This document provides a basic math review of percentages, ratios, fractions, proportions, systems of measurement (metric, household, apothecary), and methods for calculating drug dosages. It defines key terms, outlines rules and formulas for conversions between different measurement systems and units, and provides examples of dosage calculations using ratio and proportion methods.

1. Basic Math Review Tyra L. Ousley, RN, MSN

2. I. PERCENTAGES Any quantity stated as the proportion per hundred; expressed with % sign meaning “for every hundred”.

3. A. Convert a percent to a decimal RULES: Delete the % sign Divide the remaining number by 100, which is the same as moving the decimal point 2 places to the left. Ex: 25% = 25/100 = 0.25 50% = ___________ 75% = ___________ 67% = ___________

4. B. Convert a decimal to a percentage RULES: Multiply the decimal number by 100 (move the decimal point 2 places to the right) and Add % sign Ex: 0.25 x 100 = 25% 0.50 = _______% 0.75 = _______% 0.67 = _______%

5. C. Converting a common fraction to a percentage RULES Convert the fraction to a decimal by dividing the numerator by the denominator 3/8 (0.375) Move the decimal point two places to the right, round off if necessary 37.5 or 38 Add the % sign 37.5% or 38%

6. Examples 4/5 2/3 7/8 3/4

7. Convert a percent to a fraction RULES: Delete the % sign Write the remaining number as the numerator Write the 100 as the denominator Reduce the common fraction to the lowest term Ex: 25% = __________ 50% = __________ 75% = __________

8. II. RATIOS AND FRACTIONS IN PROPORTIONS Numerical ways to compare items. A proportion is a set of two equal ratios or fractions

9. Ratios in proportions Written with a double colon separating the ratios (Example: 3:1 :: 6:2 ) The outer numbers (3&2) are the extremes. The inner numbers (1&6) are the means The product of the extremes must equal the product of the means Solve for X in this proportion 3:1 :: 6:X 2.5 : 1.2 :: X : 3.2 ¼ : 2 :: 1/3 : X

10. B. Fractions in proportions Cross products should be equal 5 X --- = --- 2 4 Rewrite the problem to multiply cross products 2 x X = 5 x 4 Obtain the cross products 2X = 20 Solve for X by dividing both sides by 2 Find X (10)

11. Example: X = 1 55 2.2 X = 0.5 75 50 80 = 60 10 X

12. Convert a fraction to a decimal RULE: To convert a fraction to a decimal, divide the numerator by the denominator. Ex: 1/ 4 = _________ 2/5 = ____________ 4/10 = _____________

13. Convert decimal to a fraction Decimal fractions are fractions with a denominator of 10, 100, 1000 or any multiple or power of 10. Ex: 0.1 = _________ 0.01 = _______ 0.001 = ___________

14. SYSTEMS OF DRUG MEASUREMENT I. METRIC SYSTEM Basic units of measurement: Meter (m) – unit of length Liter (L) – unit of volume Gram (G, GM, Gm) – unit of weight

15. METRIC SYSTEM WEIGHT ABBREV CONVERSION FACTOR Gram g 1g=1000 mg milligram mg 1 mg=1000 mcg =0.001 g microgram mcg 1 mcg=0.001 mg = 0.000001 g kilogram kg 1 kg=1000 g

16. Metric Conversions To convert a smaller unit to a larger one, move the decimal point to the left or divide by the appropriate multiple of 10 Example: milligrams to grams 1000 milligrams / 1000 = 1 To convert a larger unit to a smaller one, move the decimal point to the right or multiply by the appropriate multiple of 10 Example: gram to milligrams 1 gram x 1000 = 1000 mg

17. Larger to smaller unit MULTIPLY (L-S-M) Smaller to larger unit DIVIDE (S-L-D) Identify conversion factors Convert 2 grams to equivalent milligrams Equivalent conversion= 1g=1000mg 2 g = 2 x 1000=2000 mg- by multiplication OR 2.000 = 2000 mg(moving decimal 3 places to right)

18. II. HOUSEHOLD SYSTEM Usually used at home Drop gtt (standard measure varies) Teaspoon t (tsp) 1 t = 60 gtt Tablespoon T(tbs) 1 T = 3 t Ounce(fluid) oz 2 T = 1 oz Ounce(wt) oz 1 lb = 16 oz Cup cup 1 cup = 8 oz Pint pt 1 pt = 2 cups Quart qt 1 qt = 4 cups = 2 pints Gallon gal 1 gal = 4 qt

19. III. Apothecaries’ System Uses Roman numerals Unit of measurement is placed before the Roman numeral (Example: 5 grains is written as grains v ) Basic units of measurement Minim: for liquid volume Grain (gr): for solid weight

20. IV. Avoirdupois System Used for ordering and purchasing some pharmaceutical products and for weighing patients in clinical settings Units of weight include grains, ounces, pounds

21. V. Unit System USP – United States Pharmacopeia Units IU – International Units Common drugs in units Insulin Heparin

22. VI. Milliequivalent System Most electrolytes are measured in mEq Example: Potassium Chloride

23. APPROXIMATE EQUIVALENTS 1 g = gr(grains) xv = 1 ml = 1 cc gr 1 = 60 mg 1 t = 5 ml 1 T = 3 t = 15 ml = ½ oz 1 oz = 30 ml = 6 t 1 L = qt I = oz 32 = pt ii = 4 c pt I = = 500ml = oz 16 = 2 cups 1 cup = 240 ml = oz 8 1 kg = 2.2 lbs 1 inch = 2.54 cm

24. Conversions for Other Clinical Applications: Time and Temperature Chapter 5

25. Time is an essential part of the drug order

26. What are some issues related to using the traditional time method?

27. 24-Hour Clock

28. Traditional and 24-Hour Clock AM Int’l. Time PM Int’l Time 12:00 midnight 2400 12:00 noon 1200 1:00 0100 1:00 1300 2:00 0200 2:00 1400 3:00 0300 3:00 1500 4:00 0400 4:00 1600 5:00 0500 5:00 1700 6:00 0600 6:00 1800 7:00 0700 7:00 1900 8:00 0800 8:00 2000 9:00 0900 9:00 2100 10:00 1000 10:00 2200 11:00 1100 11:00 2300

29. What Time Is It? 3:15 p.m. 4:45 a.m. 5:30 p.m. 10:10 p.m. 12:35 a.m. 0017 1010 1730 2310 0635

30. What Is Wrong? Give two Tylenol at 9:00 Blood pressure to be taken at 2510 Insulin given at 23:10 p.m.

31. Celsius and Fahrenheit Scales Convert between Fahrenheit and Celsius temperatures:

32. Celsius and Fahrenheit Scales

33. IMPORTANT FORMULAS TEMPERATURE CONVERSIONS Celsius °F-32 °C = ----------- OR 5/9 ( °F – 32) 1.8 Example: 101 °F (101 – 32) ------------ OR 5/9 (101 – 32) 1.8 = 69 /1.8 OR (5 x 69)/9 = 38.3 °C

34. TEMPERATURE CONVERSION FAHRENHEIT ° F = 1.8 °C + 32 OR 9/5 °C + 32 Example: 38.3 °C 1.8 x 38.3 + 32 OR (9 x 38.3) ------------ + 32 5 = 100.9 °F

35. Calculate the Temperatures 40˚ Fahrenheit 75˚ Fahrenheit 18˚ Celsius 65˚ Celsius

36. ORAL DOSAGE FORMS Steps: 1. Ensure that all measurements are in the same system of measurement and the same size unit of measurement. If not, convert. 2. Calculate using this formula D = desired amount or order H = available or have on hand Q = quantity D H = Amount to be given X Q

37. Oral Dosage Forms: Liquid Preparations Steps: Ensure that all measurements are in the same system of measurement and the same size unit of measurement. If not, convert. Calculate using this formula D H X Q = Amount to be given

38. Converting between measurement systems Example: grains to milligrams Order: Aspirin gr v Available : Aspirin in mg. Set up the first ratio with the conversion factor 1 gr : 60 mg Set up the second ratio with the unknown quantity in the appropriate position 5 gr : X Use these ratios in proportion 1 gr:60 mg :: 5 gr: X Solve for X (unknown) based on the principle that the product of the means equals the product of the extremes 1 gr x X = 60 mg x 5 gr X = 300 mg

39. Pounds to kilograms A patient weighs 217 pounds. Convert to kg to compute the amount of medication to be given 1 kg : 2.2 lb X kg : 217 lbs 1 kg : 2.2 lb :: x kg : 217 lb 2.2 lb X = 1 X 217 lb X = 217/2/2 X = 98.6 kg

40. Examples The physician writes an order for secobarbital 0.2 gm every 6 hours prn for sleep. Each secobarbital capsule is labeled 100 mg. The nurse should administer______ capsules per dose.

41. Examples The physician orders 500 mg of amoxicillin by mouth to be given every 6 hours. Available are 250 mg of amoxicillin capsules. The nurse should administer _________ capsule(s) for each dose.

42. Examples The physician writes an order for acetaminophen 240 mg po for an elderly adult. You have on hand 80 mg acetaminophen oral liquid in 0.8 ml. The nurse should administer _________ ml per dose.

43. Examples The physician orders amoxicillin 250 mg po. The pharmacy supplies amoxicillin suspension 250 mg/5 ml. in a 50 ml. bottle. The nurse should instruct the client to take _________ ml per dose.

44. Practice Questions: A physician’s order reads 2 Tbs milk of magnesia. How many milliliters will the nurse administer? The Physician’s order reads Tylenol supp. Gr x every 4 hrs p.r.n. for temp. > 101 F. The package label states that each suppository contains 10 grains of Tylenol. How many suppositories should the nurse administer? The order states Lithium Carbonate gr x p.o. tid. The drug is labeled Lithium Carbonate 300 milligrams/capsule. How many capsules should the nurse give?

45. The order for Coumadin is 5 mg. It is available in 2.5 mg tablets. How many tablets should be given? The physician’s order is Ferrous Sulfate 300 mg p.o. tid X 1 week. How many tablets in total should be dispensed for the patient?

46. Calculation for individualized drug dosing Based on actual body weight Used to individualize medication administration for children and adults

47. Steps Convert pounds(lbs) to kilograms (kg) Determine the drug dose per body weight by multiplying drug dose X body weight X frequency Choose one of the four methods of drug calculation for the amount of drug to be given Basic formula Ratio proportion Fraction equation Dimensional analysis

48. The physician orders morphine sulfate 1.8 mg IM stat. The child weighs 79 lbs. Is the dose safe? Verifying Safe Dosages

49. Verifying Safe Dosages Convert 1 lb to kg

50. Verifying Safe Dosages Calculate mg/kg as recommended by a drug resource Resource indicates the usual IM/SC dosage may be initiated at 0.05 mg/kg/dose The dose is safe

51. Kee, pp. 98 -109

52. REFERENCES Broyles, B. (2003) Dosage Calculation Practice for Nurses. Canada: Delmar Erickson, B. ( 1991). Nurse’s Clinical Guide Dosage Calculations. Pennsylvania: Springhouse Corporation Kee, J and Marshall, S.(2004). Clinical Calculations. 5 th Edition. Missouri: Elsevier Pickar, G. ( 2008). Dosage Calculations. 8 th Edition. Canada: Delmar

53. ANY QUESTIONS ????