Chapter 1 Tools of Algebra. In Chapter 1, You Will… Review and extend your knowledge of algebraic...
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Transcript of Chapter 1 Tools of Algebra. In Chapter 1, You Will… Review and extend your knowledge of algebraic...
In Chapter 1, You Will…
Review and extend your knowledge of algebraic expressions and your skills in solving equations and inequalities.
Solve absolute value equations and inequalities by changing them to compound equations and inequalities.
1-1 Properties of Real Numbers
What You’ll Learn …
To graph and order real numbersTo identify and use properties of real
numbers
Number Classification
• Natural numbers are the counting numbers. 1,2,3,4,…..
• Whole numbers are natural numbers and zero. 0,1,2,3,4,….
• Integers are whole numbers and their opposites. ….-3,-2,-1,0,1,2,3,….
• Rational numbers can be written as a fraction. 7/5, -3/2, 0, 0.3, -1.2, 9
• Irrational numbers cannot be written as a fraction. 2 , 7 ,
• All of these numbers are real numbers.
Real Numbers
Rational Numbers Irrational Numbers
Integers
Whole Numbers
04/2
625
-4
-10 5
-3
58
-2 3 0.37
0.31
10
- 123
23
0.1011001000…
Example 1: Real World Connection
Many mathematical relationships involving variables are related to amusement parks. Which set of numbers best describes the values for each variable?
a. The cost C of admission for n people
b. The maximum speed s in meters per second on a roller coaster of height h in meters
c. The park’s profit (or loss) P in dollars for each week w of the year
Example 1: Check Your Understanding
The number is the ratio of the number of adult tickets sold to the number of children’s tickets sold. Which set of numbers best describes the values of ? Which set of numbers best describes the average cost per family for tickets?
Example 1: Check Your Understanding
A pilot uses the formula to find the distance in miles that can be seen when flying at an altitude of miles. Which set of numbers best describes the values for each variable?
Example 3: Ordering Real Numbers
An inequality is a mathematical sentence that compares the value of two expressions using an inequality symbol.
< Less than
< Less than or equal to
> Greater than
> Greater than or equal to
Compare and . Use the symbols and .
The opposite or additive inverse of any number is .
* The sum of opposites is 0.
The reciprocal or multiplicative inverse of any nonzero number is .
* The product of reciprocals is 1.
Properties of Real Numbers
Find the opposite and the reciprocal of each number.
A.
B.
C.
D.
Example 4: Check Your Understanding
Properties of Real Numbers
Property Addition Multiplication
Closure is a real number is a real number
Commutative
Associative
Identity or or
Inverse
𝑎(𝑏+𝑐)=𝑎𝑏+𝑎𝑐Distributive