Algebra 2 1.1

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ANSWER 3. What is the difference between a daily low temperature of –5º F and a daily high temperature of 18º F ? Bell Ringer Warm-Ups

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Real Numbers Rational Numbers: Any number that can be written as a fraction where the numerator and denominator are both integers and the denominator doesn’t equal zero Natural (Counting) numbers: N = {1, 2, 3, …} Whole numbers: W = {0, 1, 2, 3, …} Integers: Z = {0, 1, 2, 3, …} Irrational Numbers: Any number that isn’t a rational number Irrational Numbers Rational Numbers Integers Whole Numbers Natural Numbers -5 -2 -1 0 1 2 3 Real Numbers

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EXAMPLE 1 Graph real numbers on a number line SOLUTION

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EXAMPLE 2 Standardized Test Practice SOLUTION From lowest to highest, the elevations are – 408, –156, –86, – 40, –28, and –16.

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GUIDED PRACTICE for Examples 1 and 2 ANSWER

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GUIDED PRACTICE for Examples 1 and 2

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EXAMPLE 3 Identify properties of real numbers Identify the property that the statement illustrates. SOLUTION Inverse property of multiplication Commutative property of addition SOLUTION

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EXAMPLE 4 Use properties and definitions of operations Use properties and definitions of operations to show that a + (2 – a) = 2. Justify each step. SOLUTION Definition of subtraction = a + [(– a) + 2] Commutative property of addition = [a + (– a)] + 2 Associative property of addition = 0 + 2 Inverse property of addition = 2 Identity property of addition

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Identify the property that the statement illustrates. SOLUTION Identity property of addition. Associative property of multiplication. SOLUTION GUIDED PRACTICE for Examples 3 and 4

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Identify the property that the statement illustrates. SOLUTION Identity property of multiplication. Distributive property. SOLUTION GUIDED PRACTICE for Examples 3 and 4

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Use properties and definitions of operations to show that the statement is true. Justify each step. SOLUTION Def. of division GUIDED PRACTICE for Examples 3 and 4 Comm. prop. of multiplication Assoc. prop. of multiplication Inverse prop. of multiplication Identity prop. of multiplication = 4

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Use properties and definitions of operations to show that the statement is true. Justify each step. SOLUTION GUIDED PRACTICE for Examples 3 and 4 Assoc. prop. of addition Combine like terms. Comm. prop. of addition = (3x + 4x) + 6 = 7x + 6

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EXAMPLE 5 Use unit analysis with operations SOLUTION = 9 dollars per hour = 125 miles SOLUTION

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EXAMPLE 5 Use unit analysis with operations SOLUTION = 66 feet per second

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EXAMPLE 6 Use unit analysis with conversions The distance from Montpelier, Vermont, to Montreal, Canada, is about 132 miles. The distance from Montreal to Quebec City is about 253 kilometers.

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EXAMPLE 6 Use unit analysis with conversions SOLUTION

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SOLUTION SOLUTION GUIDED PRACTICE for Examples 5 and 6 11.50 dollars per hour 4.5 hours Solve the problem. Use unit analysis to check your work.

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SOLUTION Solve the problem. Use unit analysis to check your work. GUIDED PRACTICE for Examples 5 and 6 about 37 mph

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SOLUTION Perform the indicated conversion. GUIDED PRACTICE for Examples 5 and 6 450 ft

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SOLUTION Perform the indicated conversion. GUIDED PRACTICE for Examples 5 and 6 32 pints

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SOLUTION Perform the indicated conversion. GUIDED PRACTICE for Examples 5 and 6 504,576,000 sec

Homework 1.1 : 

Homework 1.1 pp. 6 – 9 Exs. 1– 5, 9 –13, 17– 37 odd, 39 – 44, 57– 60, 63