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 that cannot be written as a fraction

Together the numbers make up the real number line.

5,2,,e

Rational Numbers

Can be broke into class Integers No fractionsWhole Numbers

Just Positive numbers and zeroNatural Numbers

Positive number

So the number 5 is an Natural number, a whole number, an integer, a rational number and a Real number same as

The number – 176 would be an integer, a rational number and a Real Number

The number would be a rational number and a Real Number as would

25

15

7

64.0

Properties of Real Numbers

Commutative property of Addition3 + 8 = 8 + 3

Commutative property of Multiplication

Why state property of Addition, does not subtract work the same why?

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Associative Property

Associative property of Addition

(3 + 2) + 8 = 3 + (2 + 8)

Associative property of Multiplication

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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 number5 + (-5) = 0

In Multiplication is the reciprocal of the number

18

18

Distributive Property

Here is where you multiply across addition or subtract.

Of course we would use Order of Operation to add 4 + 6 first.

But what about this one

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147)2(7 xx

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.

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Homework

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