Transcript Properties of Real Numbers


The graph shows the cost of bowling
for one person.
a. Make a table.
b. How much does 8
games cost for one
person?
c. What is the total
cost if 4 people
each bowl 4 games? EXPLAIN!
# of
Games
1
Process
3(1)
Cost per
person
$3
2
3(2)
$6
3
3(3)
$9
∶
∶
∶
8
3(8)
$24
n
3(n)
$3n
b. Each game costs $3 for one period.
It costs $24 for one person to play 8
games.
c. Each game costs $3 per person. So
it costs $12 for one person to play 4
games. Therefore, it will cost $48
total for 4 people to play 4 games
each.
Thurs
9/3
Learning Objective:
To graph, order & identify
properties of real #s
Lesson Hw: Pg. 15 # 23 – 33 odd,
1-2
35 – 40 ALL, *50 CC
Algebra II
 To
 To
graph & order real numbers
identify properties of real
numbers
 Use
natural numbers to count
1, 2, 3, …
 NO
ZERO!!!
 Natural
numbers & zero
0, 1, 2, 3, …
 Include
ZERO, think w“hole”
 Natural
numbers, their
opposites, and zero
…–3, –2, –1, 0, 1, 2, 3, …
 Numbers
you can write as a
quotient of integers (fractions)
5
3
1
4
 Decimals terminate (end)
0.5
 Decimals
1. 3
1.75
repeat
1.16
 Decimals
do not repeat nor end
2 ≈ 1.414213 … .
𝜋
 Cannot
be written as a fraction
Real Numbers (R)
1
…- ,
2
0.222, 1, 2,
Rational #
2
3
… –3, –2, –1, 0, 1, 2, 3…
Integers
1, 2, 3… Natural #
𝜋
Irrational #
0, 1, 2, 3… Whole #
5

9=3
R, Q, Z, W, N
R, Q
7

9
–
7
R, Q, Z

7 ≈ 2.6457 …
R, I

9 < 3.8

10 > 3.1
28

9
< 3.2
24

4
> 𝜋
10 ≈ 3.162 …
28
9
= 3.1
 Opposite
– aka additive inverse,
of any number a is –a .
12 & –12
–7 & 7
 Reciprocal
– aka multiplicative
inverse, of any nonzero number
a is
1
.
𝑎
8 &
1
8
5&
1
5
Addition
Multiplication
a
+b is a real #
 ab
is a real #
a
+b=b+a
 ab
= ba

(a+b)+c=a+(b+c)
 (ab)c
= a(bc)
Addition
a+0=a
0 + a = a


0 is the additive
identity
a
+ (–a) = 0
Multiplication
a ∙1= a
 1 ∙ 𝑎= a


1 is the
multiplicative
identity
a
∙
1
𝑎
=1, a≠ 0
Addition
Multiplication

3 ∙ 4 ∙ 5 = 4 ∙ 3 ∙ 5 Commutative
Prop of Mult.
2
 −
3
 3(x
3
−
2
=1
Inverse Prop
of Mult.
+ y) + 2x = (3x + 3y) +2x
Distributive Prop
Use properties of real numbers to
show that 𝑎 + [ 3 + (−𝑎)] = 3
𝑎 + [ 3 + (−𝑎)] = a + [(-a) + 3 ]
=[ a + (-a) ] + 3
=0+3
=3
𝑎 + [ 3 + (−𝑎)] = a + [(-a) + 3 ]
Commutative Prop of Add.
=[ a + (-a) ] + 3
Associative Prop of Add.
=0+3
Inverse Property of Addition
=3
Identity Property of Addition
 Are
there two integers with a
product of –12 and a sum of –3?
 Explain.