1.1 A2.notebook
August 26, 2011
1.1 Properties of Real Numbers
Kudos
Warm up
Know ­ how to classify, order, and graph real
numbers. Know properties of real numbers. Know
definitions of:
absolute value
opposite
inverse
Understand­how number groups are related and why.
See the relationships between number sets.
Do­ Given a real number be able to identify what
number group it belongs to and place it on a number
line. Be able to identify properties that are
demonstrated in math problems.
Aug 16 ­ 9:16 PM
What kinds of numbers are there?
In your groups generate a list of different numbers.
Solve.
1. 3x ­4 = 7
2. 3x ­ 5x = 2x + 1
Challenge:
3. Aug 12­7:08 PM
How can we group these numbers into categories?
1. As a group organize the generated list of numbers into categories of your choosing.
2. Label your categories with names and include a definition.
Aug 16 ­ 9:16 PM
Aug 16 ­ 9:16 PM
Whole Numbers
How do you think someone in another country might group the numbers? Do you think it would be the same or different? Why?
Definition: The whole numbers are the natural numbers
but the set also includes zero, "the hole". Aug 16 ­ 9:32 PM
Aug 16 ­ 9:16 PM
1
1.1 A2.notebook
August 26, 2011
Integers Numbers
Definition: The integers are the natural numbers, their opposites and zero.
Rational Numbers
Definition: Can be written as quotients of integers. Can be written as terminating decimals or
repeating decimals.
Multiplicative Identity: Additive Identity: a + 0 = a
Aug 16 ­ 9:32 PM
Aug 16 ­ 9:32 PM
Irrational Numbers
Natural Numbers
Definition: The natural numbers are the numbers used for counting. When you count you start with....1.
Aug 16 ­ 9:32 PM
Are any of the groups subsets of one another? Can you arrange into a Venn Diagram?
Aug 16 ­ 9:32 PM
Definition: Can't be written as quotients of integers (fractions). Their decimal representation neither terminates
(ends) or repeats.
Aug 16 ­ 9:32 PM
Ordering and comparing­visualize using number line.
a) graph on a number line
b) use <, >, = to put numbers in ascending order
c) use <, >, = to put numbers in descending order
Aug 12­6:56 PM
2
1.1 A2.notebook
August 26, 2011
Properties of Real Numbers
Ordering and comparing­visualize using number line.
a) graph on a number line
b) use <, >, = to put numbers in ascending order
c) use <, >, = to put numbers in descending order
1. The opposite or additive inverse of any numbers a is ­a. The sum of opposites is 0.
2. The reciprocal or multiplicative inverse of any numbers a is . The product of the reciprocals is 1.
3. The absolute value of a number is its distance from zero on the number line and the distance is always positive.
For what values od x does
Aug 12­7:03 PM
Aug 16 ­ 9:57 PM
Practice
Properties of Real Numbers
Property
Closure
Addition
Multiplication
a + b is a real number
Commutative
(Move)
Associative
(Talk)
Identity
a + 0 =a, 0 + a = a
Inverse (or opposites)
Distributive
Aug 12­6:42 PM
2(x +1/2)=2x +2(1/2) =2x + 1
Aug 12­7:21 PM
Homework
Homework
#2 Pg. 8-10: 1-24, 26-84 evens
4(m)1/4 = 4(1/4)m
= [4(1/4)]m
= 1m
= m
Aug 24­11:10 AM
Aug 16 ­ 9:53 PM
3