Unit7Vol2.notebook
January 25, 2013
Warm Ups
Algebra with Career Applicaons
Blitzer 5.4 Irraonal Numbers
Jan 28­7:14 AM
Jan 28­8:06 AM
Irraonal numbers
Perfect Square
We have discussed raonal numbers are numbers that can be wrien as a rao of two integers. Irraonal numbers are number that cannot be wrien as a rao of two integers. The decimal expansions of irraonal numbers looks like decimals that never end and never repeat with an exact paern. Examples: Jan 28­7:14 AM
Know your perfect squares!
Jan 28­7:14 AM
1
Unit7Vol2.notebook
January 25, 2013
Simplifying Radicals
A square root is asking the queson what number mes itself equals the number inside.
There are two ways to simplify: Greatest square factor and prime factorizaon. Greatest Square Factor: • Look for the greatest factor that is a perfect square. • Break up into two square roots
• Simplify
Simplify: Prime Factorizaon:
• Prime factor the number in the square root. • Take out any matching pair as a single number
• Simplify
Jan 28­7:14 AM
Mulplying Radicals
General Rule: Mulply outside mes outside and inside me inside. Simplify if possible. Examples
Jan 28­7:14 AM
Examples
You may choose to simplify, then mulply, then check to see if it can be simplified further. Jan 28­7:14 AM
Jan 28­7:14 AM
2
Unit7Vol2.notebook
Dividing Radicals
General Rule: Divide outside by outside and inside by inside. You CANNOT leave a radical in the denominator. Jan 28­7:14 AM
Examples
January 25, 2013
Raonalizing the Denominator
When you have a radical in the denominator, you need to write it as a raonal number. Mulply by the square root of a number that will create a perfect square in the denominator and simplify. Jan 28­7:14 AM
Adding and Subtracng Radicals
• Make sure that you have like terms. The numbers in the radicals need to be the same, and then you can add the numbers in front, keeping the radical the same. • You may need to simplify the radicals first. • If the numbers in the radicals are not the same, they cannot be combined. Jan 28­7:14 AM
Jan 28­7:14 AM
3
Unit7Vol2.notebook
January 25, 2013
Assignment: Blitzer p. 269 # 3 ­ 66 mult of 3
Examples
Assignment: Blitzer p. 269 # 3 ­ 66 mult of 3
Jan 28­7:14 AM
Jan 28­7:21 AM
p. 269 # 3 – 66 mult of 3
Algebra with Career Applicaons
Blitzer 5.4 Day 2
Applicaons of Irraonal Numbers
Feb 4­8:29 AM
Feb 4­8:29 AM
4
Unit7Vol2.notebook
p. 269 #79
The graph shows the median heights for boys of various ages in the United States from birth through 60 months (5 years old). Use the graph to esmate the median height, to the nearest inch of boys who are 50 months old. January 25, 2013
p. 270 #82
The data for one of two groups shown by the graphs is modeled by where H is head circumference, in cm, at age x months. According to the model, what is the head circumference at birth? According to the model, what is the head circumference at 9 months?
The formula models the median height, h, in inches of boys who are x months of age. According to the model, what is the head circumference at 14 months? Round to the neares hundredth. According to the formula, what is the median height of boys who are 50 months old? Round to the nearest
tenth. Does the given model describe healthy children, or severe auscs?
Blitzer p. 269 # 77, 78, 80, 81
Feb 4­8:29 AM
Feb 4­8:29 AM
Blitzer p. 269 # 77, 78, 80, 81
Feb 4­8:35 AM
Feb 7­11:14 AM
5
Unit7Vol2.notebook
Feb 7­11:18 AM
January 25, 2013
Feb 7­11:18 AM
p. 269 # 77, 78, 80, 81
Algebra with Career Applicaons
78) 30 mph; She was not speeding
80) a. 36 cm b. 44.7 cm c. 46.9 cm
d. This model describes the head circumferences of healthy children Blitzer 5.5
Real Numbers and Their Properes
Jan 28­7:24 AM
Jan 28­7:24 AM
6
Unit7Vol2.notebook
January 25, 2013
Classifying Real Numbers
Classify each of the following numbers. Real Numbers
Raonal Numbers
Integers
Irraonal Numbers
Whole Numbers
Natural Numbers
Jan 28­7:24 AM
Jan 28­7:24 AM
Commutave Property
Associave Property
For addion or mulplicaon
a + b = b + a
(a)(b) = (b)(a)
For addion or mulplicaon
(a + b) + c = a + (b + c)
(ab)c = a(bc)
My commute is 18 miles from school to home. How far is it from home to school?
Gauss, Newton and Leibnitz are associates. Are Gauss and Newton, Leibnitz associates?
Jan 28­7:24 AM
Jan 28­7:24 AM
7
Unit7Vol2.notebook
Distribuve Property
January 25, 2013
Using properes to do mental math
Mixing addion and mulplicaon. a(b + c) = ab + ac
Mulply (without a calculator). (2)(18)(50)
If I have apples for Ben and Cathy, it is the same as Ben having apples and Cathy having apples. Add 16 + 13 + 37
Mulply (14)(98)
Jan 28­7:24 AM
Jan 28­7:24 AM
Review Unit7 Vol 2
Grade:
Subject: AWCA
Date:
Assignment: BLITZER p. 276 # 1 ­ 4(on handout), 5 ­ 37 odd
Feb 8­2:47 PM
Jan 31­12:51 PM
8
Unit7Vol2.notebook
1
Select all that apply. What type of number is 5? January 25, 2013
2
Select all that apply. What type of number is A Natural Number
A Natural Number
B Whole Number
B
C Integer
C Integer
D Rational Number
D Rational Number
E Irrational Number
E
F
Real Number
Whole Number
Irrational Number
F Real Number
Jan 31­1:01 PM
3
Select all that apply. What type of number is Jan 31­1:03 PM
4
Select all that apply. What type of number is ­3?
A Natural Number
A Natural Number
B Whole Number
B
Whole Number
C Integer
C Integer
D Rational Number
D Rational Number
E
E Irrational Number
F Real Number
Irrational Number
F Real Number
Jan 31­1:06 PM
Jan 31­1:10 PM
9
Unit7Vol2.notebook
5
Select all that apply. What type of number is January 25, 2013
6
Select all that apply. What type of number is 0?
A Natural Number
A Natural Number
B Whole Number
B
C Integer
C Integer
D Rational Number
D Rational Number
E Irrational Number
E
F Real Number
F Real Number
Jan 31­1:03 PM
7
What property is utilized here? (3 x+4y)2 = 6x + 8y
Whole Number
Irrational Number
Jan 31­1:11 PM
8
What property is utilized here? 3(­2)(5)=3(5)(­2)
A Communitive Property
A Commutative Property
B Associative Property
B
C Distributive Property
C Distributive Property
Jan 31­1:18 PM
Associative Property
Jan 31­1:20 PM
10
Unit7Vol2.notebook
9
January 25, 2013
What property is utilized here? (4 +2) + 8 = 4 + (2 + 8)
10.
A Commutative Property
B Associative Property
C Distributive Property
Jan 31­1:23 PM
Jan 31­1:24 PM
p. 276 # 2, 4
Given: Algebra with Career Applicaons
Natural Number
Whole Number
Integers
Rational
Number
Irrational Real Number
2. 4. Answers Blitzer 5.5
Review Jan 28­7:27 AM
Jan 28­7:27 AM
11
Unit7Vol2.notebook
1
January 25, 2013
2
A B C Feb 8­1:27 PM
3
Feb 8­1:42 PM
4
<
A B
>
=
C Feb 8­1:44 PM
Feb 8­1:45 PM
12
Unit7Vol2.notebook
5
January 25, 2013
6
A B C <
>
=
A B
C Feb 8­1:50 PM
7
Feb 8­1:52 PM
8
Feb 8­1:53 PM
<
>
=
Feb 8­1:54 PM
13
Unit7Vol2.notebook
9
January 25, 2013
10 Dominic has 63 toy cars and 84 toy trains. He wants to divide them into groups that contain the same number of vehicles. Also, each group must contain the same type of vehicle (all cars or all trains). What is the largest number of toys that can be put into each group? Feb 8­1:55 PM
Feb 8­1:56 PM
11 A hill is at 573 feet above sea level, and a crater next to it is at 271 feet below sea level. What is the difference in the height between the hill and the crater? Feb 8­1:59 PM
12
Feb 8­2:00 PM
14
Unit7Vol2.notebook
13
January 25, 2013
A
group science project is completed by three students. The first student completes of the project and the second student completes of the project. What fraconal part of the project is completed by the third student? Feb 8­2:01 PM
14
Feb 8­2:04 PM
15
A A B B
C C D D E E
Feb 9­8:25 AM
Feb 9­8:27 AM
15
Unit7Vol2.notebook
16
18
January 25, 2013
17
A A B B
C C D D E E
Feb 9­8:28 AM
Feb 9­8:29 AM
Feb 9­8:30 AM
Feb 8­2:05 PM
A B C D E 16
Unit7Vol2.notebook
January 25, 2013
Review Review # 37 ‐ 42
Given: Natural Number
Whole Number
37. Integers
Rational
Number
X
X
38. 41.
42.
Jan 28­7:27 AM
X
X
X
X
X
Real Number
X
X
39. 40. Irrational X
X
X
X
X
X
X
Jan 28­7:27 AM
17