1. 1.1 Apply Properties of Real Numbers

2. At the end of this lesson you will…
Use a number line to graph and order real numbers.
Identify properties of and use operations with real numbers.

3. Order the numbers from least to greatest.

4. Real Numbers These are the numbers most often used in algebra.
Subsets of real numbers: whole, integers, rational, and irrational.
You can picture real numbers as points on a line….called a real number line.
There are no “holes” or “gaps” in this number line. It is complete.
The point on a number line that corresponds to a real number is the graph of the number.
The number that corresponds to a point on a number line is the coordinate of the point.

5. The point labeled 0 is the origin.

6. A number line can be used to order real numbers
A number line can be used to order real numbers. The inequality symbols, <, <,>,and > can be used to show the order of two numbers.
1< 2 since 1 is to the “left” of 2
3>-3 since 3 is to the “right” of -3

7. When you add or multiply real numbers, there are several properties to remember:
Let a, b, and c be real numbers.
Property
Addition
Multiplication
Closure
a+b is a real number
ab is a real number
Commutative
a+b = b+a
ab = ba
(a+b)+c = a+(b+c)
(ab)c = a(bc)
Associative
Identity
a+0 =a, 0+a=a
a*1=a, 1*a=a
Inverse
a+(-a)=0
The following property involves both addition and multiplication.
Distributive
a(b+c) = ab + ac

8. Subtraction is defined as adding the opposite, and division as multiplying by the reciprocal.
a – b = a + (-b)
Definition of subtraction
Definition of division

9. The difference between 7 and –10 is:
7-(-10) =
Subtract by adding the “opposite”.

10. The quotient of –24 and 1/3 is:
Division is defined as multiplying by the reciprocal.

11. When you use the operations of addition, subtraction, multiplication, and division in real applications, you should use unit analysis to check that your units make sense.
345 miles – 187 miles = 158 miles