1-1B: Properties of Real Numbers
Objectives:
• To identify opposites and reciprocals of Real numbers.
• To identify properties of Real numbers.
• To take the absolute value of Real numbers.
Opposites and Reciprocals:
• An opposite (or additive inverse) of is so that ( ) + ( ) = 0.
• A reciprocal (or multiplicative inverse) of is so that ( ) ( ) = 1.
Examples:
Find the opposite and reciprocal of the following:
opposite
(a)
4
(b)
(c)
9.2
reciprocal
Properties of Real Numbers:
Think of these properties as "rules" to the game of Algebra!
These rules allow us to get from one step in a problem to another legally.
if a and b are Real,
then a + b is also Real
Closure
Associative
associate = to "hang out" with
Commutative
commute = to move from one place to another
Identity
ID = tells who you are
Inverse
Distributive
Examples:
invert = to "flip"
distribute = to hand out or share
(worksheet)
if a and b are Real,
then (a)(b) is also Real
Absolute Value:
• An absolute value of a Real number is its distance from 0 to that number on the number line.
­10
­9
­8
­7
Examples:
­6
­5 ­4
­3
­2
­1
0
1
2
3
4
5
6
7
8
9
10
rational
real
irrational
real
natural whole
integer rational
real
irrational
real
natural whole
integer rational
real
rational
real
rational
real
Counterexamples:
Prove a statement false by finding one exception to that "rule".
Example:
HW #83) The reciprocal of each whole number is a whole number.
Prove this wrong by finding one example...
we need to find a whole number whose reciprocal is not a whole number.
Counterexample: 5 is a whole number, but the
reciprocal of 5 is , which is not a whole number.