Transcript 1.2 Properties of Real Numbers

1.2 Properties of
Real Numbers
Here we will classify real numbers
Use the properties to evaluate
expressions.
Real Numbers

Rational numbers 4 , 0.08, 1/5, 7/11
Numbers that can written as a fractions

Irrational Numbers
 Numbers
 , e, 2 , 5
that cannot be written as a fraction
Together the numbers make up the real number line.
Rational Numbers

Can be broke into class
 Integers
No fractions
 Whole Numbers
Just Positive numbers and zero
 Natural Numbers
Positive number
So the number 5 is an Natural number, a
whole number, an integer, a rational 25
number and a Real number same as
The number – 176 would be an integer, a
rational number and a Real Number
7
15
The number
would be a rational
0.46 number and
a Real Number as would
Properties of Real Numbers

Commutative property of Addition
3+8=8+3
Commutative property of Multiplication
68  8 6
Why state property of Addition, does not
subtract work the same why?
Associative Property

Associative property of Addition
(3 + 2) + 8 = 3 + (2 + 8)

Associative property of Multiplication
3  4  5  34  5
Identity element

What is a number that you can add to any
number and not change it.

What is a number that you can multiply to
any number and not change it?
Additive and Multiplicative Inverse

The inverse is the number that brings you
back to the Identity element.

In addition it is the opposite of the number
5 + (-5) = 0
In Multiplication is the reciprocal of the number
1
8 1
8
Distributive Property

Here is where you multiply across addition
or subtract.
34  6  3  4  3  6
Of course we would use Order of
Operation to add 4 + 6 first.
7( x  2)  7 x  14
 But what about this one

Distributive does what its name
mean.

When you distributive paper, everyone in
the row would get a paper.
It would multiply every term (little algebra
expression) in the parentheses.
Simplify an Expression
With using the properties you have
something I call Adding Like Terms
 Adding Like Terms is where you add the
coefficients of the terms with the same
degree and variable.

5x  7 x  12x
Homework

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