DO NOW Turn in Pre-Assessment Write a few sentences comparing rational and irrational numers –Must give an example of each –State a topic involving each type Look ahead in textbook!!

Algebra 2 Chapter 1 Lessons 1.1 Real Number and Number Operations

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

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 Real Numbers

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

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

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

GUIDED PRACTICE for Examples 1 and 2 Which list shows the numbers in increasing order? 2. – 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.

1.1 Properties of Addition and Multiplication Let a, b, and c be real numbers. PropertyAdditionExampleMultiplicationExample Closure a + b is a real number = -1 ab is a real number ½ (4) = 2 Commutativea+b=b+a-3+7=7+-3ab=ba-4(3)=3(-4) Associative(a+b)+c=a+(b+c)(2+6)+1=2+(6+1)(ab)c=a(bc)(2*7)1=2(7*1) Identity a+0=a, 0+a=a -2+0=-2, 0+-2=-2 a*1=a, 1*a=a ¾ *1= ¾ 1* ¾ = ¾ Inversea+(-a)= =0 a* 1/a = 1, a≠0 2* ½ = 1 Distributive a(b+c)=ab+ac (combines adding & multiplying) 2(1+4)=2*1+2*4

EXAMPLE 3 Identify properties of real numbers Identify the property that the statement illustrates. a = b. 13 = SOLUTION Inverse property of multiplication Commutative property of addition SOLUTION

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

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

Classwork Guided practice Page 6. #1-14

Homework Page 6. #15, 19, 22, 24, 27, 31