Post on 26-Sep-2020
1-1 Properties of Real Numbers
Objectives (What You'll Learn):To graph and order real numbersTo identify and use properties of real numbers
Title: Jun 25 5:52 PM (1 of 10)
Check Skills You'll Need :
Simplify
1. -(-7.2) 2. 1 - (-3)
3. -9 + (-4.5) 4. (-3.4)(-2)
5. -15 6. -2 + 3 3 5 5
*GO FOR HELP - Skills Handbook page 873
Title: Jun 25 6:00 PM (2 of 10)
Subsets of Real Numbers
Real Numbers Examples: -5, -√3, - 1/2, 1, √5, 8/3
Rational NumbersExamples: 1/2, 0.3, 1, 2 2/3, -5/4, -1.07
Integers ..., -2, -1, 0, 1, 2,...
Whole Numbers 0, 1, 2, 3,...
Natural Numbers1, 2, 3,...
Irrational NumbersExamples:
-√3, π, ∛40
Title: Jun 25 6:07 PM (3 of 10)
Subsets of Real Numbers
Real Numbers Examples: -5, -√3, -1/2, 1, √5, 8/3
Rational NumbersExamples: 1/2, 0.3, 1, 2 2/3, -5/4, -1.07
Integers ..., -2, -1, 0, 1, 2,...
Whole Numbers 0, 1, 2, 3,...
Natural Numbers1, 2, 3,...
Irrational NumbersExamples:
-√3, π, ∛40
Numbers
used
for c
ountin
g!
Natural numbers and 0!
Positive and Negative Natural Numbers and zero!
Numbers that c
an be writt
en
as quotien
ts of in
tegers!
Numbers that can't be written
as quotients of integers!
Title: Jun 25 6:07 PM (4 of 10)
Example 1 : Many mathematical relationships involving variables are related to amusemet parks. Which set of real numbers best describes the values for each variable?
A) The cost C in dollars of admission for n people.
C - rational numbers (such as $7.25)
n - whole numbers
B) The park's profit (or loss) P in dollars for each week w of the year.
P - rational number
w - one of the first 52 natural numbers
Title: Jun 25 6:30 PM (5 of 10)
Example 2 : Graph the numbers - 3/2, 1.7 and √5 on the number line.Hint : Re-write each number as a decimal first and it will be easier to graph.
-3/2 =
1.7 =
√5 =
Example 3 : Compare - √0.08 and - √0.1. Use the symbols < and >. Pull from here!
-√0.08 -√0.1
-√0.1 -√0.08
1 02345 1 2 3 4 5
< >
Title: Jun 25 7:00 PM (6 of 10)
Definitions : The opposite or additive inverse of any number a is -a. The sum of opposites is 0.
The reciprocal or multiplicative inverse of any nonzero number a is 1/a. The product of reciprocals is 1.
Example 4 : Find the opposite and the reciprocal of each number.
A) 4 1/5 B) -0.002
Opposite: Opposite:
Reciprocal: Reciprocal:
Title: Jun 25 7:00 PM (7 of 10)
Properties of Real Numbers :
Let a, b, and c represent real numbers.
Property Addition Multiplication
Closure a + b is a real number ab is a real number
Commutative a + b = b + a ab = ba
Associative (a + b) + c = a + (b + c) (ab)c = a(bc)
Identity a + 0 = a, 0 + a = a a(1) = a, 1(a) = a
Inverse a + (-a) = 0 a(1/a) = 1, a not = 0
Distributive a(b + c) = ab + ac
Example 5 : Which property is illustrated?
A) 4 + (-5) = (-5) + 4 Commutative Property of Addition
B) 6(xy) = 6x(y) Associative Property of Multiplication
Title: Jun 25 7:00 PM (8 of 10)
Definition : The absolute value of a real number is its distance from zero on the number line.
Example 6 : Find the following absolute values.
A) |-9| =
B) |0| =
C) |3 - 9| =
Title: Jun 25 8:06 PM (9 of 10)
HOMEWORK:page 8 (3 - 66) multiples of 3
Title: Jun 25 8:17 PM (10 of 10)