Download Algebra I A - Meeting 8

Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 8
Homework # 6 – Word Problems
pg 79 #57
In golf, your score on a hole is the number of strokes above or
below an expected number of strokes needed to hit a ball into a
hole. As shown in the table, each score has a name. When you
compare two scores, the lesser score is the better score.
Name
Double Eagle
Eagle
Birdie
Par
Bogey
Double
Bogey
Score
-3
-2
-1
0
1
2
a) Compare: For three holes, you score an eagle, a double bogey, and a
birdie. Your friend scores a double eagle, a bogey, a bogey, and a par. Who
has the better total score?
b) Explain: Your friend scores a double eagle and an eagle for the next two
holes. Is it possible for you to have a better score on all five holes after your
next two holes? Explain your reasoning.
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 8
Section 2.4 – Multiply Real Numbers
Properties of Multiplication
Property
Definition
Algebra
Example
Commutative
The order in which you multiply two
numbers does not change the product.
a*b=b*a
4 * (-3) = -3 * 4
Associative
The way you group three numbers in a
product does not change the product.
(a * b) * c = a * (b * c)
(-3 * 2) * 4 = -3 * (2 * 4)
Identity
The product of a number and 1 is that
number.
a*1=1*a=a
2*1=2
Zero
The product of a number and 0 is 0.
a*0=0*a=0
-5 * 0 = 0
Negative 1
The product of a number and -1 is the
opposite of the number.
a * (-1) = -1 * a = - a
- 2 * (-1) = 2
Multiplicative Identity – is the number 1.
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 8
Section 2.4 – Multiply Real Numbers
Example # 1
Find the product: -2 * (c * (-0.5)). Justify your steps.
-2 * (c * (-0.5)) = (c * (-0.5)) * (-2)
Commutative Property
= c * (-0.5 * (-2))
Associative Property
=c*1
Multiplication Property
=c
Identity Property
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 8
Section 2.4 – Multiply Real Numbers
Example # 2
From 1900 to 1940, a 250-foot wide beach on the Atlantic coast was eroding at
a rate of about -0.02 feet per year.
From 1940 to 2000, it was eroding at a rate of about -0.12 feet per year.
Approximate the width of the beach in 2000.
Write a verbal model.
New
Original
Average rate
Time
Width of the Beach = Width of Beach + of erosion
* passed
(feet per year)
(years)
(feet)
(feet)
Calculate the Width of the Beach in 1940 (New width of the Beach).
Use the elevation in 1900 as the Original Elevation of the Beach.
The time span is 1940 – 1900 = 40 years. Substitute Values into the verbal model
New width of the Beach = 250 + (-0.02)*(40)
Multiply -0.02 and 40
Width of Beach in 1940 = 250 + (-0.8)
Add 250 and -0.8
Width of Beach in 1940 = 249.2
Did we answer the Question?
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 8
Section 2.4 – Multiply Real Numbers
Example # 2 (con’t)
From 1900 to 1940, a 250-foot wide beach on the Atlantic coast was eroding at
a rate of about -0.02 feet per year.
From 1940 to 2000, it was eroding at a rate of about -0.12 feet per year.
Approximate the width of the beach in 2000.
Calculate the Width of the Beach in 2000. (Final width of the Beach).
Use the elevation in 1940 as the New Original Elevation of the Beach.
The time span is 2000 – 1940 = 60 years. Substitute Values into the verbal model
Final Width of the Beach = 249.2 + (-0.12)*(60)
Multiply -0.12 and 60
Width of Beach in 2000 = 249.2 + (-7.2)
Add 249.2 and -7.2
Width of Beach in 2000 = 242
Approximate Width of the Beach in 2000 is 242 feet
Chapter 2 – Properties of Real Numbers
Section 2.4
Homework # 7
pg 91 # 17 – 43 odd; # 44, # 51
Algebra I A - Meeting 8