The panther has decided to
befriend the lion.
The tiger is left out.
In algebra:
x  (y  z )
This is a statement of the
Associative Property:
( x  y)  z  x  ( y  z )
The variables do not change
their order.
The Associative Property
also works for multiplication:
( xy)z  x( yz )
Sometimes executives ask
for help in distributing
papers.
The distributive property only
has one form.
x( y  z )  xy  xz
The
identity
property
makes
me
think
about
my
identity.
The identity property for addition
asks,
“What can I add to myself
to get myself back again?
0x
x_
The identity property for
multiplication
asks,
“What can I multiply to myself
to get myself back again?
1 x
x(_)
A statement of the inverse
property for addition is:
x  ( x )  0
A statement of the inverse
property for multiplication is:
1
x   1
x
 
Some examples of the inverse
property for multiplication are:
1
5   1
2 3
5

1


3 2 
0,1
The above set of numbers is the set
we will work with for this problem. If
we add any two numbers in the set,
do we always get a number in the
set? If so, it has the property of
closure. We also say the set is
closed. Is it?
No, because 1 + 1 = 2
0,1
Is the above set closed over
multiplication?
Yes:
1X1=1
1X0=0
0X0=0
1, 2,3,...
Is the set of natural numbers closed
over subtraction?
No:
4 – 6 = -2
Determine which property of numbers is
illustrated:
1.
2.
3.
4.
5.
(3x  2)4  4(3 x  2) Commutative for mult.
3a  0  3a Identity for addition
r (t  n)  rt  rn Distributive
(9q) y  9(qy ) Associative for multiplication
6  ( y  3)  6  (3  y ) Commutative for addition
6. m2 (1)  m2
Identity for multiplication
Determine which property of numbers is
illustrated:
7. (m  3)  g  m  (3  g ) Assoc for addition
Inverse for addition
8. 3  (3)  0
9. w(a  b)  wa  wb Distributive
1
10. d    1 Inverse for multiplication
d 
SAT Question:
Which of the following number sets has the
property that the sum of any two numbers in the
set is also in the set?
I is correct. The sum of
I.
Even integers
any two even numbers is an
II. Odd integers
even number.
III. Composite numbers
II is not correct. The sum
A. I
of any two odd numbers is
an even number.
B. II
C. III
III is not correct. The sum
D. I and II
of some composite
E. I and III
numbers is prime.
Ex. 20 + 9 = 29
Get ready for a “Small Quiz”
to be written
on your grade sheet.
Quiz. Copy the problems and write the
answer.
1. Evaluate 6( x  4) for x  2
2. Evaluate p  2q for p  3, q  4
Put your grade paper on the front of
your row, quiz side down.