1. 1-1 REAL NUMBERS
& NUMBER
OPERATIONS
Today’s Objectives:
I will use a number line to graph and
order real numbers.
I will identify properties of and use
operations with real numbers.

2. Number
Classifications
 Real:
 Rational: can be written as a ratio
(fractions: ½, ¼, 1/5)

Natural: counting #s
(1,2,3,4,5…)
 Whole: natural #s and 0
(0,1,2,3,4,5…)
 Integer: whole #’s and their opposites
(...-3,-2,-1,0,1,2,3…)
 Irrational: can not be written as a ratio because their
decimals do not terminate or repeat
 Imaginary:

3. Subsets of the
Real Numbers
Q - Rational
Z - Integers
I - Irrational
W - Whole
N - Natural

4. Classify each number
-1 real, rational, integer
6 real, rational, integer, whole,
natural
7 real, irrational
1
2 real, rational
0 real, rational, integer, whole
-2.222 real, rational

5. Number Lines
 Real #s can be pictured as points on a line called a
REAL NUMBER LINE .
 Numbers increase from left to right
 Point labeled 0 is the ORIGIN .
 The point on a # line that corresponds to a real # is
the GRAPH of the number.
 Drawing the point is called GRAPHING the
number or PLOTTING the point .
 The # that corresponds to a point on a line is the
COORDINATE of the point.

6. Ordering 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.

7. Decide which number is greater
using < or >. Then graph the
numbers on a number line.
1) 4 ___ 4/3 2) -3/2 ___ -11/3
0 0
– – – – –│ – – – – – – – – – –│ – – – – –
3) -2 ___ √2 4) -4.5 ___ -√24
0 0
– – – – –│ – – – – – – – – – –│ – – – – –

8. Properties of
Real Numbers
 Let a, b, and c be real numbers.
Property Addition Multiplication
Closure a + b is a real # ab is a real #
Commutative a+b=b+a ab = ba
Associative (a + b) + c = a + (b + c) (ab)c = a(bc)
Identity a+0=a a • 1 = a, 1 • a = a
Inverse a + (-a) = 0 a • 1/a = 1, a≠0
Distributive a(b + c) = ab + ac

9. Name the Property
1) 5 = 5+0 1) Additive Identity
2) 5(2 x +7) = 10x+35 2) Distributive
3) Commutative for
3) 8 • 7 = 7 • 8 Multiplication
4) (7+8)+2 = 2+(7+8) 4) Commutative for
Addition
5) 7+(8+2) = (7+8)+2
5) Associative for
6) 5 • 1/5 = 1 Addition
6) Multiplicative
Inverse

10. Operations with
Real Numbers
 Sum:
the answer to an addition problem
 Difference:
the answer to a subtraction problem
 Product:
the answer to a multiplication problem
 Quotient:
the answer to a division problem

11. Identifying
Properties of Real
Numbers
 The opposite, or additive inverse , of
any number a is –a.
 The reciprocal, or multiplicative
inverse , of any nonzero number a is 1/a.
 Subtraction is defined as adding the
opposite .
 Division is defined as multiplying by
the reciprocal .

12. Unit Analysis
 When you use the operations of addition,
subtraction, multiplication, and division in real
life, you should use unit analysis to check
that your units make sense.