2. EL CENTRO COLLEGE Developmental Math 0090 REVIEW ECC by Diana Moore

3. DMAT 0090, Objectives DMAT 0090 has 20 course objectives. The objectives correspond to course description stated in the college catalog. DMAT 0090 has 20 course objectives. The objectives correspond to course description stated in the college catalog. The only prerequisite for DMAT 0090 is an adequate assessment test score. The only prerequisite for DMAT 0090 is an adequate assessment test score.

4. DMAT 0090, Objective #1 Demonstrate knowledge of the base ten numeration system using both words and symbols. Demonstrate knowledge of the base ten numeration system using both words and symbols.

5. Demonstrate knowledge of the base ten numeration system using both words and symbols. 5 6 8. 2 5 Express this number in words. This number is: five hundred sixty-eight and twenty-five hundredths Consider place value hundreds tens ones thousands tenths hundredths thousandths ---- and -----

6. Demonstrate knowledge of the base ten numeration system using both words and symbols. Express this statement in numerical form. two thousand, forty-five and sixteen thousandths 2 0 4 5. 0 1 6 Consider place value hundreds tens ones thousands tenths hundredths thousandths ---- and -----

7. Use the operations of addition, subtraction, multiplication and division on the set of whole numbers. Use the operations of addition, subtraction, multiplication and division on the set of whole numbers. DMAT 0090, Objective #2

8. Use the operations of addition, subtraction, multiplication and division on the set of whole numbers. Find the sum of the following whole numbers: 16, 289, 7 and 1203 16 289 7 + 1203 12 0 1515 The sum is 1515

9. 7 8 _ / 1 / 1 2 5 3 3 8 Use the operations of addition, subtraction, multiplication and division on the set of whole numbers. Find the difference of the following whole numbers: 8092 and 2754 8 0 9 2 – 2 7 5 4 The difference is 5338.

10. Use the operations of addition, subtraction, multiplication and division on the set of whole numbers. Find the product of the following whole numbers: 3072 and 419 3072 x 419 27648 30720 1228800 The product is 1287168. 1287168

11. Subtract 8 Use the operations of addition, subtraction, multiplication and division on the set of whole numbers. Find the quotient of the following whole numbers: 3698 and 28 28 3698 multiply 1 x 28= 28 Subtract 5 Subtract 2 9 bring down 1 divide 36 28 3 divide 89 28 multiply 3 x 28= 84 multiply 2 x 28= 56 8 bring down 2 divide 59 28 The quotient is 132 and the remainder is 2.

12. Use the proper order of operations to simplify numerical statements. Use the proper order of operations to simplify numerical statements. DMAT 0090, Objective #3

13. Use the proper order of operations to simplify numerical statements. Order of operations Grouping symbols Exponents Multiply or divide (in order from left to right) Add or subtract (in order from left to right)

14. Use the proper order of operations to simplify numerical statements. Simplify the expression: 8 2 + 7(6 – 2) 2 Grouping symbols: 8 2 + 7(4) 2 Exponents: 64 + 7(16) Multiply or divide: 64 + 112 (in order from left to right) Add or subtract: 176 (in order from left to right)

15. Evaluate a given algebraic expression with rational numbers. Evaluate a given algebraic expression with rational numbers. DMAT 0090, Objective #4

16. Evaluate a given algebraic expression with rational numbers. Given x = 3, y = 7, and z = 9, evaluate the expression: 5x – (z – y) 2 Substitute5(3) – (9 – 7) 2 Grouping symbols: 5(3) – (2) 2 Exponents: 5(3) – 4 Multiply or divide: 15 – 4 (in order from left to right) Add or subtract: 11 (in order from left to right) The value of the expression is 11

17. Use both the division rules and prime factorization of whole numbers to find the least common multiple. Use both the division rules and prime factorization of whole numbers to find the least common multiple. DMAT 0090, Objective #5

18. Use both the division rules and prime factorization of whole numbers to find the least common multiple. Division Rules Division by 2: last digit is even Division by 3: sum of digits is divisible by 3 Division by 5: last digit is 0 or 5

19. Use both the division rules and prime factorization of whole numbers to find the least common multiple. Use the division rules and the given number to determine the following. 3549 is divisible by 3. 6009 is divisible by 2. 4580 is divisible by 5. True: 3 + 5 + 4 + 9 = 21 21 is divisible by 3 False: The last digit is not even. True: The last digit is zero.

20. Use both the division rules and prime factorization of whole numbers to find the least common multiple. Use prime factorization to find the LCM of the following numbers: 81 and 18 1 3 3 9 3 27 3 81 1 3 3 9 2 18 81 = (3)(3)(3)(3) 18 = (2)(3)(3) (2)(3)(3)(3)(3) LCM = 162

21. Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers. Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers. DMAT 0090, Objective #6

22. Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers. Add: 2 3 15 10 + Prime factorization 15 = (3)(5) 10 = (2) (5) (2) (3) (5) LCD = 30 2 3 15 10 ( ) + ( ) 2 3 4 9 30 30 + 13 30 The sum is

23. 6 8 Add: 3 2 5 3 + 5 and 3 are prime numbers LCD = 15 3 2 5 3 ( ) + ( ) 3 5 6 8 9 10 15 15 + 4 15 Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers. 6 8 14 19 15 = 15

24. Reduce the answer = 1 6 Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers. Subtract: 7 3 15 10 - 15 = (3)(5) 10 = (2) (5) (2) (3)(5) LCD = 30 7 3 15 10 ( ) - ( ) 2 3 14 9. 30 30 - 5. 30

25. Subtract: 1 2 5 3 3 10 15 15 - 8 5 - 5 and 3 are prime numbers LCD = 15 1 2 5 3 ( ) - ( ) 3 5 2 8. 15 Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers. 7 +15 15

26. 2 3. Prime factorization (3)(5) (2)(5) 1 1 / / / / Cross cancel Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers. Multiply: 2 3 15 10 1 25 Multiply The product is 1. 25

27. (2)(3)(7) (5)(5) Prime factorization 5 (2)(3) 1 1 1 / / / / / / Cross cancel Multiply: 2 1. 5 6 8 4 Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers. 35 Multiply 1 4225 Improper 5 6 fraction = 35 Reduce

28. 2 10 Change to 15 3 reciprocal Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers. Divide: 2 _ 3 15 10 2 (2)(5) Prime factorization (3)(5) 3 1 / / Cross cancel 4 9 Multiply The quotient is 4 4. 9

29. 10 5 Change to 3 12 reciprocal Use the operations of addition, subtraction, multiplication, and division on positive fractions or mixed numbers. Divide: 1 _ 2. 3 5 (2)( 5) 5 Prime factorization 3 (2)(2)(3) 1 / / Cross cancel 25 Multiply 18 3 2 10 _ 12 Improper 3 5 fraction = 1 7 18 Mixed number

30. Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers. Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers. DMAT 0090, Objective #7

31. and Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers. 2525 Convert the following fractions to decimals. = 5 2.0 2 0 0 0.4 1616 = 6 1.000 6 40 36 4 0.166 = 0.16 Example 1 Example 2 2525 = 0.4 1616 _ = 0.16

32. Line up the decimals points 11.560 28.900 27.000 + 1.203 Find the sum of the following decimal numbers: 11.56, 28.9, 27 and 1.203 The sum is 68.663 Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers. __0 _00 000 optional: add zeros 11000 0 68.663

33. Line up the decimals points 6 3. 0 0 - 1 4. 2 8 Find the difference of the following decimals numbers: 63 and 14.28 Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers. 0 0 required: add zeros The difference Is 48.72 5 1 2 _ 9 0 / / 1 / 1 _ 4 8. 7 2

34. Find the product of the following decimal numbers: 30.72 and 41.9 30.72 x 41.9 27 648 30 720 1228 800 The product is 1287.168. 1287.168 Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers.

35. . place the decimal point multiply 7 x 25= 1 7 5 2.5 3.6 9 Subtract 11 Find the quotient of the following decimal numbers: 3.69 and 2.5 multiply 1 x 25= 2 5 Subtract 1 9 Subtract 1 5 9 bring down 1 divide 36 25 4 divide 119 25 multiply 4 x 25= 10 0 0 add zero 0 bring down 7 divide 190 25 0 add zero 0 bring down 2 Change fractions to decimals and perform the operations of addition, subtraction, multiplication and division on decimal numbers. 6 divide 150 25 The quotient is 1.476

36. Solve applied problems using a variety of methods, including proportions and first degree equations. Solve applied problems using a variety of methods, including proportions and first degree equations. DMAT 0090, Objective #8

37. Solve applied problems using a variety of methods, including proportions and first degree equations. Steps for solving application problems Identify Setup Solve Check Explain

38. Solve applied problems using a variety of methods, including proportions and first degree equations. A car traveled 160 miles in 3 hours. If the car continues at the same speed, how far will he travel in 5 hours? Identify 160 miles = 53 1 / 3 mph 3 hours Setup: (53 1 / 3 mph)(5 hrs) Solve 160. 5 = 266 2 / 3 3 1 Explain: The car will travel 266 2 / 3 miles.

39. Solve applied problems using a variety of methods, including proportions and first degree equations. A car traveled 160 miles in 3 hours. If the car continues at the same speed, how far will he travel in 5 hours? Identify 160 miles = x miles Setup 3 hours 5 hours Solve 3(x) = 160(5) 3x = 800 x = 266 2 / 3 Explain: The car will travel 266 2 / 3 miles.

40. Solve 3 2 3 2 3 2 ( ) Solve applied problems using a variety of methods, including proportions and first degree equations. How many 2 / 3 cup jars can be filled from an 8 cup pitcher? Identify 1 jar = 2 / 3 cup total = 8 cup x = number of jars Setup 2 3 Explain: You can fill 12 jars. x = 8 x = 12

41. Solve applied problems using a variety of methods, including proportions and first degree equations. The sum of two number is 19. One number is 5 more than the other. Identify The two numbers are x and x + 5 Setup 1 st number + 2 nd number = sum Solve x + x + 5 = 19 2x + 5 = 19 2x = 14 x = 7 second number x+5 = 12 Explain: The two numbers are 7 and 12.

42. Use percents to describe common fractions and decimals, to make comparisons between numbers and to solve for the rate, base, and amount in applied problems. Use percents to describe common fractions and decimals, to make comparisons between numbers and to solve for the rate, base, and amount in applied problems. DMAT 0090, Objective #9

43. Use percents to describe common fractions and decimals, to make comparisons between numbers and to solve for the rate, base, and amount in applied problems. Convert the following to percents 3535 3535 (100%) 60% Example 2: 0.175 0.175(100%) 17.5% Example 1:

44. < Use percents to describe common fractions and decimals, to make comparisons between numbers and to solve for the rate, base, and amount in applied problems. Place or = in the space between the numbers 3535 3535 (100%) 60% 0.601 0.601(100%) 60.1%

45. Use percents to describe common fractions and decimals, to make comparisons between numbers and to solve for the rate, base, and amount in applied problems. rate amount 100 base 13 25 = What percent of 25 is 13? R 100 = 25R = 13(100) Cross Multiply 25R = 1300 Solve R = 52 The rate is 52%

46. rate amount 100 base Use percents to describe common fractions and decimals, to make comparisons between numbers and to solve for the rate, base, and amount in applied problems. 27 B = 30% of what number is 27? 30 100 = 30B = 27(100) Cross Multiply 30B = 2700 Solve B = 90 The base is 90.

47. Use percents to describe common fractions and decimals, to make comparisons between numbers and to solve for the rate, base, and amount in applied problems. A 150 What number is 40% of 150? 40 100 = 100A = 40(150) Cross Multiply 100A = 6000 Solve A = 60 The amount is 60. rate amount 100 base =

48. Interpret a chart or graph. Interpret a chart or graph. DMAT 0090, Objective #10

49. The bar graph above illustrates the number of cars sold in the first seven months of 2001. How many cars were sold in March? Approx. 35 cars How many cars were sold in June and July? Approx. 15 + 20 = 35 cars How many more cars were sold in April than May? Approx. 58 – 45 = 13 cars Interpret a chart or graph. 70 60 50 40 30 20 10 0 J F M A M J J In which month were the most cars sold? January, 60 cars were sold

50. Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles. Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles. DMAT 0090, Objective #11

51. Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles. Rectangle: A = LW Parallelogram:A = bh Triangle:A = 1 bh 2 Trapezoid:A = 1 h(a + b) 2 Area of Polygons:

52. Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles. Any Polygon:P = add all sides Any Quadrilateral:P = add 4 sides Rectangle: P = 2L + 2W Triangle:A = a + b + c Perimeter of Polygons:

53. Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles. Given the polygon: 3 ft 5 ft4 ft 5 ft 8 ft Identify the figure:___________________. trapezoid Find the area:_______________________. Find the perimeter:___________________. 1 h(a+b) = 4(3+8) 2 2 = 22 ft 2 add all sides 8+5+3+5 = 21 ft

54. Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles. Area:A =  r 2 Circumference:C = 2  r or C = dr r = radius, d = diameter,  = 3.14 Circle formula: r d

55. Use the formulas for perimeter and area of common geometric figures including, triangles, quadrilaterals, and circles. Given the Circle: Identify the figure:___________________. circle with radius Find the area:_______________________. Find the circumference:_______________.  r 2 = 3.14(5) 2 = 78.5 ft 2 2  r = 2(3.14)(5) = 31.4 ft 5 ft

56. Use operations with signed (real) numbers. Use operations with signed (real) numbers. DMAT 0090, Objective #12

57. Use operations with signed (real) numbers. Addition Rules Add like signs p + p = p n + n = n Subtract unlike signs p + n = subtract & find sign n + p = subtract & find sign

58. Use operations with signed (real) numbers. Which rule applies to the expression 3 + 4 p + p = p 3 + 4 = 7 positive 3 plus positive 4 equals positive 7 Add 3 + 4 and keep the positive sign.

59. Use operations with signed (real) numbers. Which rule applies to the expression –5 + (–9) n + n = n –5 + (–9) = –14 negative 5 plus negative 9 equals negative 14 Add 5 + 9 and keep the negative sign.

60. Use operations with signed (real) numbers. Which rule applies to the expression 15 + (–8) p + n = subtract & find the sign 15 + (–8) = 7 positive 15 plus negative 8 equals positive 7 Subtract 15 – 8 and use the sign of the number with the largest absolute value.

61. Use operations with signed (real) numbers. Which rule applies to the expression 6 + (–9) p + n = subtract & find the sign 6 + (–9) = –3 positive 6 plus negative 9 equals negative 3 Subtract 9 – 6 and use the sign of the number with the largest absolute value.

62. Use operations with signed (real) numbers. Which rule applies to the expression –6 + 8 n + p = subtract & find the sign –6 + 8 = 2 negative 6 plus positive 8 equals positive 2 Subtract 8 – 6 and use the sign of the number with the largest absolute value.

63. Use operations with signed (real) numbers. Which rule applies to the expression –7 + 3 n + p = subtract & find the sign –7 + 3 = –4 negative 7 plus positive 3 equals negative 4 Subtract 7 – 3 and use the sign of the number with the largest absolute value.

64. Use operations with signed (real) numbers. Subtraction Rules: Change to addition Subtract like signs p – p change to p + n n – n change to n + p Add unlike signs p – n change to p + p n – p change to n + n

65. Use operations with signed (real) numbers. Which addition rule applies to the expression 6 – 9 p + n = subtract & find the sign 6 + (–9) = –3 positive 6 plus negative 9 equals negative 3 Subtract 9 – 6 and use the sign of the number with the largest absolute value.

66. Use operations with signed (real) numbers. Which addition rule applies to the expression –6 – (–8) n + p = subtract & find the sign –6 + 8 = 2 negative 6 plus positive 8 equals positive 2 Subtract 8 – 6 and use the sign of the number with the largest absolute value.

67. Use operations with signed (real) numbers. Which addition rule applies to the expression 3 – (–4) p + p = p 3 + 4 = 7 positive 3 plus positive 4 equals positive 7 Add 3 + 4 and keep the positive sign.

68. Use operations with signed (real) numbers. Which addition rule applies to the expression –3 – 7 n + n = n –3 + (–7) = –10 negative 3 plus negative 7 equals negative 10 Add 3 + 7 and keep the negative sign.

69. Use operations with signed (real) numbers. Multiplication and Division Rules: Multiply and divide like signs p(p) = p and p / p = p n(n) = p and n / n = p Multiply and divide unlike signs p(n) = n and p / n = n n(p) = n and n / p = n

70. Use operations with signed (real) numbers. Which rule applies to the expression 3(4) p(p) = p 3(4) = 12 positive 3 times positive 4 equals positive 12

71. Use operations with signed (real) numbers. Which rule applies to the expression –6 –2 n = p n –6 = 3 –2 Negative 6 divided by negative 2 equals positive 3.

72. Use operations with signed (real) numbers. Which rule applies to the expression 3(–8) p(n) = n 3(–8) = –24 positive 3 times by negative 8 equals negative 24.

73. Use operations with signed (real) numbers. Which rule applies to the expression 16 –4 p = n n 16 = –4 –4 Positive 16 divided by negative 4 equals negative 4.

74. Identify numerical coefficients, variables and constants. Identify numerical coefficients, variables and constants. DMAT 0090, Objective #13

75. Identify numerical coefficients, variables and constants. Given the algebraic expression: 2x + 7y – 9 What are the coefficients? 2, 7, and –9 What are the variables? x and y What are the constant terms? –9

76. Identify and apply the commutative, associative and distributive properties. Identify and apply the commutative, associative and distributive properties. DMAT 0090, Objective #14

77. Identify and apply the commutative, associative and distributive properties. Given a + (b + c) = (a + b) + c Identify the property. Associative property Complete the statement. 4 + (7 + 9) = (4 + 7) + 9 4 + 16 = 11 + 9 20 = 20

78. Identify and apply the commutative, associative and distributive properties. Given a + b = b + a Identify the property. Commutative property Complete the statement. 12 + 16 = 16 + 12 28 = 28

79. Identify and apply the commutative, associative and distributive properties. Given a(b + c) = ab + ac Identify the property. Distributive property Complete the statement. 8(3 + 9) = 8(3) + 8(9) 8(12) = 24 + 72 96 = 96

80. Combine like terms with the distributive property. Combine like terms with the distributive property. DMAT 0090, Objective #15

81. Combine like terms with the distributive property. Simplify the expression: 2x – 3(4x – 1) + 5 2x – 3(4x – 1) + 5 2x – 12x + 3 + 5 distribute –3 –10x + 8 add like terms The simplified expression is –10x + 8

82. Demonstrate that a given number is a solution to a first degree equation. Demonstrate that a given number is a solution to a first degree equation. DMAT 0090, Objective #16

83. Demonstrate that a given number is a solution to a first degree equation. Given x = -5, show that x is the solution to the equation: 7x – 1 = –36 7x – 1 = –36 7(–5) – 1 –36 Substitute –35 – 1 –36 Simplify –36 –36 The solution is x = –5 Both sides have the same value.

84. Solve first degree equations of the form Solve first degree equations of the form a + x = b a + x = b ax = b ax = b a(bx + c) = d a(bx + c) = d Where a, b, c, and d are rational numbers. DMAT 0090, Objective #17

85. Solve first degree equations of the form a + x = b ax = b a(bx + c) = d Where a, b, c, and d are rational numbers. Use the addition property of equality. Solve the equation. x + 5 = 2 x + 5 + (–5) = 2 + (–5) x + 0 = –3 x = –3 The solution is x = –3

86. Solve first degree equations of the form a + x = b ax = b a(bx + c) = d Where a, b, c, and d are rational numbers. Use the addition property of equality. Solve the equation. –2 + x = 7 –2 + x + (2) = 7 + (2) x + 0 = 9 x = 9 The solution is x = 9

87. Solve first degree equations of the form a + x = b ax = b a(bx + c) = d Where a, b, c, and d are rational numbers. Use the multiplication property of equality. Solve the equation. –5x = 20 –5 –5 x = –4 The solution is x = –4

88. Solve first degree equations of the form a + x = b ax = b a(bx + c) = d Where a, b, c, and d are rational numbers. Use the multiplication property of equality. Solve the equation. x 9 = –4 x9x9 9( ) = 9(–4) x = –36 The solution Is x = –36

89. Solve first degree equations of the form a + x = b ax = b a(bx + c) = d Where a, b, c, and d are rational numbers. Use the both property of equality. Solve the equation. 3(x – 8) = 36 distribute 3x – 24 = 36 addition 3x – 24 + (24) = 36 + (24) simplify 3x = 60 division 3 3 Simplify Solution x = 20

90. Plot points on the rectangular coordinate system; identify x and y intercepts for a given graph. Plot points on the rectangular coordinate system; identify x and y intercepts for a given graph. DMAT 0090, Objective #18

91. Plot points on the rectangular coordinate system; identify x and y intercepts for a given graph. Graph the ordered pairs. A(2,4) B( – 3, – 2) C(5, – 1) D(0,3) E(2,0) F( – 3,5) A BCDEF

92. Plot points on the rectangular coordinate system; identify x and y intercepts for a given graph. Find the x and y intercepts. The x intercept is (1,0) The y-intercept Is (0,–3)

93. Compute average, median and mode on a given set of data. Compute average, median and mode on a given set of data. DMAT 0090, Objective #19

94. Compute average, median and mode on a given set of data. Find the average of the following numbers: 76,29,42,81,and 29 average = total n 76 + 29 + 42 + 81 + 29 5 257 5 The average is 51.4 =

95. Compute average, median and mode on a given set of data. Find the median of the following numbers: 76,29,42,81,and 29 Write numbers in order. Change: 76, 29, 42, 81, 29 To: 29, 42, 76, 81 The median is 42. (middle number)

96. Compute average, median and mode on a given set of data. Find the mode of the following numbers: 76,29,42,81,and 29 Write numbers in order.(optional) Change: 76, 29, 42, 81, 29 To: 29, 42, 76, 81 The mode is 29. (most number of occurrences)

97. Solve for a variable other than A in an area formula for a rectangle, triangle, or parallelogram. Solve for a variable other than A in an area formula for a rectangle, triangle, or parallelogram. DMAT 0090, Objective #20

98. Solve for a variable other than A in an area formula for a rectangle, triangle, or parallelogram. The area of a rectangle is 48 square feet. The length is 12 feet. Find the width. Use the formula: LW = A L = 12 A = 48 Solve the equation: 12W = 48 W = 4 The width is 4 feet.

99. Solve for a variable other than A in an area formula for a rectangle, triangle, or parallelogram. The area of a triangle is 50 square feet. The height is 10 feet. Find the base. H = 10 A = 50 Solve the equation: (10B) = 50 Use the formula: BH = A 1212 The base is 10 feet. 1212 5B = 50 B = 10

100. Solve for a variable other than A in an area formula for a rectangle, triangle, or parallelogram. The area of a parallelogram is 50 square feet. The height is 10 feet. Find the base. H = 10 A = 50 Solve the equation: 10B = 50 B = 5 The base is 5 feet. Use the formula: BH = A

101. End of review Thank you for your attention. We hope this review has been informative. Please evaluate this presentation.

102. Evaluation I. Rate the following on a scale of 5 : strongly agree to 1 : strongly disagree A) The presentation was informative. B) All course objectives were covered. C) The examples were helpful. II. Write your comments.