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Chapter 1 Review

Chapter 1 Review. College Algebra. Remember the phrase “ P lease E xcuse M y D ear A unt S ally” or PEMDAS. ORDER OF OPERATIONS 1. P arentheses - ( ) or [ ] 2. E xponents or Powers 3. M ultiply and D ivide (from left to right) 4. A dd and S ubtract (from left to right).

jolene-ramirez
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Chapter 1 Review

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  1. Chapter 1 Review College Algebra

  2. Remember the phrase“Please Excuse My Dear Aunt Sally” or PEMDAS. ORDER OF OPERATIONS 1. Parentheses - ( ) or [ ] 2. Exponents or Powers 3. Multiply and Divide (from left to right) 4. Add and Subtract (from left to right)

  3. Evaluate 7 + 4 • 3. Is your answer 33 or 19? You can get 2 different answers depending on which operation you did first. We want everyone to get the same answer so we must follow the order of operations.

  4. Once again, evaluate 7 + 4  3 and use the order of operations. = 7 + 12 (Multiply.) =19(Add.)

  5. Example #114 ÷ 7 • 2 - 3 = 2 • 2 - 3 (Divide l/r.) = 4 - 3 (Multiply.) = 1(Subtract.)

  6. Example #23(3 + 7) 2 ÷ 5 = 3(10) 2 ÷ 5 (parentheses) = 3(100) ÷ 5 (exponents) = 300 ÷ 5 (multiplication) =60 (division)

  7. Example #320 - 3 • 6 + 102 + (6 + 1) • 4 = 20 - 3 • 6 + 102 + (7) • 4 (parentheses) = 20 - 3 • 6 + 100 + (7) • 4 (exponents) = 20 - 18 + 100 + (7) • 4 (Multiply l/r.) = 20 - 18 + 100 + 28 (Multiply l/r.) = 2 + 100 + 28 (Subtract l/r.) = 102 + 28 (Add l/r.) =130 (Add.)

  8. Answer Now Which of the following represents 112 + 18 - 33· 5in simplified form? • -3,236 • 4 • 107 • 16,996

  9. Answer Now Simplify16 - 2(10 - 3) • 2 • -7 • 12 • 98

  10. Answer Now Simplify24 – 6 · 4 ÷ 2 • 72 • 36 • 12 • 0

  11. Evaluating a Variable ExpressionTo evaluate a variable expression: • substitute the given numbers for each variable. • use order of operations to solve.

  12. Example # 4 n + (13 - n)  5 for n = 8 = 8 + (13 - 8)  5 (Substitute.) = 8 + 5 5 (parentheses) = 8 + 1 (Divide l/r.) = 9(Add l/r.)

  13. Example # 5 8y - 3x2+ 2n for x = 5, y = 2, n =3 = 8  2- 3  52 + 2  3 (Substitute.) = 8  2 - 3  25 + 2  3 (exponents) = 16- 3  25 + 2  3 (Multiply l/r.) = 16 -75 + 2  3 (Multiply l/r.) = 16 - 75 + 6 (Multiply l/r.) = -59 + 6 (Subtract l/r.) = -53 (Add l/r.)

  14. Answer Now What is the value of -10 – 4x if x = -13? • -62 • -42 • 42 • 52

  15. Answer Now What is the value of 5k3 if k = -4? • -8000 • -320 • -60 • 320

  16. Answer Now What is the value ofif n = -8, m = 4, and t = 2 ? • 10 • -10 • -6 • 6

  17. Evaluating Algebraic Expressions

  18. Expressions An expression is NOT an equation because it DOES NOT have an equal sign. There are 2 types of expressions. • 5 + 84 Numerical • 3x + 10 Algebraic Notice there are no equal signs in these expressions so they are not equations!

  19. Expressions A numerical expression contains only numbers and symbols and NO LETTERS. 5 times 3 plus 8 (5•3) + 8

  20. Expressions An algebraic expression contains only numbers, symbols, and variables. It is sometimes referred to as a variable expression. • The product of 3 and x 3x • The sum of m and 8 m + 8 • The difference of r and 2 r - 2

  21. Expressions What is a variable? A variable represents an unknown value. 2) 10 – ? 1) 4 + x 4) 20 3) 5y A variable can be any letter of the alphabet since it represents an unknown.

  22. Expressions Word Phrases for multiplication are: • The product of 5 and a number c • Seven times a number t • 6 multiplied by a number d 5 • c or 5c 7 • t or 7t 6 • d or 6d

  23. Expressions The Placement rule for multiplication is: • The product of 5 and a number c • Seven times a number t • 6 multiplied by a number d 5 • c or 5c • Always write the variable AFTER the number. 7 • t or 7t 6 • d or 6d

  24. Expressions Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. m = 2 6 + m ? 6 + 2 8

  25. Expressions Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. r = 3 7 + r ? 7 + 3 10

  26. Expressions Evaluate the variable expression when n = 6. 1) 2) Evaluate just means solve by substitution.

  27. Expressions Evaluate the variable expression when n = 6. 4) 3) Evaluate just means solve by substitution.

  28. Expressions Evaluate the algebraic expression when n = 8. 1) 2)

  29. Expressions Evaluate the expression if a = 3 and b = 4. 1) 2)

  30. Expressions Evaluate the expression if a = 3 and b = 4. 3) 4)

  31. Expressions Evaluate the expression if x = 5 and y = 3. 2) 1)

  32. Substitute & Evaluate #2 Evaluate ifx = 3 and y = 4 Evaluate means solve. Show the substitution. Show your work down. Circle your answer. Show your work one step at a time down. No equal signs!

  33. Combining Like Terms • In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! • To simplify an expression we collect like terms. Like terms include letters that are the same and numbers.

  34. Let’s try one… • Step One: Write the expression. 4x + 5x -2 - 2x + 7 • Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it. 4x, 5x, and -2x -2 and 7 • Simplify the variable terms. 4x+5x-2x = 9x-2x = 7x • Simplify the constant (number) terms. -2+7 = 5 • You have a simplified expression by writing all of the results from simplifying. 7x + 5

  35. Another example… • 10x – 4y + 3x2 + 2x – 2y 3x2 10x, 2x -4y – 2y • 3x2+ 12x– 6y Remember you cannot combine terms with the same variable but different exponents.

  36. Now you try… Simplify the following: • 5x + 3y - 6x + 4y + 3z • 3b - 3a - 5c + 4b • 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4 • 5xy – 2yx + 7y + 3x – 4xy + 2x A A A A

  37. You Try #1 • Simplify the following: • 5x + 3y - 6x + 4y + 3z 5x, -6x 3y, 4y 3z -x+ 7y+ 3z

  38. You Try #2 • Simplify the following: • 3b - 3a - 5c + 4b 3b, 4b -3a -5c -3a+ 7b – 5c

  39. You Try #3 • Simplify the following: • 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4 4ab, -ab -2a2b, 2a2b 5, 4 ab2 3ab+ ab2+ 9

  40. You Try #4 • Simplify the following: • 5xy – 2yx + 7y + 3x – 4xy + 2x 5xy, -2yx, -4xy 7y 3x, 2x -xy+ 7y+ 5x

  41. Properties by Mr. Fitzgerald

  42. Distributive • Commutative • “order doesn’t matter” • Associative • “grouping doesn’t matter” • Identity properties of one and zero • Inverse “opposite” Five Properties

  43. Which Property?

  44. 1. Which Property? (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition

  45. 2. Which Property? 3 + 7 = 7 + 3 Commutative Property of Addition

  46. 3. Which Property? 8 + 0 = 8 Identity Property of Addition

  47. 5. Which Property? 6 • 4 = 4 • 6 Commutative Property of Multiplication

  48. 6. Which Property? 17 + (-17) = 0 Inverse Property of Addition

  49. 7. Which Property? 2(5) = 5(2) Commutative Property of Multiplication

  50. 9. Which Property? 3(2 + 5) = 3•2 + 3•5 Distributive Property

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