1. Basics of Operator Math Your Name and contact info

2. Western RCAP Rural Community Assistance Corporation (916) 447-2854 www.rcac.org Midwest RCAP Midwest Assistance Program (952) 758-4334 www.map-inc.org Southern RCAP Community Resource Group (479) 443-2700 www.crg.org Northeast RCAP RCAP Solutions (800) 488-1969 www.rcapsolutions.org Great Lakes RCAP WSOS Community Action Commission (800) 775-9767 www.glrcap.org Southeast RCAP Southeast Rural Community Assistance Project (866) 928-3731 www.southeastrcap.org RCAP National Office 1701 K St. NW, Suite 700 Washington, DC 20006 (800) 321-7227 www.rcap.org | info@rcap.org Rural Community Assistance Partnership Practical solutions for improving rural communities

3. Funded under an EPA grant  Training and Technical Assistance for Small Drinking Water Systems to Achieve and Maintain Compliance Through Assessing and Addressing Deficiencies Acknowledgement 3

4. At the end of this session you should be able to:  Convert between different units of measure.  Be able to determine perimeter, area, and volume.  Use the dosing equation and other simplified equations. Learning objectives

5. Pre-Test

6. MODULE 1 MATH BASICS

7. Convert between liters and gallons, Centigrade to Fahrenheit. Determine how much water is in a storage tank or a pipe. How much paint do you need to paint a tank? How much chemical do you need to add? Why do you need math?

8. Review math concepts  Working with fractions  Understanding and using conversion factors  Percentages  Area and volume Tactics for solving problems  Solving of an unknown  Working with word problems Outline

9. Basic Concepts

10. Math OperationSymbolExample MultiplicationxQ = V x A Q = V A No spaceQ = VA ( ) ( )Q = (V) (A) Division÷R = D ÷ 2 –––––R = D 2 /R = D/2 per R equals D per 2

11. Different ways to write the same multiplication problem = 0.32 591 7 45

12. What do you do first when you have a complex equation? (2 + 3) 2 + 3(4 ÷ 2) = Order of operation

13. “Please excuse my dear Aunt Sally” Please -Parentheses Excuse - Exponents My - Multiplication Dear -Division Aunt-Add Sally -Subtract Order of operation

14. “Please excuse my dear Aunt Sally” (2 + 3) 2 + 3 x (4 ÷ 2) = (5) 2 + 3 x (2) = 25 + 6 = 31

15. = ((5 x 2) + 6) / 8

16. Solve 1. (5 x 3) + 2 (3+2) = 2. (4 + 3 x 2) – 4 x 2 = 3.

17. Last number is 5 or greater – round up Last digit is 4 or less – keep the same Round the following numbers 45.5101.491 45.4101.5 Rounding

18. Round to one place after the decimal Round to whole number 56.4 56.5456.48888 115.001144.890.51 Approximate using rounding (no calculator) What is 50.115 x 1.95 = Practice

19. MODULE 2 WORKING WITH FRACTIONS

20. Review and confirm your understanding of fractions. Verify that you can  Multiply and divide fractions.  Set up and work with fractions from the formula/ conversion table. Learning Objective

21. Fractions

22. Divide the numerator by the denominator Converting from fractions to decimals

23. Any number divided by itself equals 1 1 mile = 5280 feet

24. Multiply the numerators Multiply the denominators Divide the numerator by the denominator to convert to decimal Multiplying fractions

25. 12 23

27. What is ?

28. Practice Provide the result in decimal form.

29. MODULE 3 WORKING WITH CONVERSION FACTORS

30. Use conversion factors for common units in water treatment and distribution. Learning objectives

31. Some conversions are weight to volume/volume to units: 1 gallon = 8.34 pounds 1 cubic foot = 7.48 gallons 1 PSI = 2.31 feet head 1 gallon = 231 cubic inches 1 cu. ft. = 62.4 pounds 1 acre-feet = 325,851 gallons Some conversions are subsets of larger units: 1 day = 1,440 minutes1 day = 24 hours 1 gallon = 4 quarts 1 acre = 43,560 square feet 1 mile = 5,280 feet 1 yard = 3 feet 1 liter = 1,000 milliliters1 gram = 1,000 milligram 1 kilo = 1,000 grams1 metric ton = 1,000 kilos Conversions

32. Other conversions change U.S. Standard to Metric: 1 gallon = 3.785 liters 1 kilo = 2.2 pounds 1 ppm = 1 mg/L 1 hectare = 2.47 acres 1 gpg = 17.1 mg/L 1 liter = 1.057 quarts 1 ounce = 29.6 milliliters 1 meter = 3.28 feet Conversions

33. 1 hour = 60 minutes Using conversion factor 1 acre foot = 326,000 gallons Since both sides of the equations are equivalent :

34. 1 hour = 60 minutes If units are equivalent, it doesn’t matter what is on top 1 acre = 43,560 square feet

35. Note: Units cancel out. Step 1 Step 2 Step 3 Step 4 How many minutes are in 4 hours? 4 hours x -- = __ minutes

36. How much does 4 gallons of water weigh in pounds? 4 gallons x -- = __ pounds

37. How many seconds are there in 1 hour? In some cases, you may need multiple conversions

38. o C = 5/9 ( o F - 32) o F = (9/5 x o C) + 32 Or o F = (1.8 x o C) + 32 Temperature conversions Source: CDPHE 2014

39. 1. How many nickels are there in $2.00? 2. You have 20 pounds of water. How many gallons of water is this? 3. How many cubic feet per second (cfs) are there in 4 million gallons per day (MGD)? 4. What is 4 o C in o F? What is 20 o F in o C? 5. A quarter in football is 15 minutes. The maximum time between plays is 40 seconds. What would be the minimum numbers of plays that could be run in a game? You try

40. 1. Convert 20 gpm to MGD 2. Covert 6000 cf to gallons 3. Convert 7 days into seconds 4. Covert 120 feet of static head into psi Additional problems

41. MODULE 4 PERCENTAGES

42. Percent means parts of 100  Symbol: % Examples  Tank is 1/2 full: 50%  Tank is 1/4 full: 25% Percentages

43. Divide the part by the whole and multiply by 100 To determine percentages

44. Percent (%) divided by 100 will give a decimal value Percentages can be converted to decimals

45. Part per million to percentage 1 ppm = 1 part per million parts

46. If you read 85 meters in a day, and you have 2,100 customers, what percentage of your customers’ meters did you read? How many meters would be 10% of your 2,100 customer meters? whole x percent (decimal form) = part

47. If you read 85 meters in a day, and you have 2,100 customers, what percentage of customers’ meters did you read? How many meters would be 10% of your 2,100 customer meters? 2,100 customers x 0.10 = 210 customers

48. How much 65% calcium hypochlorite (HTH) is required to obtain 7 pounds of chlorine? The part is 7 pounds, which is 65% of the whole Convert the percentage to a decimal Chlorine

49. How many pounds of chlorine do you have in one gallon of Chlorox (7.85% chlorine)? Percentage solution *Note: The weight of 8.34 lb/gallon is for pure water. The weight of Chlorox is slightly greater.

50. 1. Write percentages in decimal form a. 10% b. 1% c. 0.1% 2. Your system has 6,435 valves. Your goal is to turn each valve in three years. What percentage and how many valves would you need to turn in one year? What percentage and how many valves would you need to turn each week? Problems

51. MODULE 5 AREA AND VOLUME

52. Understand and apply basic geometry  Describe and calculate the perimeter, area, and volume of a rectangle  Describe and calculate the circumference, area, and volume of a cylinder  Apply unit conversion factors  Use the Formula/Conversion Table Learning Objectives

53. Examples of area: square feet (ft²), square meters (m²), acres and hectares. TRIANGLE CIRCLESQUARE or RECTANGLE 2-Dimensional Shapes

54. CYLINDERCUBECONE Examples of volume: cubic feet (ft³), cubic meters (m³), and acre feet (af). 3-Dimensional Shapes

55. Feet may be abbreviated ft ft 2 = ft x ft (area) = square feet ft 3 = ft x ft x ft (volume) = cubic feet Math note

56. Width Dimension #2 Length Dimension #1 Parts of a Square or Rectangle

57. Perimeter Perimeter = Length + Width + Length + Width Perimeter= 2 x (Length + Width) Width Dimension #2 Length Dimension #1

58. What would be the perimeter? If the length was 10 feet and the width was 20 feet? Perimeter = Length + Width + Length + Width Perimeter = 2 x (Length + Width) Width Dimension #2 Length Dimension #1

59. What is the perimeter of a football field? The length of a football field is 120 yards The width of a football field is 53.3 yards

60. 2-Dimensional problems  How much paint do I need to cover the outside of a tank?  What is the surface area of a contact basin?  What is the flow rate? (velocity times area) Q = VA Area

61. Area = (Length)(Width) Width Length Area=Length times width

62. What is the area if: Length is 4 feet and width is 10 feet?

63. Volume of a cube = (Length)(Width)(Height) Volume = Length x Width x Height (or Depth) Length Width Depth or height Volume

64. What would be the volume if: Length = 2 feet Height = 4 feet Width = 4 feet 2 ft 4 ft V = Length x Width x Height V= 2 ft x 4 ft x 4 ft V = 16 ft 3

65. Take the Rubik’s cube provided. Determine:  Perimeter  Area  Volume (Note: Units will be in blocks) Then add a second cube to make a rectangle. Determine perimeter, area, and volume. Activity

66. What would be the volume of a basin that is 10 feet wide, 20 feet long, and 10 feet deep? How many gallons would the basin hold if full? Problem

67. Radius Diameter Circumference Parts of a Circle

68. The radius is equal to half the diameter Diameter = 2 x Radius Radius = Diameter / 2

69. Circumference Question: How would you write this equation if you had the radius measurement? Circumference = π (diameter ) π (pi) is equal to 3.14 Circumference = 3.14 (diameter)

70. Circumference Circumference = 2 x π x radius

71. Circumference = diameter x π What would be the circumference if the diameter was 10 feet?

72. 3.5 MG storage tank (20 feet tall) has a radius of 161 ft. What is the circumference? What would be the circumference of:

73. Area Area of a circle= π (radius)² = 3.14 x radius x radius or Area of a circle= 0.785 (diameter 2 ) = 0.785 x diameter x diameter Area

74. What would be the area of a circle that has a radius of 10 feet? What would be the area of a circle that has a diameter of 10 feet? Area = π (radius)² or Area = 0.785 (diameter 2 )

75. Depth or Height Area Length Volume of a Cylinder

76. Volume = (0.785) (diameter 2 ) (Height) Volume = ( π ) (radius 2 ) (Height) Volume of a Cylinder Depth or Height

77. What would be the volume (in gallons) of a storage tank that has a diameter of 10 feet and a height of 5 feet? Volume = (0.785) (diameter 2 ) (Height) Depth or Height

78. You have a storage tank that has a diameter of 100 feet and a height of 10 feet.  How much fence would you need to go around the tank (assume the fence is 10 feet away from the tank)?  How paint would you need to paint the outside of the tank if one can of paint covers 100 square feet?  How much water does the tank hold (in gallons) if completely full? If 75% full? Problem

79. MODULE 6 WORKING WITH EQUATIONS

80. Get the unknown you are trying to solve for alone on one side of the equation. Solving for an unknown Dosing equation Flow rate Q = A x V

81. If you know flow rate and area, find the velocity: Solving for an unknown 1. Start by writing the equation 2. Get the letter you need alone Flow rate = Area x Velocity Q = A x V

82. If you know the amps and ohms and are trying to find volts: Solving for an unknown 1. Write down the equation 2. Multiple both sides of the equation by ohms.

83. Important point: Do the same thing to both sides of the equation. Solving for an unknown

84. What happens if what you are trying to solve for is in the denominator?

85. Dosing equation

86. If you know feed rate and MGD and wanted to determine the dose, divide both sides of the equation by (capacity, MGD)(8.34 lbs/gal).

87. To find the quantity above the horizontal line, multiply the pie wedges below the line together. To solve for one of the pie wedges below the horizontal line, cover that pie wedge, then divide the remaining pie wedge(s) into the quantity above the horizontal line. Given units must match the units shown in the pie wheel.

88. 1. You know force and pressure. Find the area. 2. You know the detection time and volume of your basin. Find the flow rate. 3. You know the area. Find the diameter. 4. You know feed rate and dosage. Determine the Capacity in MGD. Your Turn Force = (Pressure) (Area) Area of a circle = 0.785 (diameter) 2

89. 1.Make a drawing of the information. 2.Place data on the drawing. 3.Write down “What do I need to determine?” 4.Write down any equations that you are going to need. 5.Make conversions if necessary. 6.Fill in the data in the equation. 7.Make the calculation and write down the answer. 8.Ask yourself, does this make sense? Word Problems

90. A blue tank at 500 feet above sea level is 10 feet high and has a diameter of 20 feet. The tank is half full. What is the volume of the tank? Note: Watch out for information you don’t need

91. A blue tank at 500 feet above sea level is 10 feet high and has a diameter of 20 feet. The tank is half full. What is the volume of the tank? Note: Watch out for information you don’t need

92. Problem 1: A new section of 8 inch diameter pipe is to be filled with water for testing. If the length of the pipe is 3,500 feet, how many gallons of water will be needed to fill the pipe?

93. Problem 2: A 12 inch water main has to be disinfected to 50 ppm. The main is 4,000 feet long and has 1 valve installed every 500 feet for isolation. How many pounds of chlorine will be needed to disinfect the entire main?

94. Problem 3: A cylindrical cistern with a radius of 5 feet and a height of 10 feet is filled with water. If 3 pounds of chemical is dissolved in the water, what will be the dosage in milligrams per liter? a. 112 mg/L b. 75 mg/L c. 61 mg/L d. 27 mg/L

95. Problem 4: A settling basin is 120 feet long, 20 feet wide, and has a water depth of 15 feet. What is the detention time, in hours, in the basin when the flow is 9 MGD?

96. Problem 5: A chlorine dosage of 0.35 mg/L is applied at the pump station preceding the plant. The 36 inch force main is 23,000 feet long and the flow is 5,560 gpm. What is the theoretical contact time for the chlorine prior to entering the plant? a. 1 hour 48 minutes b. 2 hours 24 minutes c. 3 hours 38 minutes d. 4 hours 4 minutes

97. ABC Formula and Conversion Factors Sheet http://www.abccert.org/pdf_docs/ABCWTFTC090613_AB C-C2EPBrand.pdf AWWA www.awwa.orgwww.awwa.org Math for Distribution System Operators, 2007 Math for Water Treatment Operators, 2007 Basic Science Concepts and Applications, 4 th ed. 2010 Rural Community Assistance Corporation, www.rcac.org Resources

98. Practice

99. MODULE 7 PRACTICE PROBLEMS

100. Post-test Post-test will be handed out. 10 questions – try to finish in 12 minutes. Use formula sheet and a calculator.

101. THANKS FOR ATTENDING! YOUR NAME CONTACT INFO