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Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 7
Section 2.1 – Use Integers and Rational Numbers
Classify the set of numbers listed below:
Real Numbers
0.75
4
-5
-5 0.75
-1/3
14
0
4
Rational Numbers
-1/3
4
14
Integers
4
0
Whole
Numbers
4
0
-5 0.75
-1/3 0
-5
0
Irrational Numbers
14
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 7
Section 2.1 – Use Integers and Rational Numbers
Whole Numbers – are the numbers 0, 1, 2, 3,...
Integers – are the numbers …-3, -2,-1, 0, 1, 2, 3,...
Positive Integers – are integers that are greater than 0.
Negative Integers – are integers that are less than 0.
Rational Numbers – are any integers that can be written as ratios or fraction.
Irrational Numbers – are numbers that cannot be written as a quotient of two integers.
Radicals (Square Roots) – If b2 = a, then b is a square root of a.
Real Numbers – are the collection of all numbers, both rational and irrational.
Opposites – are two numbers that are the same distant from zero on a numberline, but
are on opposite sides of zero.
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 7
Section 2.1 – Use Integers and Rational Numbers
Absolute Value – is the distance from zero to the number on a number line.
The symbol |a| represents the absolute value of a.
Example # 1
For the given value of a, find the |a|.
a) a = -16.2
c) a = 8.4
b)
2
a=
3
d)
4
a=
3
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 7
Section 2.2 – Add Real Numbers
Properties of Addition
Property
Definition
Algebra
Example
Commutative
The order in which you add two numbers
does not change the sum.
a+b=b+a
4 + (-3) = -3 + 4
Associative
The way you group three numbers in a sum
does not change the sum.
(a + b) + c = a + (b + c)
(-3 + 2) +4 = -3 + (2 + 4)
Identity
The sum of a number and 0 is the number.
a+0=0+a=a
2+0=2
Inverse
The sum of a number and its opposite is 0.
a + (-a) = -a + a = 0
5 + (-5) = 0
Additive Identity – is the number 0.
Additive Inverse – is the opposite of the number
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 7
Section 2.2 – Add Real Numbers
Example # 2
The table shows how much weight two dieters lost or gained per month. Which
dieter had the greater weight loss at the end of three months?
Month Dieter A Dieter B
Calculate the Total Weight Loss (TWL) for each dieter.
1
-3.3
-7.6
Dieter A
2
-5.1
+1.2
TWL = -3.3 + (-5.1) + 0.5
TWL = -7.8 + 1.2 + (-0.8)
3
+0.5
-0.8
TWL = -3.3 + ((-5.1) + 0.5)
TWL = -7.8 + (1.2 + (-0.8))
TWL = -3.3 + (-4.6)
TWL = -7.8 + 0.4
TWL = -7.9
TWL = -7.4
Dieter A
Dieter B
Compare the Total Weight Loss (TWL) for each dieter.
|-7.9 | to |-7.4|
7.9 > 7.4
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 7
Section 2.3 – Subtract Real Numbers
Subtraction Rule: to subtract b from a, add the opposite of b to a.
a – b = a + (-b)
14 – 6 = 14 + (-6)
Example # 3
Evaluate the expression x – y + 2.3, when x = 8.8 and y = -1.4.
x – y + 2.3 = 8.8 – ( -1.4) + 2.3
Substitute 8.8 for x and -1.4 for y
= 8.8 + 1.4 + 2.3
Add the opposite of -1.4
= 12.5
Add
Chapter 2 – Properties of Real Numbers
Section 2.1, 2.2, & 2.3
Homework # 6
pg 68 # 42 – 50
pg 77 # 32 – 42 even; # 57
pg 82 # 11 – 19 all; # 32 – 34 all; # 38
Algebra I A - Meeting 7