Transcript Slide 1 - Appoquinimink High School

Warm Up Problem
• 1. The area of a circle 6 meters in diameter
exceeds the combined areas of a circle 4
meters in diameter and a circle 2 meters in
diameter by how many square meters?
a)
b)
c)
d)
0
3 pi
4 pi
5 pi
Homework
• Page 11 (26-29,36-39,63-66)
• Page 17 (51-56, 58)
Numbers
September 7, 2010
Vocabulary
• Set: Collection of items.
• Element: Items of a set.
• Subset: A set whose elements belong to
another set.
• Empty Set: Set containing no elements.
• Finite Set: A definite or finite number of
elements.
• Infinite Set: Unlimited or infinite number of
elements.
Types of Numbers
Rational Numbers (Q)
Integers (Z)
Whole Numbers (W)
Natural Numbers
(N)
Irrational
Numbers
Set Notations
• Roster Notation: Elements are listed
inside {}.
{1,2,3,4,5,6}
• Interval Notation: Elements indicating
the endpoints of the set as follows.
– Parenthesis’s: Represents the endpoints are
not included in the answer. (4,12)
– Brackets: Represents the endpoints are
included in the answer. [1,21]
Words
All real
numbers
Except 1
Positive Odd
Numbers
Numbers
within 3 units
of 2.
Roster
Notation
Cannot be
written in
roster
notation.
{1,3,5,7,…}
Cannot be
written.
Interval
Notation
1  x  5
Inequality
Notation
x < 1 or x > 1
(,1)or (1, )
Cannot be
notated.
[-1,5]
Cannot be
notated.
1  x  5
Practice
Write in interval notation.
-10<x<10
-15
-10
-5
0
Order the given numbers from least to
greatest and classify each number by
the subsets of the real numbers.
3
3 2, 7,5.125, 4 , 4.6
5
Properties of Numbers
Words
Numbers
Algebra
3+0=3
N+0=0+N=N
Multiplicative Identity:
The product of a number and
1 is the original number.
2
2
1 
3
3
N*1=1*N=N
Additive Inverse:
The sum of a number and its
opposite, or additive inverse,
is 0.
5 + (-5) = 0
N + (-N) = 0
Additive Identity Property:
The sum of a number and 0
is the original number.
Multiplicative Inverse:
The product of a nonzero
number and its reciprocal, or
multiplicative inverse is 1.
1
8 1
8
1
n   1, (n  0)
n
Words
Closure Property:
The sum or product of any
two real numbers is a real
number.
Numbers
2+3=5
2(3) = 6
Algebra
a b
ab 
Commutative Property:
Add or multiply real
numbers in any order
without changing the result.
7 + 11 = 11 + 7
a+b=b+a
7(11) = 11(7)
ab = ba
Associative Property:
Sum or product of three or
more real numbers is the
same regardless of the way
the numbers are grouped.
(5 + 3) + 7 = 5 + (3 + 7)
(a + b) + c = a + (b + c)
(5 * 3) * 7 = 5 * (3 * 7)
(ab)c = a(bc)
Distributive Property:
When you multiply a sum by
a number, the result is the
same whether you add and
then multiply or vise versa.
5(2 + 8) = 5(2) + 5(8)
a(b + c) = a(b) + a(c)
(2 + 8)5 = (2)5 + (8)5
(b + c)a = (b)a + (c)a
Examples
• Find the additive and multiplicative inverse.
-9
2
3
• Identify the property.
(3 3  5)2  (3 3)2  (5)2
(3  6)  (6)  3  [6  (6)]
• The base price for an airplane ticket from
Austin to Houston is $185. The final price
includes an additional $16 for airport fees
and $12 fuel surcharge. Jose’ purchased a
ticket online for 40% off the base price.
Explain how to use mental math to find
Jose’s final price to the nearest dollar.
Practice Problems
• Identify the property.
1
5c  1
(1  5c) 
2
2
• An art supply company is having a sale on certain
items. Colored Pencils ($8.89), Sketch books
($9.96), Acrylic Paints ($11.99), and Paint Brushes
($14.99). Write an expression and simplify.
– Cost of 3 sketch books at a 10% discount and 5 acrylic
paints at a 25% discount.
Exit Slip
• A store is offering a 25% discount on every
item purchased. To find the total discount on
a purchase, Gary found the sum of the prices
and then multiplied the sum by a quarter.
Maria found the total discount by multiplying
each price by quarter and then adding the
discounts. Do both methods give the same
results? Use properties of real numbers to
explain why or why not.
Place exit slip in the bin on my desk when finished.