1. Algebra 2

2. Objectives 1. Know the classifications of numbers 2. Know where to find real numbers on the number line 3. Know the properties and operations of real numbers

3. Classification of Real Numbers …., -4, -3, -2, -1, 0, 1, 2, 3, 4,… whole numbers integers

4. Classification of Real Numbers rational numbers - numbers that can be written as a fraction or a decimal that repeats or terminates irrational numbers - numbers that can’t be written as a fraction or a decimal that repeats or terminates (π, e, √3)

5. Classification of Real Numbers ClassificationExamples counting (natural) whole integers rational irrational

6. Using a Number Line Locate these numbers on a number line: 1.Convert to decimal 2.Determine range and mark line 3.Plot original values

7. PropertyAdditionMultiplication closurea + b = real numberab = real number

8. PropertyAdditionMultiplication closurea + b = real numberab = real number commutative

9. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + a

10. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba

11. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative

12. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)

13. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc)

14. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identity

15. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = a

16. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a

17. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inverse

18. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0

19. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1

20. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1 distributive

21. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1 distributivea(b + c) = ab + ac opposite of a = -a(additive inverse) inverse of a = 1/a (multiplicative inverse)

22. PropertyAdditionMultiplication closurea + b = real numberab = real number commutativea + b = b + aab = ba associative(a + b) + c = a + (b + c)(ab)c = a(bc) identitya + 0 = aa x 1 = a inversea + -a = 0a x 1/a = 1 distributivea(b + c) = ab + ac Identify the property: 5 + -5 = 0 2(3 · 5) = (2 · 3)5 4(3 + 7) = 4 · 3 + 4 · 7 5 + 3 = 3 + 5 (x + 5) + 4 = x + (5 + 4) 1x = x 2/3 · 3/2 = 1 2 · 3 · 4 = 3 · 2 · 4

23. sum – answer to an addition problem difference – answer to a subtraction problem product – answer to a multiplication problem quotient – answer to an division problem Key Vocabulary

24. Algebra 2

25. Objectives 1. Evaluate algebraic expressions 2. Simplify expressions 3. Apply expressions to real world examples

26. Remember PEMDAS? Parenthesis, Exponents, Multiplication, Division, Addition Subtraction Order of Operations = PEMA Multiplication/division and addition/subtraction have equal priority in an expression. In this case, we just apply the “left to right” rule.

27. PEMA  Please Excuse My Aunt  Penguins Eat Many Alligators  Plaid Eggshells Marinate Aliens  Private Earlobes Memorize Anteaters  Public Education Manipulates Adolescents

28. Examples  Evaluate these expressions. 1) 2) 2-16

29. Examples  Evaluate...  when x = -4.  when x = 3.  when x = ½. -53 108 28

30. Simplifying Expressions like terms - terms that have the same variables with the same powers Simplify these expressions:

31. 1.1 pg. 7 #27, 28, 33-38, 43, 45, 47, 49 1.2 pg. 14 #30-32, 37-40, 48, 50