Pharmacy Calculations!

1. Pharmacy Calculations! Anything & Everything you Will Need To Know About Math in Pharmacy

2. Objectives • To become familiar with the various computational aspects of pharmacy practice. • Demonstrate use of: • Basic Arithmetic Functions • Ratios • Fractions • Decimals • Percents • Cross-Hatch • Unit Conversions • Standard & Military Time • Dose Calculations • Pediatric (Weight Based Dosing) • Drip Rates • Allegations (Compounding & Dilutions)

3. Step One

4. Don’t Panic

5. Step Two!

6. Ask Questions!

7. The Basics

8. Foundational Math • Be able to do the following (on a calculator if needed); if you have any questions please ask. (Sooner is better than later). • Addition, Subtraction, Multiplication, Division • Squaring Numbers & Square Roots • Decimals & Fractions

9. Know how to use your calculator.

10. Fractions • Fractions are a numerical way of representing part(s) of a whole. • Example:

12. Converting to a Common Denominator

13. Adding Fractions

14. Subtracting Fractions

15. Multiplying Fractions

16. Dividing Fractions

17. Decimals • Like fractions, decimals are a numerical way of representing quantities and part(s) of a whole.

18. Place Values When reading a number aloud, the “and” is where the decimal goes.

19. Converting a Fraction to a Decimal

20. Unit Conversions

21. Converting Units • Almost daily, you will have the need to perform conversions. • Converting between different measurement systems.

22. Measurement Systems • Metric System (THE BEST!) • L, mL, dL, gm, mcg, kg, m, cm, mm • Household System (This will die eventually) • C, tbsp, tsp, oz, fl oz, lb, ft, inch • Apothecary System (Really rare, but it happens) • Grain (gr), drams, scruples, oz • Avoirdupois System • Lb, oz, gr, pt, gallon

23. Conversion Factors 1 kg = 1,000gm = 1,000,000 mg = 1,000,000,000 mcg 1gm = = 1,000mg = 1,000,000mcg 1mg = = = 1,000mcg 1lb = 454gm = 7,500gr = 16oz 1kg = 2.2lb 1oz = 30gm 1gallon = 4qt = 8pt = 16cups 1cup = 8oz = 16tbsp = 48tsp = 240ml 1oz = 2tbsp = 6tsp = 30ml 1tbsp = 3tsp = 15ml 1tsp = 5ml = 1 dram 1ml = 20gtts = 10gtts (macro) = 60gtts (micro) 1 grain (gr) = 60-65mg 1km = 1,000m = 100,000cm = 1,000,000mm 1yard = 3ft = 36inches = 0.91 1inch = 2.54cm

24. Rule of Thumb • Going Small to Big: Divide • Example: 200gm to kg = 200/1,000 = 0.2kg • Going Big to Small: Multiply • Example: 2gm to mg = 2x1,000 = 2,000mg

25. The Cross-Hatch Divide 1. Start above/below the X 2. Divide across (sideways) 3. Multiply up & down *Like units MUST be NEXT to each other 2 1 Multiply 3 X

26. Let’s Practice Convert 10kg to lbs.

27. Percents • Percents; like fractions and decimals are used to describe a portion of a whole. • Converting: • Percent to Decimal: Divide by 100 • Percent to Fraction: • Put Percent as Numerator and 100 as Denominator • Reduce • Fraction to Percent: • Divide Numerator by Denominator • Multiply by 100 • Decimal to Percent: Multiply by 100

28. 7 5 Ratios A ratio is a comparison of two quantities. Ratios can be written in several ways. 7 to 5, 7:5, and name the same ratio. 12 inches = 1 foot 3 feet = 1 yard 36 inches = 1 yard

29. 15 ÷ 3 9 ÷ 3 bikes skateboards Example Write the ratio 15 bikes to 9 skateboards in simplest form. 15 9 Write the ratio as a fraction. = 5 3 Simplify. = = 5 3 The ratio of bikes to skateboards is , 5:3, or 5 to 3.

30. shirts jeans 24 ÷ 3 9 ÷ 3 Check It Out! Example 2 Write the ratio 24 shirts to 9 jeans in simplest form. Write the ratio as a fraction. 24 9 = 8 3 Simplify. = = 8 3 The ratio of shirts to jeans is , 8:3, or 8 to 3.

31. Dosage Calculations • Use the Cross-Hatch and the idea of unit conversions to calculate doses.

36. Drip Rates & Dimensional Analysis This process can be used for any multistep conversions. As long as you use the correct conversion factor and the units cancel properly you will get the correct answer.

37. Basics of Dimensional Analysis • Can be used with any units. • First determine what the question is asking. • What are the units of your answer? • Units from the numerator can cancel with the same units in the denominator. • After only the desired unites remain: • Multiply Numerators • Multiply denominators • Reduce

38. An Example: Consider the question: Calculate the drops per minute of an infusion 1.5gm in 500ml D5W, infused at 50mg/minute, with a drip factor of 20gtts/ml. Write down all of the ratios from the problem. Determine what the question is asking. What are the units of the answer?

39. What are the units of the answer? • So, Let’s start with a conversion that uses drops in the numerator.

40. Next, we need to cancel mls • Now, We need to get ride of gms.

41. Now, to get rid of the mg • Remember to check that all of the units cancel.

42. Now Multiply • And Reduce

43. Alligations

44. Alligations • Used to calculate quantities of ingredients when combing components of different concentrations to make a new product. • Example: • Making a 5% cream from a 1% cream and a 10% cream.

46. Roman Numerals • Number system before current Arabic numeral System that we use. • Letters Represent Numbers • Numbers are ordered from left to right. • Large to small. • Never more than 3 of same numeral in a row. • Small numbers are added to large • When Small numbers are place in front of a large number the value is subtracted. • There are no place values with Roman Numerals

47. Roman Numerals Numerals Examples III IV VI VII IX XXV CMLXXX XXIV CCCXIV 3 4 6 7 9 25 1980 24 314 • I = 1 • V = 5 • X = 10 • L = 50 • C = 100 • D = 500 • M = 1,000

48. Temperature Conversions • Fahrenheit: Temperature System used by most in US. • Celsius: Temperature system used throughout the world, science, and medicine. Based upon the chemical and physical properties of water. 9 C = 5F – 160 • Plug in the value you know, and solve for the unknown.

49. International & Standard Time