Learning Targets

1. Learning Targets • · I can use a number line to graph and order real numbers. • · I can identify properties of and use operations with real numbers.

2. Algebra 2 Chapter 1 Lessons 1.1 Real Number and Number Operations

3. 1.1 Real Numbers • Rational Numbers • Can be written as a quotient of integers. • Can be written as decimals that terminate or repeat. • Irrational Numbers • Cannot be written as quotients of integers. • Cannot be written as decimals that terminate or repeat.

4. Real Numbers Natural (Counting) numbers: N = {1, 2, 3, …} Whole numbers: W = {0, 1, 2, 3, …} Integers: Z = {0, 1, 2, 3, …} 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 Irrational Numbers: Any number that isn’t a rational number Real Numbers Rational Numbers Irrational Numbers Integers -5 -2 -1 Whole Numbers 0 Natural Numbers 1 2 3

5. 5 Graph the real numbers – and 3 on a number line. 4 5 Note that –= –1.25. Use a calculator to approximate 3 to the nearest tenth: 4 3 1.7. (The symbol means is approximately equal to.) 5 So, graph – between –2 and –1, and graph 3 between 1 and 2, as shown on the number line below. 4 Learning Target #1. I can use a number line to graph and order real numbers. Example 1 SOLUTION

6. ANSWER The correct answer is D. EXAMPLE 2 Standardized Test Practice SOLUTION From lowest to highest, the elevations are – 408, –156, –86, –40, –28, and –16.

7. 7 1. Graph the numbers – 0.2, , –1, 2 , and –4 on a number line. 10 2 –4 –1 – 0.2 – 2 – 1 – 4 – 3 0 1 2 3 4 7 10 for Examples 1 and 2 GUIDED PRACTICE ANSWER

8. 2. Which list shows the numbers in increasing order? – 0.5, 1.5, – 2, – 0.75, 7 – 0.5, – 2, – 0.75, 1.5, 7 – 2, – 0.75, – 0.5, 1.5, 7 7 , 1.5, – 0.5 , – 0.75, – 2 ANSWER The correct answer is C. for Examples 1 and 2 GUIDED PRACTICE

9. 1.1 Properties of Addition and Multiplication Let a, b, and c be real numbers.

10. 1 7 + 4 = 4 + 7 13 = 1 13 EXAMPLE 3 Identify properties of real numbers Identify the property that the statement illustrates. SOLUTION Commutative property of addition SOLUTION Inverse property of multiplication

11. a + (2 – a) = a + [2 + (– a)] 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 Identity property of addition = 2

12. (2 3) 9 = 2 (3 9) 15 + 0 = 15 for Examples 3 and 4 GUIDED PRACTICE Identify the property that the statement illustrates. SOLUTION Associative property of multiplication. SOLUTION Identityproperty of addition.

13. 4(5 + 25) = 4(5) + 4(25) 1 500 = 500 for Examples 3 and 4 GUIDED PRACTICE Identify the property that the statement illustrates. SOLUTION Distributive property. SOLUTION Identityproperty of multiplication.

14. b (4 b) = 4 whenb = 0 1 1 1 b (4 b) = b (4 ) b b b = b ( 4) = (b ) 4 = 1 4 for Examples 3 and 4 GUIDED PRACTICE Use properties and definitions of operations to show that the statement is true. Justify each step. SOLUTION Def. of division Comm. prop. of multiplication Assoc. prop. of multiplication Inverse prop. of multiplication = 4 Identity prop. of multiplication

15. 3x + (6 + 4x) = 7x + 6 3x + (6 + 4x) = 3x + (4x + 6) for Examples 3 and 4 GUIDED PRACTICE Use properties and definitions of operations to show that the statement is true. Justify each step. SOLUTION Comm. prop. of addition = (3x + 4x) + 6 Assoc. prop. of addition Combine like terms. = 7x + 6

16. You work 4 hours and earn $36. What is your earning rate? You travel for 2.5 hours at 50 miles per hour. How far do you go? 36dollars 4hours 50miles (2.5hours) 1hour EXAMPLE 5 Use unit analysis with operations SOLUTION = 9dollars per hour SOLUTION = 125 miles

17. 5280feet 1hour 1minute 45miles You drive 45 miles per hour. What is your speed in feet per second? 1mile 60seconds 60minutes 1hour EXAMPLE 5 Use unit analysis with operations SOLUTION = 66 feet per second

18. Driving Distance Convert the distance from Montpelier to Montreal to kilometers. Convert the distance from Montreal to Quebec City to miles. 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.

19. 1.61kilometers 213 kilometers 132miles 1mile 1mile 253kilometers 157 miles 1.61kilometers EXAMPLE 6 Use unit analysis with conversions SOLUTION

20. You work 6 hours and earn $69. What is your earning rate? How long does it take to travel 180 miles at 40 milesper hour? for Examples 5 and 6 GUIDED PRACTICE Solve the problem. Use unit analysis to check your work. 11.50dollars per hour SOLUTION SOLUTION 4.5 hours

21. You drive 60 kilometers per hour. What is your speed in miles per hour? for Examples 5 and 6 GUIDED PRACTICE Solve the problem. Use unit analysis to check your work. about 37 mph SOLUTION

22. 150yardstofeet for Examples 5 and 6 GUIDED PRACTICE Perform the indicated conversion. SOLUTION 450 ft

23. 4 gallons to pints for Examples 5 and 6 GUIDED PRACTICE Perform the indicated conversion. SOLUTION 32 pints

24. 16 years to seconds for Examples 5 and 6 GUIDED PRACTICE Perform the indicated conversion. SOLUTION 504,576,000 sec

25. Classwork • Pair- share on #2 to #54 page 7 to 8 (Even Nos Only)