Chapter 1 Tools of Algebra. In Chapter 1, You Will… Review and extend your knowledge of algebraic expressions and your skills in solving equations and.

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Presentation transcript:

Chapter 1 Tools of Algebra

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 numbers To 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 NumbersIrrational Numbers Integers Whole Numbers 0 4/ …

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

Example 2: Graphing Numbers on a Number Line Change to Decimals

Example 2: Check Your Understanding Change to Decimals

Example 2: Check Your Understanding Change to Decimals

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

Example 3: Check Your Understanding

Properties of Real Numbers

Example 4: Finding Inverses

Example 4: Check Your Understanding

Properties of Real Numbers PropertyAdditionMultiplication Closure Commutative Associative Identity Inverse Distributive

Example 5: Identify Properties of Real Numbers

Example 5: Check Your Understanding

absolute value of a real number The absolute value of a real number is its distance from zero on the number line. Absolute Value

Example 6: Finding Absolute Value

Critical Thinking