The document discusses key concepts in algebra including variables, algebraic expressions, factors, products, powers, bases, and exponents. It provides examples of translating verbal expressions to algebraic expressions. Some key points covered are: - Variables represent unspecified numbers in algebraic expressions - Algebraic expressions consist of numbers, variables, and arithmetic operations - Factors are quantities being multiplied and their product is called the product - Exponents indicate the number of times a base is used as a factor - It is necessary to translate verbal expressions to algebraic forms using appropriate math symbols

2. What algebraic expression can be used to find the perimeter of the triangle below? Variables and Expressions a b c

3. What algebraic expression can be used to find the perimeter of the triangle below? Perimeter = a + b + c Variables and Expressions a b c

4. What algebraic expression can be used to find the perimeter of the triangle below? Perimeter = a + b + c In this algebraic expression, the letters a, b, and c are called ________. Variables and Expressions a b c

5. What algebraic expression can be used to find the perimeter of the triangle below? Perimeter = a + b + c In this algebraic expression, the letters a, b, and c are called ________. variables Variables and Expressions a b c

6. What algebraic expression can be used to find the perimeter of the triangle below? Perimeter = a + b + c In this algebraic expression, the letters a, b, and c are called ________. variables In algebra, variables are symbols used to represent unspecified numbers or values. Variables and Expressions a b c

7. What algebraic expression can be used to find the perimeter of the triangle below? Perimeter = a + b + c In this algebraic expression, the letters a, b, and c are called ________. variables In algebra, variables are symbols used to represent unspecified numbers or values. NOTE: Any letter may be used as a variable. Variables and Expressions a b c

8. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Variables and Expressions

9. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions

10. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions

11. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions

12. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions

13. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: In algebraic expressions, we often use a dot or parentheses to indicate multiplication. This is so we don’t mistake the symbol X for the letter (variable) x . Variables and Expressions

14. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: In algebraic expressions, we often use a dot or parentheses to indicate multiplication. This is so we don’t mistake the symbol X for the letter (variable) x . Examples: Variables and Expressions

15. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: In algebraic expressions, we often use a dot or parentheses to indicate multiplication. This is so we don’t mistake the symbol X for the letter (variable) x . Examples: In each expression, the quantities being multiplied are called _______, and the result is called the _______. Variables and Expressions

16. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: In algebraic expressions, we often use a dot or parentheses to indicate multiplication. This is so we don’t mistake the symbol X for the letter (variable) x . Examples: In each expression, the quantities being multiplied are called _______, factors and the result is called the _______. Variables and Expressions

17. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: In algebraic expressions, we often use a dot or parentheses to indicate multiplication. This is so we don’t mistake the symbol X for the letter (variable) x . Examples: In each expression, the quantities being multiplied are called _______, factors and the result is called the _______. product Variables and Expressions

18. It is often necessary to translate verbal expressions into algebraic expressions. Variables and Expressions

19. It is often necessary to translate verbal expressions into algebraic expressions. more than Variables and Expressions Math Translation English word(s)

20. It is often necessary to translate verbal expressions into algebraic expressions. more than addition Variables and Expressions Math Translation English word(s)

21. It is often necessary to translate verbal expressions into algebraic expressions. more than less than addition Variables and Expressions Math Translation English word(s)

22. It is often necessary to translate verbal expressions into algebraic expressions. more than less than addition subtraction Variables and Expressions Math Translation English word(s)

23. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction Variables and Expressions Math Translation English word(s)

24. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication Variables and Expressions Math Translation English word(s)

25. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of Variables and Expressions Math Translation English word(s)

26. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient Variables and Expressions Math Translation English word(s)

27. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Variables and Expressions Math Translation English word(s)

28. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: Variables and Expressions Math Translation English word(s)

29. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: a) Eight more than a number n . Variables and Expressions Math Translation English word(s) translates to

30. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: a) Eight more than a number n . 8 + n Variables and Expressions Math Translation English word(s) translates to

31. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: a) Eight more than a number n . 8 + n b) Seven less the product of 4 and a number x . Variables and Expressions Math Translation English word(s) translates to translates to

32. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: a) Eight more than a number n . 8 + n b) Seven less the product of 4 and a number x . 7 – 4x c) One third of the size of the area a . Variables and Expressions Math Translation English word(s) translates to translates to translates to

33. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: a) Eight more than a number n . 8 + n b) Seven less the product of 4 and a number x . 7 – 4x c) One third of the size of the area a . Variables and Expressions Math Translation English word(s) translates to translates to translates to

34. An expression like x n is called a ______, and is read, “ x to the n th power.” Variables and Expressions

35. An expression like x n is called a ______, power and is read, “ x to the n th power.” Variables and Expressions

36. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. Variables and Expressions

37. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent Variables and Expressions

38. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent The exponent indicates the number of times the _____ is used as a ______. Variables and Expressions

39. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent The exponent indicates the number of times the _____ is used as a ______. base factor Variables and Expressions

40. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent The exponent indicates the number of times the _____ is used as a ______. base factor Variables and Expressions exponent base 4 6 power 6 factors of 4

41. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent The exponent indicates the number of times the _____ is used as a ______. base factor NOTE: It is extremely important that you identify the base correctly. The base is exactly what the exponent is operating on (sitting on top of). Variables and Expressions exponent base 4 6 power 6 factors of 4

42. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent The exponent indicates the number of times the _____ is used as a ______. base factor NOTE: It is extremely important that you identify the base correctly. The base is exactly what the exponent is operating on (sitting on top of). Variables and Expressions exponent base 4 6 power 6 factors of 4 base is only the x base is the ( ) and everything in it.

43. 4 1 4 2 4 3 4 4 3b 5 x n Variables and Expressions Meaning Words Symbols

44. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power Variables and Expressions Meaning Words Symbols

45. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power 4 to the second power or 4 squared Variables and Expressions Meaning Words Symbols

46. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power 4 to the second power or 4 squared 4 to the third power or 4 cubed Variables and Expressions Meaning Words Symbols

47. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power 4 to the second power or 4 squared 4 to the third power or 4 cubed 4 to the fourth power Variables and Expressions Meaning Words Symbols

48. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power 4 to the second power or 4 squared 4 to the third power or 4 cubed 4 to the fourth power 3 times b to the fifth power Variables and Expressions Meaning Words Symbols

49. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power 4 to the second power or 4 squared 4 to the third power or 4 cubed 4 to the fourth power 3 times b to the fifth power x to the n th power Variables and Expressions Meaning Words Symbols

50. To evaluate an expression means to ____________. Variables and Expressions

51. To evaluate an expression means to ____________. find its value Variables and Expressions

52. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 Variables and Expressions

53. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 Variables and Expressions

54. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 = 4 = 25 = 64 = 121 Variables and Expressions

55. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 = 4 = 25 = 64 = 121 Variables and Expressions

56. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 = 4 = 9 = 25 = 36 = 64 = 81 = 121 = 144 Variables and Expressions

57. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 = 4 = 9 = 25 = 36 = 64 = 81 = 121 = 144 Variables and Expressions

58. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 = 4 = 9 = 16 = 25 = 36 = 49 = 64 = 81 = 100 = 121 = 144 = 169 Variables and Expressions

59. Find the perimeter of the triangle. The dimensions are in feet. a b c = 8 = 17 = 15 Variables and Expressions

60. Find the perimeter of the triangle. The dimensions are in feet. a b c Perimeter = a + b + c Write the expression. = 8 = 17 = 15 Variables and Expressions

61. Find the perimeter of the triangle. The dimensions are in feet. a b c Perimeter = a + b + c Write the expression. = 8 + 15 + 17 Substitute values. = 8 = 17 = 15 Variables and Expressions

62. Find the perimeter of the triangle. The dimensions are in feet. a b c Perimeter = a + b + c Write the expression. = 8 + 15 + 17 Substitute values. = 40 Simplify. = 8 = 17 = 15 Variables and Expressions

63. Find the perimeter of the triangle. The dimensions are in feet. a b c Perimeter = a + b + c Write the expression. = 8 + 15 + 17 Substitute values. = 40 Simplify. The triangle has a perimeter of 40 feet. = 8 = 17 = 15 Variables and Expressions

64. Exponents often are used in the formula for area and volume. In fact, the word squared comes from the formula for the area of a square. Variables and Expressions s s Area of a square: A = s 2 The word cubed comes from the formula for the volume of a cube. s s s Volume of Cube: V = s 3

65. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Variables and Expressions

66. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Variables and Expressions

67. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Variables and Expressions

68. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Each dimension of the cubical storage space inside a fireproof safe is 12 inches. What is the volume of the storage space? Variables and Expressions 12 in 12 in 12 in

69. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Each dimension of the cubical storage space inside a fireproof safe is 12 inches. What is the volume of the storage space? Variables and Expressions 12 in 12 in 12 in

70. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Each dimension of the cubical storage space inside a fireproof safe is 12 inches. What is the volume of the storage space? Variables and Expressions 12 in 12 in 12 in

71. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Each dimension of the cubical storage space inside a fireproof safe is 12 inches. What is the volume of the storage space? Variables and Expressions 12 in 12 in 12 in

72. End of Lesson!